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LEARNING ARITHMETIC
N. J. LENNES
Professor of Mathematics
University of Montana
DON C. ROGERS
Assistant Superintendent
Chicago Public Schools
L. R. TRAVER
Co-author Lennes Test and Practice
Sheets in Arithmetic and
Lennes Essentials of Arithmetic
Illustrated by
MILO WINTER
LAIDLAW BROTHERS
PUBLISHERS
CHICAGO
NEW YORK
SAN FRANCISCO
DALLAS
ATLANTA

COPYRIGHT, 1942
BY LAIDLAW BROTHERS, INC.
ALL RIGHTS RESERVED
Printed :n the United States of America

TEACHER'S FOREWORD
Objective. This series—LEARNING ARITHMETIC—
has as its chief objective the development of the pupil's under
standing and skill in the fundamental operations and in problem
solving. To attain this objective, correct teaching and learning
techniques have been employed, the subject matter has been
scientifically constructed and graded, and ample practice for
the development of essential skills has been provided.
Organization. To enable teachers to plan their work and
allot a proportionate and adequate amount of time to the var-
ious topics, the lessons have been grouped into fairly short
units.
Each unit covers approximately two weeks' work.
At intervals there are eight self-tests, reviewing all work
covered up to that time. These self- tests show the pupil his
strong and Weak points and also provide the teacher with diag-
nostic information covering each pupil's achievements.
The placement of topics and the gradual introduction of the
subject matter meet the requirements of the most recent in-
vestigations and courses of study.
Increased emphasis is given to the well-known "hard spots"
in arithmetic, namely: column addition, problem solving, sub-
traction, long division, addition and subtraction of fractions,
division of decimals, and percentage.
Constant stress is placed upon accuracy in computation
rather than upon speed.
A balanced treatment has been provided for both phases of
arithmetic — practice in the fundamental operations and in
problem solving. The pupil attains skill in problem solving
through his mastery of the comparatively few basic type-
problems used in everyday life.
In solving problems pupils are directed to take these natural
steps: (1) to find the facts and the question in the problem, (2)
to choose the correct operation, and (3) to make the required
computation.
An original plan is employed, by which the
pupils use the letters A, S, M, or D to record the results of their
"thinking before figuring."
The problems offer an unusually rich variety of social situa-
tions common to the experiences and needs of all children.
Pupil interest is maintained through frequent pages of related
problems based upon familiar activities.
Alert teachers and
pupils will discover suggestions for many additional projects.
3

The exercises in the fundamental operations and in problem
solving are scientifically constructed to provide adequate prac-
tice for the development and maintenance of skill in all basic
number facts, the fundamental operations, and practical type-
problems.
On pages 250-282, a complete review of the year's work in
the fundamental operations and in problem solving is given.
The material in these pages may be used for additional prac-
tice or for diagnostic purposes.
Every pupil who is able to
complete the work in these pages satisfactorily may be certain
that he is ready for the next year's work in arithmetic.
Vocabulary. Careful attention has been given throughout
the series to the use of a simple and yet adequate vocabulary.
In each grade the words used have been kept well within the
range of the reading vocabulary for that particular grade. The
vocabulary has been checked against the various word Usts
now available.
Recommendations to Teachers. Carrying out the fol-
lowing suggestions will result in successful pupil achievement:
1. Stress accuracy rather than speed. Allow pupils to work
at the speed best adapted to their own needs. See that pupils
take time to do accurate work, to prove their work, to find and
correct their errors, and to find the reason for any incorrect
work.
2. In the initial learning stage, take time to help pupils
grasp the meaning and relation of number facts, the explana-
tions and directions, the new steps in the fundamental opera-
tions, and the new type-problem situations.
The Authors
i

Contents
Unit 1. Whole Numbers, Decimals, and Fractions
Looking Forward to Year's Work
Practice in Correct Addition
Addition and Subtraction .
Bank Balances ....
Finding Bank Balances.
Multiplication and Di\'ision
Multiplying, Dividing Decimals
Page
Page
9
Sight Work in Fractions
.16
10
Addition of Fractions and Mixed
11
Numbers
17
12
Subtraction of Mixed Numbers
.
18
13
Multiplication of Fractions
.
19
14
Division of Fractions
....
20
15
Problems
21
Unit 2. Rounded Numbers. Accounts and Records
Approximate Whole Numbers .
Rounding Off Numbers.
Rounding Off Quotients
Standings of Basketball Teams
Keeping Farm Records .
Oat and Wheat Accounts .
22
Keeping School Records
23
School Attendance Records
24
Sales Records
.
.
.
.
25
Adding Horizontally
26
Decimals and Fractions.
27
Problems
Test in Fundamentals
First Self-Test
34
Problem Test
28
29
30
31
32
33
35
Unit 3. Equations. Percentage
Equations
.......
36
How to Solve Equations
...
37
Learning More about Equations .
38
Steps Used in Soh-ing Equations .
39
Problem Practice
40
Solving Equations
41
Percentage
42
Comparing Fractions, Per Cents .
43
Bas- ^, Rate, and Percentage
.
.
44
Fractional Per Cents
....
45
Finding the Rate
46
Finding the Base
47
Unit 4. Percentage
Fractional Equivalents .
Sight Work in Percentage .
Per Cent Decrease or Increase.
Problems
Sight Work in Percentage .
Add, Subtract, Multiply, Divide?
48
Methods in Soh-ing Problems .
54
49
Problem Practice
55
50
Buying by the Ton
56
51
Cancellation
57
52
Indicating Solutions
....
58
53
Add, Subtract, Multiply, Divide?. 59
Test in Fundamentals
Mixed Test .
.
.
Second Self-Test
60
Test in Problems without Numbers
61
Test in Problem Solving
Unit 5. Family Budgets and Records
Planning Budgets
64
Problems
65
Family Budgets
66
Family Budgets
67
Family Records
68
Ten Days in January .... 69
Calories and Food Elements
Table of Food Values
Calories Needed
Problems in Food Values
Comparing Costs of Calories
Buying Food in Containers
Unit 6. Home Problems
Installment Buying
76
Dollar Cost of Credit .... 77
Rate of Interest
78
Installment Interest
....
79
Automobiles on Time-Payments . 80
Problems
81
Owning a House.
Home Problems ....
Operating an Automobile .
Automobile Problems
Cost of Hiring Help
.
Family Financial Statements
62
63
70
71
72
73
74
75
82
83
84
85
86
87

Test in Fundamentals
Third Self-Test
Page
Page
88
Test in Solving Problems ...
89
Unit 7. Using Percentage
Retail Disrotints
90
Trade Discounts
91
Problems in Trade Discount
92
Order of Discounts
93
Problems
94
Practice in Discounts
... .
95
Interest on Borrowed Money
Principal and Interest .
Bank Discount
.
.
Practice in Discounting Notes
Selling a Promissory Note .
Proljlems of Discount
Unit 8.
Different Rates of Interest.
Interest Problems
Manufacturing Plants
Interest and Depreciation .
Effects of Low Interest Rates
Problem Practice
Interest, Profit, and Loss
102
Margin and Profit
103
Overhead and Loss
.
104
Per Cent Cost, Margin. Overhead
.
105
Problems without Numbers
.
106
Setting the Selling Price
.
107
Problem Practice
....
Unit 9.
Selling on Commission .
Problem Practice
Discounting Notes at tlie b.mk
Problems on Bank Discounts
Trade Acceptances .
Computing Interest betwet-n I ^ciLes
Business Problems.
Test in Fundamentals
Test in Solving Problems
Unit 10.
Formulas
Formulas and Their Uses
Sight Work ....
Working with P'oimula:>
Using Formulas .
Finding Interest
Cancellation, Finding Interest
Fourth Self- Test
Problem Test
....
Problem Test
....
114
115
116
117
118
119
126
127
Home Problems
An Interesting Comparison
.
130
Interest on Investment in House . 131
Depreciation of a House
.
132
Interest Schedule on a House .
.
133
Schedule of Payments on a House . 134
Renting or Buying a House
.
^
.
135
Insurance
Fire Insurance
....
Rate of Premiums and Risk
Life Insurance
....
Rates of Premiums .
Sight Work
Problem Practice
Unit 11. Lumber Measure. Compound Interest
The Meaning of Board Foot
Measuring Lumber
Finding the Cost of Lumber-
•r rttion
n St()< k
Problem Practice
Practice in Percentage
Prolilem Practice
Test on Formulas
Unit 12
Organizing a Small Corp-
Dividends on Corijorut
Partnership and Corpo
Corporation Bonds
Problem Practice
Practice in Percentuu*
Unit 13.
The Stock Exchange
Buying Stocks and Bonds
Brokers and Brokerage .
Selling Stock ....
Buying and Selling Stocks
Sight Work ....
142
Interest on Savings Pei)osits .
143
Interest Compounded .\nnually
144
Deposits and Withdiawals
145
Compound Inteiest .
146
Compound Interest Tables.
147
Compound Interest ....
Fifth Self -Test
.
154
Test in Solving Problems .
Corporations. Stocks and Bonds
b56
Saving Money to Invest Safely
157
Postal Savings Accounts
158
United States Savings Bonds
159
United States Savings Bonds
160
Problem Practice
161
Problem Practice
Stocks and Bonds. Graphs
U." -<es of Graphs
16S
169
170
171
172
173
Changes in Prices of Stocks
Depreciati(;n
Family Budgets ....
Profit and Loss ....
Problems
96
97
98
99
100
101
108
109
110
111
112
113
120
121
122
123
124
125
128
129
136
137
138
139
140
141
148
149
150
151
152
153
155
162
163
164
165
166
167
174
175
176
177
178
179
6

Sixth Self -Test
Page
Test in the Four Fundamentals . 180
Problem Test
Test in Problems without Numbers 181
Problem Test
Unit 14. Cost of Local and State Governments
Why Taxes Are Necessary .
Budgets for County and City
Costs of Local Governments
The Tax Rate
...
The Tax Table ....
Problem Practice
184
185
186
187
188
189
The State Government .
Cost of State Government
State Taxes ....
Tax Problems
Sight Work Problems
Problem Piactice
Page
.
182
.
183
190
191
192
193
194
195
Unit 15. Federal Taxes. Scale Drawing
The Federal Government .
Cost of the Federal Government
Comparing Costs of Governments
Federal Taxes
Tax Problems
Problem Practice
....
196
Scales on Maps and Drawings.
197
Scale Practice
198
Standard Time
199
Standard Time
200
Time and Rotation of the Earth
201
Problem Practice
.
.
.
.
'
202
203
204
205
206
207
Test in Fundamentals
Seventh Self -Test
.
.
208
Problem Test
209
Unit 16. Square Root. Ratio and Proportion
Squares and Square Roots .
Squares and Square Roots .
Approximate Square Roots
Square Roots of Decimals .
The Right Triangle .
.
.
Problem Practice
210
211
212
213
214
215
Diagonals of a Rectangle
Problem Practice
The Meaning of Ratio .
Proportion
....
Uses for Proportion .
Proportion
....
Unit 17. Similar Triangles. Areas and Volumes
Similar Triangles
222
Proportions, Similar Triangles.
.
223
Finding Distance
224
Problem Practice
225
Measuring Distances Indirectly . 226
Practice
227
Areas
Circumference of a Circle .
Rectangular Solids, Cylinders
Area of a Cylinder .
Volume of Pyramid and Cone
Surface and ^'olume of Sphere
Unit 18. The Metric System. Review
Metric Units
234
Weight, Capacity, and Height.
.
235
Sight Work
236
Problems
237
Relations among Metric Units.
.
238
Problem Practice
239
Special Practice in Decimals .
Practice in Fractions
Practice in Fractions, Decimals
Practice in Percentage .
Practice in Percentage .
The Great Pyramid ....
Eighth Self-Test
Testing What You Have Learned . 246
Problem Test
247
Problem Test
Problem Test
216
217
218
219
220
221
228
229
230
231
232
233
240
241
242
243
244
245
248
249
Testing Your Readiness for Next Year's Work .... 250-282
Index
283-288 .

^^m 'n
S'
,!'.

Unit /. Whole Humbers^ decimals^ and fractions
Looking Forward to the Year's Work
You are at the beginning of your last year in ele*
mentary arithmetic.
The arithmetic that you will be
studying this year will be of direct help to you in your
everyday life from now on: in high school, in college, and
in the years to follow.
You will find that business and finance today are a
very important part of the subjects of history, civics, and
government. In order to understand the contents of
such subjects, you will need to have some knowledge of
taxes, insurance, loans, interest, stocks and bonds, and
profit and loss— all of which you will learn about in
arithmetic this year.
Remember also that many of the principles which you
are learning to use in arithmetic are the foundation for
algebra, geometry, and the sciences.
In business you wiU be much more successful and will
feel much more at home if, in addition to knowing well
the fundamentals of arithmetic, you are acquainted with
such topics as banking and insurance; if you know how
to keep records and figure interest; if you know some-
thing about stocks and bonds.
The work this year, as in other years, will consist of
these two steps: (1) Planning the steps in the solution of
many kinds of problems, such as people hving in our
kind of world are caUed upon to solve.
(2) Performing
the fundamental operations of addition, subtraction,
multipKcation, and division with integers, fractions, and
decimals.

Practice in Correct Addition
In business establish-
ments the fundamental
operations of arithmetic
are now usually carried on
by using computing ma-
chines, of which the add-
ing machine, such as is
shown at the right, is best
known. But even in these
places some computing is
constantly being done
with pencil and paper.
In the home a very considerable amount of adding,
subtracting, multiplying, and dividing must be done.
In your study of arithmetic, practically aU computing
must be done in "longhand."
In order to be able to do
this work easily and accurately, it is necessary to have
a Httle brush-up practice from time to time.
Add downward. Check by adding upward.
59
326
487
8420
639
475
816
5978
6000
1394
5437
3109
35
513
954
61
590
7410
567
798
76
748
8187
97
374
8365
7084
7808
36
73
97
954
246
253
9259
9141
39
29
4196
8290
1564
9105
817
1842
478
296
933
2414
64
958
9887,
4178
6815
679
5
258
95
8386
570
6719
98
9726
3519
98
134
241
652
454
668
934
75
40
978
3569
2354
565
5388
5925
10

Addition and Subtraction
Subtract. Prove by adding remainder and subtrahend.
1. 5409
10946 38972
57698 45837 54730
2738 10878
3949 49799
2978
2146
2. 8194
5997
8647
4108
29894
19897
45790
10392
87372
45678
24713
9347
3. 7400
6908
80401
53604
12908
3192
41057
23465
48576
44673
39421
22948
In adding and subtracting decimals,
write the numbers so that the decimal
points wiQ be in a straight line.
It is
best to annex zeros so that all numbers
will show the same number of decimals.
Thus, to add 324.6, 79.84, and 94, write
the nimibers as shown at the right.
To subtract 18.96 from 20, write the
numbers as shown in the second box.
324.60
79.84
94.00
498.44
20.00
18.96
1.04
Write in columns and add:
4. 3 .64+28.02 + 192,86+4087.2+13.96+9.18
8.3+27.74 + 7.402 + 980+5.24 + 1.281+7.05
910.4+7.189+81.2+4.57+8.98+476+23.64
$1.67+$19.32 + $35.25 + $92.87+$88.75+$5.50
Write in columns and subtract:
8.
1 5.32 - 2.89
86.34 - 1 4.00 602.8
-
397.92
7.19-3.87
4.75 -. 98
20.4 -12.76
121.4 -87.98
5.19-3.99
.564-. 09 3
$102.1 6 -$83.82 $47.31 -$2.87 $200.00 -$189.46
$207.60 -$9.54 $12.00 -$7.1 4 $29.42 -$8.67
11
5.
6.
7.
9.
10.
11.
12.

Bank Balances
A person who has a checking account usually starts
each month with a balance in the bank. Din-ing the
month, he makes certain deposits and draws out money
by writing checks on the bank. To find the balance at
the end of the month, he adds the deposits to the balance
at the beginning of the month, and from this sum
(credits) he subtracts the total amount of the checks
(withdrawals)
.
1. The numbers below represent foiu* different check-
ing accounts for the same month. Find the total credits
and the total withdrawals, and then subtract.
Jan.
Jan.
Jan.
Jan.
Balance
$491.64
$1204.61
$104.17
$ 5.59
Deposits
450.00
781.75
341.60
184.70
Total
Checks
$ 4.49
$ 11.80
$45.00
$35.00
64.80
15.90
21.80
16.40
126.40
270.61
13.65
18.21
80.00
24.50
3.87
7.65
16.57
101.75
9.52
21.50
45.20
83.16
28.40
2.75
9.60
25.00
25.00
3.81
4.25
50.60
10.00
11.40
12.53
72.30
12.00
5.65
7.56
4.80
11.43
7.48
5.34
2.36
5.80
5.20
2.81
7.41
3.40
4.30
Total
___
_
__
Balance
2. A company in San Francisco owes $15,000 in
Boston. How do you suppose this debt is paid? Discuss
the difficulty of sending $15,000 in biUs across the con-
tinent. How much would it cost to insure this amount
against loss? Is there danger that a check may be lost?
12

Finding Bank Balances
1. The numbers below represent the checking accoiuit
of a person for four months. Fiad the balance at the end
of January and write this amount in the proper place for
February. Write the balance at the end of February as
the balance at the beginning of March, and the balance
at the end of March as the balance at the beginning of
April.
Jan.
Feb.
Mar.
Apr.
Balance
$217.85
_
_
_
Deposits
350.00
$350.00
$350.00
$350.00
Total
Checks
$50.00
$29.40
$50.00
$60.00
2.87
50.00
71.60
50.00
41.65
10.00
2.40
24.65
23.40
27.50
9.60
39.20
10.00
32.65
21.50
5.00
7.80
41.12
6.89
10.00
5.35
3.87
12.35
4.25
17.20
12.50
12.40
7.14
5.50
17.80
5.23
9.57
Total
_____
Balance
—
—
—
—
Note that all this work above consists of adding and
subtracting. In the bank these computations are made
on the adding machine. But a person usually does not
have an adding machine at home, and so he has to add
and subtract as you are now doing.
2. If you know your balance the first of the month,
your deposits during the month, and yoTU- withdrawals,
how do you find your balance at the end of the month?
3. Why do people deposit their money in banks and
then pay their bills by drawing checks on the bank?
13

Multiplication and Division
Supply the words and
numbers missing below:
1. The numbers 866,
87, and 75,342 are called
,
,
and
2. The check number
(excess after casting out
9's) of 866 is
Tell how this number is found.
3. The check numbers of 87 and 75,342 are
and
4. Tell how you use check numbers in multiplication
Multiply and check:
5.
374
4090
7852
8945
3894
8479
86
287
738
367
745
654
866 (2)
2
87 (6) X6
6062
12 (3)
6928
75342 (3)
6. 4683
927
5894
367
7874
469
5449
798
6478
953
8020
284
7. 8242
7060
2854
816
5472
458
8747
692
9080
978
6754
675
8. In the example at
the right the divisor is
,
the dividend is
,
the quotient is
,
and
the remainder is
9. Tell how you use
check numbers in division.
(7)
4
400 (4) X7
385)154329 (6) 28
1540
5
329
33 (6)
Find quotients and remainders for the following:
10. 87)4789
281)64582
547)28546
643)51470
11. 75)38134 912)17914
634)89842
980)37000
12. 40)42642
143)48106
209)93870
416)33287
14

Multiplying and Dividing Decimals
To multiply decimals, multiply as with whole nimibers
and place a decimal point in the product.
1. Give the rule for placing the decimal
point in the product of two decimals.
2. Is the decimal point placed correctly
in the example at the right?
Use check numbers for the multipHca-
tion.
3. Give the rule for placing
the decimal point in the quo-
tient.
4. Is the decimal point
placed correctly at the right?
5. Use check ninnbers for
the division at the right.
6. How could you carry the
quotient to three decimal places
in the division at the right?
Multiply and check:
7. 8.3
21.4
35.82
875
680
57.9
9.7
6.9
.67
1.84
42.6
3.57
37.19
8.19)304.60,
A
A
245 7
58 90
57 33
157
819
75 10
73 71
139
8.
.59
6.4
3.91
.82
81.7
3.9
.98
487
,126
942
6.53
. 291
9. 39
.58
1.67
2.4
37.9
.94
7.6
. 165
487
.0 35
1.99
41.8
Divide and prove.
Find quotients correct to two
decimal places.
10. 94)37X
1.66)41.98
59.4)488.6
. 4 1)9718
11. 84)94.92
. 084)1 .652
15
43.8)51.50
,39)7.84

Sight Work in Fractions
Read and give the words and numbers missing below.
Answer the questions.
1, In a fraction such as f , the nimiber above the line is
called the
; the number below the line is called the
2. If a line 3 inches long is divided into 4 equal parts,
each part is
inches long.
I
ill L^^
I
3. A fraction may be regarded as an indicated division
in which the
is to be divided by the
4. The numerator and the denominator of a fraction
are called the
of the fraction.
5. If the terms of ^ are multipHed by 2,
what is the effect on the value of the fraction?
What is the effect on the value of the fraction
if both terms are multipHed by 3? by 4? by
any number?
6.Toadd^and^, change^to
add. The sum is
7. Toaddfand^, change|to_
add. The sum is
and then
i=f
h=l
1=1
andito
and then
Add each of the following pairs of fractions:
8.
9.
10.
11. In each of the preceding pairs of fractions subtract
the smaller from the larger.
16
iiiiiliiifiii1
i4r
ifiiiili11ii
liftiiiiIfii^i

Addition of Fractions and Mixed Numbers
1. Addf,I,and|.
Step 1. Find the smallest number that
contains 3, 6, and 8.
is the number.
You can see that 24
Step 2. Reduce the fractions to 24ths.
By what number must the terms of f be
multiplied to reduce it to 24ths? Answer
this question for f and f
.
Step 3. Add the new nimierators and
reduce. How do you reduce |^ to 1^1
2. Add 4|, 4f
,
and 5|.
Step 1.
Add the fractions.
Notice
that in the box at the right the new
numerators are written, but that the new
denominator is given only in the sum.
Step 2. Add the whole nimabers and to
their sum add 14 or 144. The sum is 1444
f=M
l=M
l=A
=i|
M=
24
24
24"
4|
4|
5f
9
18
16
14M If
Twenty-four is the smallest number that will exactly
contain the given denominators, 8, 4, and 3. Hence, 24
is the least common denominator (Led.) of the given
fractions.
This common denominator can usually be
found at sight.
Add the following:
3. 7|
371
18f
49i
8i
3U
1|
4f
31f
17|
21i
5*
9|
781
4. 36i
7i
291
37f
18|
47|
54|
36i
41
1
35i
821
37|
54f
691
191
27
1
12t%
15|
44^
82f
17

Subtraction of Mixed Numbers
The only difficulty in subtracting mixed numbers
occurs in the case when the fraction in the minuend is
less than that in the subtrahend.
1. Subtract 2| from 44.
orI,to
sub-
Since ^ is less than f, add 1,
Then change | and | to 12ths and
tract. Since 1 of the 4 in the minuend has
been used, there are 3 left.
So we sub-
tract 2 from 3. The answer is 1^,
Subtract the following:
3.
4i
2f
16
9
lAA
191
2|
161
7H
7i
19f
12f
69f
15t
29|
131
6i
2i
24|
151
57i
32f
811
63f
87|
33|
641
57|
59|
3H
9i
Problems
1. A housekeeper bought If lb. of meat on Monday,
2^ lb. on Tuesday, and If lb. on Wednesday. How many
pounds did she buy in the three days?
2. A pile of wood contains 18^ cords.
How many
cords are left after 2f cords have been hauled away?
3. The inside dimensions of a
picture frame are 12 in. in width and
16 in. in height. If the frame is 1^
inches wide, what are the outside
dimensions of the frame?
4. From a remnant of cloth con-
taining 11 yards, a clerk sold first
4| yards and then If yards.
How
many yards were left?
18

Multiplication of Fractions
Find the products of the following:
1.
J- ofi
2Ol2
^ ofJ-
3Ui2
iofi
2Ol3
^of-L
3Ui2
J-ofJ-
J- ofi
3 '-'^
4
2V1
3^^4
2/^5
3V1
3.
4.
Explain the work in each example below:
1
6
2_V^
3/^3
3V2— 1
4V2
5^3
7Vx3v^— 7
8/\4r/^^"~ 1 6
2
'
o XNOo
q/Np'
—
lA
3
15
^3
Find the products below.
Check your work.
5
1V3
2v3
1V4
3V5.
•
2^/ ^
"4
3 ^^"4
T-^^
A/N
6. UX4
5X3i
5iX2i
3/^5
Hxii
7iX3i
0-2 /\ O2
7. 25^X14^
^2^/\^4:
#3
8. Multiply 938 by 64|.
Step i.
To multiply 938 by |, mul-
tiply 938 by 3 and divide the product by
8. The result is 351|.
Smp 2. Multiply 938 by 64 and add
the products to 351f
.
Check the work by doing it again.
51X24
fX2|
91X14
938
64|
8 )2814
351f
3752
5628
603831
In finding the product of two mixed numbers, it is
usually best to reduce both to improper fractions.
The
multipHcation may be proved by division, as shown
below:
Multiply: 3|X2| = J3LX^ = W='iOV2.
Proof:
10^-2|=#X^ 1 1 — Q2
3
-3 3.
Find the products of the following:
9. 151X640 4|X56 82X47| 93X76|
10. 45^X350 8|X87 16X47^^ 8^52X48
H. 19fX280 9|X84 61X51|
19
44X51
12|X68
3HX86
641X12

Division of Fractions
It is clear that ^ is contained 2 times in 1, 4 times in 2,
and so on.
That is to say l-^^ = lX2=2, and 2-t -^ =
2X2=4.
Again, ^ is contained 4 times in ^ and 2 times in ^J^ .
Thatis, ^-5 -i
=
iX8=4, and i-^i=iX8 =2.
i nUS, 3— 2— 3/^^~3> ^^^ 5 • 4~5/^315*
The general rule for division of fractions is as follows:
To divide by a fraction, invert the terms of the
divisor and then multiply.
This rule includes the case when the divisor is a whole
number if we regard the whole number as having a
denominator 1. Thus, 2 =f
,
7 =^.
We can then invert
the terms and use the rule.
Example: T^2=fXi=t.
Study each of the following divisions by fractions:
1. 1-1=1:><f = J^ = 1|
t-l
=
2
2. 3i^1f = i-f=|X| To 2,0
3. 5f^4
=
^Xi=f|= lii
Divide the following. Prove answers by multiplying
the quotients by the divisors.
4.
f^l
l-^l
H-^3
3^H H-H
5.
21-
H
3i-H
4H-21
7-MI
8^21
6.
4i-2x
- 4|^H
3|-1| 7i-H 51-21
7. 121-4 -2
12i^H 12i-3i 5J^H 6i-1f
8.
25^11
32 - =-41
18i^4i 121-^
5i 8^-lf
20

Problems
1. A carpenter built a
beam by nailing a board 1^
inches thick to each side of
a plank 2^ inches thick.
How thick was the beam?
2. A mechanic imder-
took to do some repair
work for $99. How much
per 8-hour day did he earn
if he finished the work in 12
days and 3 hours (12f
days)?
3. An airplane flew 1364 miles in 7 hours and 20 min-
utes (7^ hr.). Find the average speed in miles per hour.
4. A rectangular flower bed was 3^ feet by 6^ feet.
The gardener increased its size by f foot on each side.
What are the new dimensions of the flower bed? What is
the area of the enlarged bed?
5. One room is 14 feet 8 inches (14f ft.) wide and 18
feet 4 inches long. Another room is 16 feet 3 inches wide
and 28 feet 10 inches long. What is the difference be-
tween the widths of these rooms? What is the difference
between their lengths? •
6. Mrs. Hall bought remnants containing 4^ yd.,
21 yd., and 6f yd. How many yards did she buy?
7. In a hardwood floor, narrow boards 2f inches wide
are used. How wide a floor wiU be covered if 68 of these
boards are used? Reduce answer to feet and a fraction
of a foot.
8. In problem 7, how many boards will be required
for a floor 12 feet wide? Count a fraction in the answer
as a whole board.
21

Unit 2. Rounded Numbers. Accounts and Records
Approximate Whole Numbers
You can count the pupils in youi- class and find the
exact number, for example, 36. But many large numbers
obtained from counting are kno^-n only approxunately,
or in round numbers.
Thus the census for 1940 gives 100,972,196 as the
nmnber of the people in the United States who are 4
years old or over,
. \lthough the census takers actu^y
counted tWs number, we know that it is not exact be-
cause thousands became 14 yeai-s of age, and many of
this age died while the count was bemg taken.
It is quite certam that we cannot know this figure
^^ -ithin 1000. or even ^^ •ithin 10.000 . so we say that it was
approximately 100,970,000, correct to the neai-est 10,000,
or 101.000 .000. coiTect to the nearest miUion.
1. Explain why 100,972,196 is neai-er to 100,970,000
than to 100,980,000.
2. Explain why 100,972,196 is nearer 101 mUUon than
100 million.
To round a number, replace the figures not
wanted at the right with zeros. If the last figure
replaced is 5 or more, add 1 to the figure before it.
Round the numbers below to the nearest million:
3. 209.830 .246
416.325.621
59.524.610
4. 450.379.400
849,906,728
8,217,086
Round the foUo\\-ing to the nearest billion:
5. $4,512,556,474
$19,977,965,474
$7,255,486,980
00

w
Rounding Off Numbers
CCCCCCOOOO •?:-CJ5>;>:-C««^-?J-?5«-?5««
poooooo-C -C -C
=
5,000 ,000 RURAL POPULATION
1850
o
ooo•?
=
5,000P00 URBAN POPULATION
At the right is shown the chang-
ing rural population of the United
States according to the 1940
Census.
1. Round each number to the
nearest thousand.
2. Round each number to the
nearest ten thousand. From these
rounded nimmbers, what is the
difference between the rural population in
1930? in 1940 and in 1850?
1940 57,245,573
1930 53,820,223
1920 51,552,647
1910 49,973,334
1900 45,834,654
1890 40,841,449
1880 36,026,048
1870 28,656,010
1860 25,226,803
1850 19,648,160
Rural Population 1
1940 and m
3. When the numbers are rounded to the nearest
himdred thousand, what is the difference in niral popu-
lation between 1940 and 1930? between 1940 and 1850?
4. When the numbers are rounded to the nearest
milHon, the rural population of 1940 is about how many
times that of 1850? of 1870?
5. Round the following numbers to thousands:
24,719
20,587
50,467
8,405
367,905
99,464
16,376
79,658
9,500
430,758
6. Round the following to the nearest hundredth:
.783
. 067
.4078
.0084
.054
.701
4.245
6.067
9.999
5.398
38.097
7. Multiply the following. Round products to tenths.
3.46 X. 24
6.97 X. 08
.406 X.
9
3.14X7
23

Rounding Off Quotients
As you know, a fraction means that the numerator is
to be divided by the denominator. Thus, ^ means that
1 is to be divided by 8. When this divi-
sion is carried out as shown at the right,
the quotient is exactly .125 .
However, when we reduce ^ to a deci-
mal, there is always a remainder, 1, and
the quotient may be continued endlessly
by writing 3's.
The exact quotient is
.125
8)1.000
3333
3)1.0000
.3 3 ^, or .3i The approximate quotient is .3333, correct
to four decimals, .333, correct to three decimals, or .33 ,
correct to two decimals.
.666^7
3)2.000
When we reduce f to a decimal,
every quotient figure is 6, and every
remainder is 2. The exact quotient is
.66^, and the approximate, or rounded, quotient is .667,
correct to three decimal places.
1. Reduce ^ to a decimal correct to three places.
Since the remainder,
8, is less than one half
the divisor, the quotient
is .472, correct to three
places.
2. Reduce ^ to a dec-
imal, correct to three
places.
Since the remainder,
23, is greater than one half the divisor, add 1 to the last
quotient figure, 3. The quotient is .414, correct to three
decimals.
.472
AIS41
36)17.000 29)12.000
144
116
260
252
40
29
80
72
-8
110
87
23
Reduce the following to decimals correct to 3 places:
3.
6
7
5
8
6
9
5
11
7
8
9
11
13
14
16
TT
24

Standings of Basketball Teams
23)14.000
138
1. A basketball team won 14
games and lost 9. Find its standing
correct to 3 decimal places.
The team played 23 games.
Hence, it won ^ of the games
played. The quotient is .608 with
a remainder of 16.
Hence, the
team's standing is .609.
2. The college teams of
one of the basketball con-
ferences recently had the
records shown at the right.
Find the standing of
each team correct to three
decimals.
Use zeros to
fill in the three places when
needed.
Find quotients correct to two decimal places.
.608 9
200
184
16
Team Won Lost
Pet.
1.
10
2
2.
9
3
__
3.
8
4
4.
7
5
5.
•7
5
6.
6
6
7.
5
7
8.
4
8
9.
3
9
10.
1
11
—
3. 5).47
7)12.5
,9)8.63
1.2).076
6)847
9)3:61
.1 1)6.04
37)18.7
16)700
3.25)80
. 025)62.5
.15)2.51
6. .24)60
.0 6)4.34
.8)700
750)480
7. 3 .775-4 -7.5
1 6.307 -^ 1.87
97.52 -.084
8. 2.304^.19
7.01 73 H- 2.04
56.58^8.8
Find products and round off to two decimal places.
9. 9.874X7.5
35.093 X. 078
68.07 X. 875
10. 437.6 X. 96
79.007X4.67
90.89X6.29
11. 8947X.062
4.9999X25.7
. 7643X5.26
25

Keeping Farm Records
1. Every farmer who is also a good businessman keeps
an account for each crop that he raises.
He puts all
expenditures on the left (Dr.) side of his accounts, as is
shown on the opposite page. In studying these expendi-
tures, can you think of any expenses that the farmer did
not put in?
Crops are sometimes insured against fire and hail.
In the spring and summer, the farmer pays for work
and other items on which he charges interest until he
sells his crop.
The farmer figures the value of his own work and the
use of his machinery and horses as a part of the expense
of producing the crop. If the account shows a profit,
this is over and above wages for his own work.
Such accounts are always kept by using whole num-
bers and decimals.
The value that the farmer places upon his product is
usually somewhat less than the market value at the
nearest station, for it costs something to take the pro-
ducts to market.
As much as possible of the computing required on the
opposite page should be done at sight. It can easily be
seen that 110 X $.50 (the cost of the seed oats) =$55;
50X$4.50 = $225; 120 X $5 =$600; and 90 X $.60 =$54.
Find at sight the products for the following:
2.
6X$240
9 X $87.40
4 X $9.65
7 X $3.80
3.
3 X $15.80
ex $5.87
5 X $1.41
9 X $2.45
4.
1 0X $5.37
20 X $0.37
50 X $0.75
8 X $0.67
26

Oat and Wheat Accounts
Copy the accounts below and supply the missmg niun-
bers; find the gain or loss in each account.
1. Expenditures
Receipts
Plowing
$ 90 00 1780 bu. oats
Seeding
2200 @32^
110 bu. seed oats
27 tons straw
@50^
@ $3.50
Fertilizer
18 00 Pasture
12 00
Twine
420
Other work
148 00 Total receipts
Use of land—50
acres @ $4.50
Total expendi-
Use of machinery
19 40 tures
Insurance
10 00
Interest
15 00
Gain
Total
2. Expenditures
Receipts
—
Plowing
$125 00 1687 bu. wheat
Seeding
3500 @78^
180 bu, seed
90 bu. w heat
wheat @ 95f^
@ 60^
Cutting
75 00 135 tons straw
Threshing
170 00 @ $3.50
Other work
320 00
""
Use of land— 120
acres @ $5
Total receipts
Use of machinery
44 00
Insurance
22 00 Total expendi-
Interest
18 00 tures
Gain
—
Total
27

Keeping School Records
1. From time to time
you will see statements in
the papers about the at-
tendance in your schools.
Sometimes you may see
statements about the numr
ber of pupils in all the
schools of your state. How
are these facts obtained?
The first record on the opposite page shows the at-
tendance in a school for one week. The teacher in each
room makes a report each day of the attendance in her
room. The total for each grade is then found and entered
on the record for that day. The totals for the grades are
then added to find the total for the school.
A copy of the attendance record for each school is
sent to the superintendent's office, where a simimary is
prepared for the whole city. The second record shows a
summary for another city with ten schools.
2. Get from your teacher the record of attendance for
your grade for one week. Find the average attendance
for these days.
3. Then try to secure the same records for the other
grades in your school. Make a summary like that given
on the opposite page and then find the total of each day's
attendance for one week.
4. Find out what uses are made in your school of the
daily record of attendance of all pupils.
5. Why do school principals want to have as large a
per cent as possible of the pupils of their schools in
attendance every day?
28

School Attendance Records
1. Find the total of each day's attendance for the
large school given below.
Find the total for the week.
2. Tell how you find the average of several numbers.
Find the average daily attendance in this school.
Record of Attendance of One Large School
Grade
Mon.
Tues.
Wed. Thurs.
Fri.
Grade 1
104
107
99
101
105
Grade 2
115
118
106
111
114
Grade 3
96
101
98
99
100
Grade 4
91
96
93
94
92
Grade 5
98
92
89
91
90
Grade 6
83
86
87
84
85
Grade 7
81
84
82
85
82
Grade 8
74
76
73
75
74
3. Find the total attendance for each day of the week
for the city schools given below:
Record of Attendance for a City
School
Mon.
Tues.
Wed. Thurs.
Fri.
Central
527
513
524
519
521
Franklin
187
192
194
190
186
Hawthorne 424
431
425
429
427
Lincoln
212
214
204
210
216
Lowell
341
337
331
342
340
Paxton
273
281
279
278
281
Prescott
207
204
197
210
208
Roosevelt
521
511
524
525
524
Whittier
482
496
480
491
487
WiUard
257
261
254
259
260
29

Sales Records
Records are kept in stores of the daily sales of each
clerk as well as of the total sales of the whole store.
In the table below is shown part of the record of sales
made by different clerks.
This record, when completed,
shows also the total sales from day to day. This enables
the manager to study such questions as the effect on
sales of special advertising or displays.
Record of Daily Sales by Six Clerks
Mon.
Tues.
Wed.
Thurs.
Fri.
Sat. Totals
A
B
C
D
E
F
$127.42
104.27
184.45
97.50
145.65
162.55
$102.65
94.20
149.62
101.72
142.86
130.57
$110.76
120.60
136.15
94.31
102.55
191.85
$87.60
99.20
114.13
84.47
151.19
132.62
—
—
—
Totals
—
—
—
—
~
—
—
1. On a wide sheet of paper copy this record and put
in sales for Friday and Saturday for each clerk. Leave
an extra column at the right headed ''Totals."
2. Find the total sales of these clerks for each day of
the week.
3. In your completed record, find the total for the
whole week for each clerk. Check your work by adding
these totals, and also the totals found in problem 2, and
compare the sums.
4. Several clerks are working in the same department
in a store.
It is found that week after week some clerks
sell more goods than others.
What may be the reasons
for this? Why do you suppose the owner of the store
wants to know not only how much is sold each day, but
also how much is sold by each clerk?
30

Adding Horizontally
In finding the sales of each clerk, the adding is often
done horizontally.
1. Add 481+354+659. 481 +354 +659 = 1494
Step 1. Add the figures
in ones' place.
The sum is 14. Write 4 and carry 1.
Step 2, Add the figiu*es in tens' place.
Step 3. Add the figures in hundreds' place.
Exercises
Find the wrong answers and correct them.
Do the
exercises in addition by adding horizontally.
1. 287+359 + 878 = 1524
2. 794+876+594 = 2254
3. 319+492 + 865 = 1576
4. 899+274+842 = 2015
5. 273 + 891+749 = 1813
6. 383 + 197+993 = 1573
7. 428+979+241 =1648
8. 887+649 + 529 = 2065
9. 845+796+858 = 2499
10. 962 + 579+384 = 1925
11. 749+891+273 = 1913
12. 884+208+583 = 1775
13. 426+357+109 = 892
14. 487+956 + 872 = 2315
15. 531+876 + 924 = 2331
31
6804-781=5923
9118-609 = 3609
4085-865 = 4220
7223-916 = 6307
7004-889 = 7115
4670-675 = 3995
8201-186 = 7015
46587X6 = 279522
90356X7 = 632492
$69.48X8 = $556.84
$78.09X4 = $31 2.36
7.6348X9 = 68.7132
46950-5 = 8390
64836-6 = 10806
57088 -^4 = 14272

Working with Decimals and Fractions
1. Subtract each number in row B from each in row A,
A
67.4
15.6
20.17 12.06 18.365 13.01
B
9.7
.78
.9 68
1.037 2.008 6.74
2. Multiply each number in row A by each in row B,
A
8.96
65.7
.7 48
2.07 40.09
.329
B
7.8
6.84
.906
18.5
7.03
.045
3. Divide each number in row A by each in row B,
A
567
29.6
50.8
7.83
. 904
8.06
B
.17
2.8
. 096
65.4
2.09
9
4. Add each nimiber in row A to each in row B.
A
6|
^
7|
2i
6A
3|
B
5f
9|
8i
4t%
2f
6i
5. Subtract each number in row B from each in row A,
A
7|
61
8|
9f
6f
7A
B
5|
4i
1|
2|
3|
^
6. Multiply each number in row A by each in row B.
A
16
19
25
48
51
78
B
2i
If
3f
2|
3|
41
1
32
:

Problems
1. A truck loaded with coal weighed
11,600 lb., and the empty truck weighed
2850 lb. At $9.75 per ton, what did the
coal cost?
-
2. A floor measures 12 feet 6 inches by 15 feet 9 inches.
Find the area in square yards.
(Reduce the dimensions
to mixed nimibers.)
3. How many cubic inches are there in a box 8f in.
long, 6^ in. wide, and 4|^ in. deep?
4. \i^ yard of toweling is used in making one towel,
how many towels can be made from 12 yards of toweHng?
5. Allowing .8 bushel to a cubic foot, find how many
bushels of wheat can be stored in a bin 12 feet long, 7 feet
wide, and 4^ feet deep.
6. A piece of land 120 rd. long and 80 rd. wide was sold
for $7500. What was the price per acre?
7. A farmer harvested 1524 bu. of oats from a field
96 rd. by 40 rd. What was the average number of
bushels per acre?
8. A factory floor is to be 120 ft. wide. How long
must it be to cover 15,000 sq. ft. of space?
9. An excavation was 90 feet by 75 feet by 7^ feet.
At $1.60 per cubic yard, what was the cost of excavating?
10. An automobile was driven 315 mi. in 1\ hr.
What
was the average speed per hour?
11. A baseball team won 73 games and lost 19 games.
What decimal part of the games played did this team
win? (Find result correct to thousandths.)
33

first Self-Test
Test in Fundamentals
Write in columns and add:
1. 241 .2+784.26+965.7+197.86+66.282+7.834
2. 47 .98+1.68+52.16+14.89+7.564+416.47
3. $840.94+$2147.67+$47.52+$14.93+$55.79
Write in columns and subtract:
4. 49.84-17.95
264.28-95.75 886.06 -194.28
5. 5007.9-69.87
67.491-36.43 67.94-41.875
6. $13.89 -$6.34
$94.12-$74.86 $78.10-$57.84
Multiply:
7. 89.3
69
63.4
8.73
57.59
42.8
60.64
279
1984
5.85
. 284
1.98
8. 6.87
96.8
7.56
9.85
368.5
97.4
7.83
78
480
8971
9.67
39.6
Divide. Find quotients to two decim
1478.2
965)874.94
al places.
9. 78.4)
197)381.928
10. 4 .79)9.289
44.2)124.64
287)873.947
Add:
11. 17i
8f
4f
5i
2|
47|
8i
9i
27i
2A
lOf
3J
5|
If
32A
46t%
^^
^
12. Subtract each num-
berinBfromeachinA.
13. Multiply each num-
berinlineAbyeachinB.
14. Divide each nimiber in A by each number in B,
34
A4i7i6f5i
B3f4i2f1i

Problem Test
1. On October 1, Jane Marvin had cash on hand to
the amount of $5.84. During the month she received
cash as follows: Oct. 3, allowance, $1.50; Oct. 12, for
helping a neighbor, $.45; Oct. 17, allowance, $1.50; Oct.
21, for selling magazines, $.65. She spent the following
amounts: Oct. 5, book, $.95; Oct. 12, movies, $.40; Oct.
20, candy, $.15; Oct. 27, shoes, $3.75 . Rule paper and
make up Jane's cash account.
2. On October 1, Jane's father had $317.52 in his cash
account.
During the month he deposited $175.00,
$52.60, and $89.35. He drew out $16.20, $42.60, $30.25,
$29.37, $2.46, and $57.29. Make a statement showing
his balance in the bank at the end of the month.
3. One day Mrs. Marvin bought 1^ pounds of meat at
36 cents a pound, 6 cans of corn at 12^ cents, 2 dozen
eggs at 35 cents a dozen, and a pound of butter for 42
cents. Make a biU for these purchases.
4. In a sewing class it was found that 1^ yards of
cloth would make one apron. How many yards would
the class need to make one apron for each of the 12 girls?
At 19 cents a yard, how much would the cloth cost?
5. A bag of flour containing 24 pounds was sold for 65
cents; a bag containing 5 pounds was sold for 19 cents.
Find the cost per pound, to the nearest tenth of a cent,
of ^ach of these.
6. One day the hourly temperature readings for 6
hr. were 64°, 67^ 74°, 71°, 69°, 68°.
Find the average of
these readings, correct to one decimal place.
7. Our schoolroom is 28 feet wide and 32 feet long.
At 35 cents per square foot, what is the cost of putting a
new floor in this room?
35

Unit 3. Equations. Percentage
Equations
In the box at the right are four
expressions of equality which you
have often used before.
Such an
expression is called an equation.
Each of these equations represents
a question, or problem.
Equation (1) represents: What number must be added
to 8 to make 12? Equation (2) represents: 8 subtracted
from what number gives 3?
(1) 8+_
=
=12
(2) _-8
=
=3
(3) 8X_
=
=24
(4)_^8==3
1. What does equation (3) represent?
equation (4) represent?
What does
When you understand the ideas in these simple
equations, you will see that they are the most effective
means for solving problems that have ever been devised.
In each of the four equations above
there is an unknown number repre-
sented by a
In each equation at
the right the unknown number is
represented by the letter x.
Note
that 8 times x is written 8a:, and x -4 -8
is written as a fraction.
(1)
(2)
(3)
(4)
8+x=12
Jc-8=3
8x=24
8
=3
Finding the value of the unknown number in an
equation is caUed solving the equation.
The two parts of an equation that are connected by
the equality sign are caUed the members of the equa-
tion.
In 8-f X -12, 8-f X is the left member, and 12 is
the right member.
36

How to Solve Equations
1. Solve the equation jc— 8 = 3.
x-8=3
x-8+8=3+8
In the lower grades you solved a
problem exactly like this.
That is,
you found the missing number in
_
-8 =3byadding8to3.
Solve the equation x— 8=3 by adding 8 to both
members. Clearly, adding 8 to :x:— 8 gives jc , no matter
what number x is.
Then x=3+8 = ll.
If in X—8=3 you replace x by 11, then 11—8 = 3,
which shows that the solution is correct.
2. Solve the equation x + 8 = 12.
In the lower grades you found
the missing number in
+8=12
by subtracting 8 from 12.
Solve the equation jc+8 = 12 by subtracting 8 from
both members. Then x=A. If in x +8 = 12 you replace
X by 4, then 4 +8 = 12. This shows the solution is correct.
x+8=12
x+8-8 = 12-8
x=4
3. Solve
8
The missing number in
-7-8 =3 is
found by multiplying 3 by 8.
X
Solve the equation o= 3 by multi-
plying both members by 8. Then x = 24.
24o
8 X8=3X8
jc=24
To prove this
solution, replace x by 24, giving
8
3x=24
3x-^3=24
x=8
4. Solve 3x = 24.
The missing nimiber in
X3 =24
is found by dividing 24 by 3.
Solve the equation by dividing
both members by 3, which gives jc = 8 . To prove this
solution, replace x by 8, giving 3x8 =24.
37

Learning More about Equations
1. Henry said: "Think of a number, subtract 8 froix_
it, then add 8.
The answer is the number you first
thought of." Was Henry right? Would his statement be
true, no matter what niunber you thought of?
This is exactly what we mean when we say that adding
8tojc—8 gives x.
The letter x in this statement stands
for the number— any number— Henry asked you to
think of.
2. If you subtract 8 from x+8, what is the answer?
If you start with a number, add 8 to it, and then sub-
tract 8, what is the answer?
X
3. If you multiply o by 3, what is the answer?
4. If you divide 3x by 3, what is the answer? Restate
this question without representing a number by a letter.
5. Which of the fundamental oper-
ations must you use in each of the
equations at the right to get x as the
left member?
(1)
(2)
(3)
(4)
jc-8 =3
x-h8 = 12
3x=24
6. If you add 8 to the first member
of an equation, what must you do to
the second member?
7. If you subtract 8 from the first member of an
equation, what must you do to the second member?
8. If you multiply the first member of an equation by
8, what must you do to the second member?
9. If you divide the first member of an equation by 3,
what must you do to the second member?
10. How do you solve the equation x +3^ = 15? Solve
this equation and prove your answer.
38

Steps Used in Solving Equations
The problems on page 37 show the principal steps used
in solving equations. In problem 1 we added 8 to both
members; in problem 2 we subtracted 8 from both mem-
bers; in problem 3 we multipKed both members by 8; and
in problem 4 we divided both members by 3.
In solving an equation we may (1) add the same
number to both members; (2) subtract the same
number from both members; (3) multiply both
members by the same number; or (4) divide both
members by the same number.
Solve the foUowing equations:
1.
4jc=16
x+2i = 6i
x-5.7 = 9.3
x-5=12
2ix=10
3ix=20
t'
x+2.3 = 7.5
^+5i = 6i
jc+5=7
i^='»
We shall now use equations to solve simple problems
that you could solve easily without using equations.
The purpose is to learn how equations may be used.
5. Charles said: "If
youadd6tomyage,
the sum will be 20.
What is my age?"
Let
X
represent
Charles's
age; then
:x:+6=20.
Subtract-
ing 6 from both sides of the equation, we find that
X = 14, which is Charles's age.
39
X- = C harles's age
x-h6 = 20
x+6-6== 20- -6
x== 14
Proof: 14-F6 == 20

Problem Practice
Use equations in solving the following problems:
1. Ada said: "If you subtract 7 from my age, the
remainder is 8.
my age?
What is
x-= Ada's age
X-
-1
X-
=8
=15
Proof: 15 -1-= 8
The equation, x — 7
=
8, is a statement of the
problem in the form of
an equation.
If we add
7toX—7ywefindthesumisx.
Adding 7 to the other
member also, we find that x = 15, which is Ada's age.
In equations, the names of things represented by
letters are understood but never written.
Thus, in the
problem above, it is understood that x represents a num-
ber of years.
2. In 9 years from now, Mary will be 22 years old.
How old is she now?
3. Walter had some money and spent 57 cents. Then
he had 78 cents left.
How many cents did he have at
first?
4. Sam had some money and then earned 75 cents,
when he had $1.40 (140 cents). How much money did he
have at first?
5. Tom has $2.65, which is 7 cents more than 3 times
as much as he had yesterday.
How much did he have yester-
day?
Study the equations at the
right. How is equation (2) ob-
tained from equation (1)? equa-
tion (3) from (2)?
40
X = number of cents
he had yesterday
(1) 3;c+7:= 265
(2)
3jc := 258
(3)
X-= 86
Proof:
3x86+7 == 265

Solving Equations
Solve the following equations:
1. x+7=^9
X-
-7 =19
3:c=18
i^=18
2. x+45=60
X--15 = 3
4x=14
lx=2
3. :c+32 = 49
X--12 = 1
5x=21
^-1=1
4. x+^=47
X--2i
=7
^x=12
2x=2i
5.
:»;+4.5 = 9
X-
-.5 = 1.5
ix=
2i
x+.25 = 1
6.|
=
H
X
6'
=10
1=2
I'^i
/• ooive tne equatiun T"r'
=
1
12.
Step i. Subtrac
members. Write
Step 2, Multip
hers by 4. Write
Prove the solut
;t7
equ
lyb
equ
ion
from both
ation (2).
oth mem-
ation (3).
as shown.
(1)
£+7=12
4
(2)
1=5
(3)
x=20
Proof: ^+7 = 12
8.
^+6=16
1-7
=11
i-^=^
9. 2x-7=U
4x+3 = 15
7x+4 = 25
10.
^+2=5
|+2= ,0
2; 5=2
11. 5y-2y = 9
3y+7 = 22
3x+x = 20
12.
^+5=14
1+9=13
^+12=21
13. ^
=15
2^16
1+9=15
14. 4x-10 = 70
4:»:- 1.5 = 2.5
. 5a:+1 =6
15. 3;c+49 = 100
5x-17 = 83
3a; +50 = 200
16. 2x-40 = 80
12:c+6 = 138
8:c-12 = 60
17.
^+15 = 18
"
4x
^+12 = 13i
%-11=19
41

Percentage
With the exception of the fxindamental operations,
percentage is probably used oftener in practical life than
any other part of arithmetic.
The following statements are taken from one issue of
a small daily paper:
/SU«I operated at 97y2% of Capacity^ ^Th* attendance at the state university^
\—"^ 1^ '
,.^'-*—
^
.
^
'- ^J
^
{, 11/2% below last year.
production of electric current is up^
9K% above last month.
"s
yThc attendance at high school is II
above last year.
-^
"—
""
—
s
ings were 694,640,.
which is I
n 2^% below the corres-
)
>nding week of last year. ^-J
An imderstanding of percentage is necessary in order
to read intelligently even the simplest newspaper. Per
cents are used so very generally because we need a simple
basis for making comparisons. To use common fractions
would be hopelessly complicated.
Per cents are much more convenient than common
fractions.
For the milk sold to creameries, farmers are
paid according to the amount of butterfat the milk con-
tsdns. This butterfat content is given in per cents, to the
nearest tenth of 1 per cent.
1. On the opposite page is given, below each common
fraction, the equivalent per cent of butterfat. Change
each fraction to a per cent and compare your answers
with the per cents given. Note how easy it is to see the
difference in the successive per cents, and how difficult it
would be to compare the fractions.
42

Comparing Fractions with Per Cents
Butterfat Content of Samples of Milk
Fraction tIs
5VV
250
s'A
AmjVih
Percent 3.2% 3.4% 3.6% 3.8% 4.0% 4.2% 4.4%
Fraction A% TI5
i-o
i^ T5Z)
tIs
29
SOO
Percent 4.6% 4.8% 5.0% 5.2% 5.4% 5.6% 5.8%
Following is another example in which information is
expressed much more clearly and effectively by per cents
than would be possible by common fractions:
Proportion of Negroes in Our Population
from 1820 to 1930
1820 18% 1850 16% 1880 13% 1910 11%
1830 18% 1860 14% 1890 11% 1920 10%
1840 17% 1870 13% 1900 12% 1930 9%
The meaning of per cent will become clearer if you
think of cents as parts of a dollar.
Thus, 10 cents is 10
per cent of a dollar; 37 cents is 37% of a dollar, and so on.
An ordinary decimal may be changed to a per cent by
multiplying it by 100. What amounts to the same thing
is to move the decimal point two places to the right
Thus, .145=14.5%, .037=3 .7%, 1.25 = 125%. It fol-
lows that a per cent may be changed to a decimal by
moving the decimal point two places to the left.
!• Change to per cents: 7.2, 15.4, 1.54, .043
2. Change to decimals: 24%, 7.5%, 245%, 3.8%
43

Base, Rate, and Percentage
The number of which a certain rate per cent is found
is called the base, tho rate per cent is usually called
simply the rate, and the product of the base and the
rate is called the percentage. Thus, in "25% of 400 =
100/' 25% is the rate, 400 is the base, and 100 is the
percentage.
If the base, rate,
and percentage are denoted by
by r, andp,thenhr=p.
25%of400=100
. 25X400 = 100
Starting with formula (1) at the right,
we can now obtain formulas (2) and (3)
by using the rule stated on page 39. If
we divide both members of (1) by 6, we
have r =^; and if we divide both mem-
b
(1) br- =
P
(2) r
b
(3) b-.
Ar
bersbyr, wehaveh
Thus, by a direct use of a very simple idea, we have
obtained formulas (2) and (3) from formula (1). This
is a very important use of equations, since it simpHfies
very much the solving of problems that, by the use of
ordinary arithmetic, often cause trouble.
As you wiU recall, to use the above formulas, you must
reduce the rate per cent to a decimal.
Find:
1. 5%of100
4% of 200
40% of 600
2. 10%of40
6% of 500
75% of 300
3. 8%of600
12% of 48
150% of 60
4.
7% of 504
6% of 370
80% of 600
5. 97o of 450
7% of 850
4% of 1250
44
X

Fractional Per Cents
Fractions of per cents are written either as common
fractions or as decimals. Thus, we may say that 14^%
or 14.5% of a certain sample of sugar beets is sugar.
Decimal parts of a per cent are generally used in
scientific work, as, for example, in measurements that
cannot be found exactly. Thus, to give the sugar con-
tent of sugar beets, use 14.5% rather than 14^%.
In the case of interest rates, when these are known
exactly, fractional parts of per cents are usually ex-
pressed as common fractions.
1. Find 7f % of $1840.
A solution using the common frac-
tions is shown at the right.
Solve this problem by using .0775 in-
stead of .07|. Which solution is shorter?
Find the percentage in the following:
Base Rate
Base Rate
$1840
. 07f
4)55 20
13 80
128 80
$142.60
Base Rate
2. 850 6i%
1250 12i%
1800 5%
3. 15.3 37%
1648 62i%
500
41%
4. 26.5 2H%
8640 66|%
840
6f%
5. 640
334r%
1830 5i%
824
6|%
6. Find 13.7% of 6420. Describe each step. In this
problem, which number is the base, which is the rate,
and which is the percentage?
7. A man borrowed $7600 and paid 4|% of this
amount in interest each year. How much interest did he
pay? In this problem, which number is the base?
45

Finding the Rate
The problem of j&nding what per cent one nimiber is
of another occurs very frequently. The following prob-
lems are of this type:
1. Out of 50 words, I spelled 47 correctly,
cent did I spell correctly?
2. Our team played 17 games and won 10.
cent of the games played did it win?
3. A suit marked $35 was
reduced to $27. By what per
cent was the price reduced?
What per
What per
. 2285 or 22.9%
35)8.0000
70
100
70
300
280
200
In the last of these prob-
lems, we know that the reduc-
Q
tion was ^ of the price. Find
the per cent reduction as
shown at the right.
Finding the rate per cent consists in
reducing a fraction to a per cent, as indicated
by the formula at the right.
Exercises
Reduce the following fractions and mixed niunbers to
per cents, either exactly or correct to the nearest tenth of
1%. Notice that in each fraction the numerator is the
percentage and the denominator is the base.
2.
3.
4.
1
2
i
3
4
i
1
1
•J
i
i
f
i
4
5
1
To
T%
T%
T%
T^
t\
1
f
f
i
f
f
JL
9
1
i
1
1
20
^
7
20
Uu
46
112i5i101

Finding the Base
Finding the base when
the rate and the percentage
are given is required in such
problems as the following:
1. A certain creamery
can run profitably if it has
2500 pounds of butterfat
each day. If the milk re-
ceived contains, on an
average, 4.2% butterfat,
how many pounds of milk
must the creamery receive daily?
2500 is 4.2% or .042 of what
number?
59 523.8
.042a)2500.000a0
The number is 2500-^ .042=59,523.8, or 59,524 in
round nimibers.
The easiest way to think of such problems is to re-
member the formulas br =p and h = ".
Remember that r
r
must be written as a decimal.
Of the three types of problems in percentage, the one
in which the base is to be found occurs least often. How-
ever, the methods for solving these problems are now
so easily obtained from the fundamental formula that
these problems will cause you Httle trouble.
Decide
which number is the base, which is the rate, and which is
the percentage, and then use the formula.
Find each base correct to the nearest unit.
Percent-
age Rate
2.
3.
20
35
5%
8%
Percent-
age
Rate
50
10%
316
6%
47
Percent-
age
Rate
5760
1250
6i%
4i%

Unit 4. Percentage
Fractional Equivalents of Per Cents
Work involving percentage occurs so often in the
practical uses of arithmetic that it may be well at this
time to study percentage a little further.
Percentage is
a tool that we should be able to use with ease.
In many problems, it is convenient to change fractions
to per cents or per cents to fractions. Thus, to find 25%
ofanumber,wemaytake^ofit,andtofind5%ofa
number, we may take -^ of it.
Again, 150% of a number
is 1^ times the number.
1. Study these fractional equivalents of per cents:
50%= \
33i%=\
12i%=\
20%=\
25%=\
66f% =1
37|% =
I
40%=f
75%= f
16f% =i
621%=5
60% =1
10% =3^
83i%=f 87i%=| 80% =1
These equivalents are also useful in estimating num-
bers. Suppose you read that 35% of those who graduate
from the high schools in your city go to college; you
know that a little over ^ (33^%) of them go to college.
In the following, use fractions instead of per cents if
thereby the work may be shortened:
2. 25% of 640
50% of 326
75% of 60
3. 331% of 1281
66f% of 96
47% of 850
4. 871% of 8464
125% of 296
87i%o of 56
5. 117% of 1862
73% of 75
80% of 975
48

Sight Work in Percentage
Many problems involving percentage can be solved
at sight if the relation between fractions and per cents is
kept in mind.
1. 16 is what per cent of 20?
Weseeatoncethat16is^orfof20,andthatthe
answer is 80%.
2. ^ is 25% of what number?
Since 25% =^, the problem is: ^ is ^ of what number?
2-^4=2X4=2. The answer is 2.
3. 3iswhatpercentof9? of12? of15? of4?
4. 12 is 75% of _? 25is33i%of_?
-
5. 45is10%of_? 40is125%of_?
6. Find 150% of 900. 66|%of210. 4^% of 200.
.
7. 48 is what per cent of 200? of 96?
8. 300 is what per cent of 150? of 200?
9. Three inches is what per cent of 1 ft.? of 1 yd.?
10. A baseball team won 12 out of 20 games played.
What per cent of the games played did this team lose?
11. If, in a problem in percentage, the base is 250 and
the percentage is 50, what is the rate?
12. If 60% of the population are qualified voters, how
many voters are there in a city having a population of
50,000?
13. If 50% of the qualified voters in problem 12 ac-
tually voted, how many voted?
14. A tennis racket priced at $4 was reduced to $3.
The reduction was what per cent of the original price?
15. In a problem in percentage, the base is 75 and the
rate is 66f%. What is the percentage?
49

$37.50
.88
3 0000
30 000
$33.0000
Per Cent Decrease or Increase
1. The price of a coat marked $37.50 was decreased by
12%. What was the price then?
Since the original price of the suit is
100% of itself, we know that reducing
the price by 12% leaves 88% of the
original price.
Hence, we find the re-
duced price by taking 88% of the orig-
inal price. The answer is $33.00.
We may prove this answer by finding 12% of $37.50
and subtracting the result from $37.50.
2. Last year the attendance in our school increased
nearly 13% above that of the preceding year. If our at-
tendance this year is 1578 and if our
rate per cent increase for the next year
will be the same as it was this year,
what will be our attendance next year?
Find answer to the nearest unit.
We see at once that the answer may be
found by taking 113% of 1578.
Sight Work
1. The price of an article has been decreased by 15%.
What per cent of the original price is the new price?
2. A building lot costing $1200 has increased in value
by 10%. How much is it worth now?
3. Ray, who now weighs 112 pounds, wants to play
football. His teacher says he should increase 8% in
weight by next year.
If he does, how much will he
weigh then?
4. Ray's father, who now weighs 190 poimds, is too
heavy and wants to decrease his weight by 10%. If
he does, how much will he weigh then?
50

Problems
1. The weight of a cer-
tain grade of steers de-
creased 37% by butcher-
ing. If the weight of a
live steer is 1180 pounds,
what is the weight of the
meat after butchering?
2. A producer of beef
cattle has found that
young animals put on final
feeding will gain about 35% in six months. A bunch
of steers weighing 41,800 pounds were put on final feed-
ing on May 1. How much will they weigh November 1?
3. A house costing $6800 when new depreciated 33%
in 10 years.
How much was this house worth when 10
years old?
4. In 1932 Mr. George's salary of $3600 was reduced
20%. The salary remained at the new level for six years,
when it was increased 20%. What was his salary then?
How do you explain the difference between his earher
and later salaries? What is the base in each case?
5. A house costing $14,500 when new decreases in
value 2^% of its original cost each year. What per cent
will it decrease in 6 years? in 10 years? in 20 years?
in 5 years? in 15 years? Find the value of this house at
the end of each of these periods.
6. A new automobile costing $960 decreases 30% the
first year. How much is it worth then?
7. During the second year, the automobile in problem
6 depreciates 20% of its value. During the third year,
it depreciates 10% of its value. What wiU be the value
of this automobile when it is 3 years old?
51
-< ^*

Sight Work in Percentage
1. Tom weighs 80 pounds. If in two years he gains 15
per cent, how much will he weigh then?
2. A sample of sugar beets contains 16% sugar. How
many pounds of sugar are there in one ton of these beets?
3. A certain grade of milk is found to contain 4.7 per
cent of butterfat. How many pounds of butterfat are
there in 500 poimds of this milk?
4. If 20% of a certain grade of ore is metal and 50%
of the metal is copper, how many pounds of copper are
there in 50 tons (100,000 pounds) of this ore?
5. If, in 1940, about 25
oooc
per cent of our population i4yr.
MMMI
were 14 years old or under,
^^ *"^^^
u
u
UT
what per cent were over
ooc
14 years old? Taking the is -24yr. SMS .
1940 population as ap-
ZA\//WZ/
proximately 132,000,000,
^^^^
MUyUUMMI
find the number of people & over
wVwVVwVi
14 years old or under in
our population.
^^
EACH FIGURE EQUALS
6. The price of fuel oU
lo.ooo.ooo people
that had been selling for 6 cents a gallon was increased to
7 cents. By what per cent was the price increased?
7. If you know the base and the percentage, how do
you find the rate? If you know the percentage and the
rate, how do you find the base?
8. A pair of field glasses was on sale for $20. The
sale price was 20 per cent below the regular price. What
was the regular price?
9. If 22% of the ore from a certain mine is copper,
how many tons are required to yield 22 tons of copper?
52
I

Add, Subtract, Multiply, or Divide?
For each step write A, S, M, or D. Work the problems.
1. Our football team has a schedule of 8 games. Five
have already been played. What per cent of the games
are still to be played?
2. Last year Mr. Hammond filled a com crib holding
3460 bushels of corn, but by the time he sold the corn it
had shrunk to 2950 bushels.
What per cent had it
shrunk? Find the answer to the nearest per cent.
3. In one month John's uncle delivered 9765 pounds
of milk at the creamery. This milk averaged 4.4 per
cent butterfat. How much butterfat did he deHver?
Find answer to the nearest pound.
4. The principal of a school announced that last year
46 per cent of the pupils were boys and that 36 per cent
of the boys took an active part in athletics.
At these
rates, how many boys can be expected to take part in
athletics this year, when there are 1250 pupils?
5. A family with an income of $3600 spent $600 in
operating a car.
What fractional part of the income was
spent on the car? What per cent of the income is this?
What per cent is left for other purposes?
6. If the flour made from a certain grade of wheat
weighs 76 per cent of the weight of the wheat, how many
pounds of wheat are required to make enough flour to
fill a 98-pound sack? Find answer to the nearest poimd.
7. If the weight of the flour in bread is 75 per cent of
the weight of the bread, how many pounds of flour are
required to make 1000 one-pound loaves of bread?
8. If you know a man's salary and the per cent of it
that he saves, how do you find the amount of money that
he spends?
53

Special Methods in Solving Problems
There are many little methods that are very con-
venient in solving problems.
The price of many articles is given at so much per
hundred or so much per thousand. Thus, building bricks
are priced at so much per thousand, as are also shingles
for roofing. Lumber is sold at so much per thousand
board feet.
Such prices are given as so much per M,
meaning per thousand.
Cattle are sold at so much per hundred pounds, and
the areas of roofs are given in units of a hundred square
feet.
If you look at the reports from the livestock market
in any daily paper, you will
And price quotations such
as are shown at the right.
The first line means that
prime steers were sold at
$12.15 per hundred pounds.
Steers (prime) $12.15
Cows
$ 9.15
Hogs (prime) $10.95
Lambs
$11.15
$12.15
12.80
$155.52
1. At $12.15 per hundredweight (cwt.), what was the
value of a steer weighing 1280 pounds?
Since the price is per 100 pounds,
point off two decimals in the weight
(that is, divide by 100) and then multi-
ply $12.15 by 12.80.
The answer is
$155.52. Check this product. In such problems we
find the answer to the nearest cent.
2. At $27.50 per M, what is the cost of the 24,850
bricks needed for a house? Point off
three places in the number of bricks and
multiply $27.50 by the result.
Check
the product shown at the right.
54
$27.50
24.850
$683.38

Problem Practice
1. At $21.60 per M, what is the cost of 7450 bricks?
2. At $36.00 per M (one thousand board feet), what
is the cost of 1600 feet of lumber? ("Feet of lumber"
always means "board feet.")
3. At $1.15 per hundred pounds, what is the cost of
sending by freight merchandise weighing 6495 pounds.
Find answer to the nearest cent.
4. At $10.90 per hundredweight, what is the value of
a steer weighing 1285 pounds?
5. A carpenter bought 3200 feet of lumber tor $134.50.
What was the price per thousand feet?
6. If you know the nimiber of shingles used on a
house and the price per M, how do you find the cost?
7. At $4.70 per M, what is the cost of 5850 shingles?
8. One month we used 4190 cubic feet of gas in our
house. At $1.45 per thousand cubic feet, what was the
cost of this gas?
9. The following month we used 5203 cubic feet of gas.
At $1.45 per thousand cubic feet, what was the cost of
this gas?
10. A farmer sold beef cattle weighing 31,940 pounds
at $9.30 per hundredweight. After paying $189.50 in
expenses, how much did he have left from this sale?
11, A barn roof to be covered with shingles is found to
contain 2876 square feet. At $14.50 per 100 square feet,
what is the cost of this roof?
For practical purposes, the area of this roof is taken
to be 29 squares.
One "square" is 100 square feet.
29X$14.50=_?
55

Buying by the Ton
The prices of some articles, such as coal, hay, and
cattle feed, are given by the ton.
1. At $8.25 per ton, what is the cost of a load of coal
weighing 11,960 pounds?
The first step is to find the number
of tons in this load. This is done by
pointing off three places and then di-
viding by 2. This is the same as dividing
2)11.960
5.98
8.25
49.34
by 2000 (the ninnber of pounds in a ton). The next
step is to multiply by 8.25. The answer is $49.34.
2. If you know the number of pounds in a load of
coal, how do you find the number of tons?
3. What does 4900 lb. of coal cost at $8.40 per ton?
4. A truck loaded with coal weighed 11,850 pounds,
and the empty truck weighed 4250 pounds. At $7.40
per ton, what was the cost of the coal?
5. A car held 142,800 lb. of coal. At $1.17 per ton,
how much did the railway charge for carrying this coal?
6. A farmer sold 4 loads of hay weighing 2750 pounds,
2640 pounds, 2130 pounds, and 2480 pounds. At $18
per ton, what did he receive for the hay?
7. A farmer bought 21,300 pounds of cattle feed. At
$18.60 per ton, what was the cost of this feed?
8. At $,65 per ton, how much did it cost the farmer
in problem 7 to haul the feed to his farm?
56

(1)
Cancellation
The simplest sort of canceling occurs in reducing
fractions to lowest terms. Thus, as
shown at the right, both terms of -^
are divided by 3, reducing the frac-
tion to f
.
In multiplying fractions we have,
in effect, the same operation. Thus,
in fXy, 2 is canceledfrom 4 and 6,
giving I Xf=T^.
In If Xl5 we cancel 5 from 35
and 15.
1. Study the process shown
at the right. Note how 6, 4, 7,
and 2 are canceled in succession.
2
^2
155
5
3
i^)i^
14
24
(3)S5
7
372
Find answers, canceling when
possible.
8
^33
8
3X3
2. fXf
|X^
|X|Xt%
lixfxf
3. 1|X2t%
3fX6f
2^X4fX3i
5fX3iX6f
4.
f-l
l-l
f-^l
A--i
A-i
5. 4i-|
6i-l| 3i-H
J--H
61^1
6.
7,
8.
9.
21X26
X72
14X10
12X14X16
27
5X7X9X2
3X3X14
24X42X3
3X3X4
X80
X4i
15X21
150X6X3
100X4
120X240X80
25X72X360
256X96X65
20X144X32
57

Indicating Solutions
As you well understand, the first step in solving a
problem is to plan the solution.
The plan of solution
can often be represented by a simple expression, which
we call an indicated solution.
When handled skillfully,
the indicated solution forms an effective tool in solving
problems.
180X240
160
X$95
1. A farm is 180 rods wide by 240
rods long. At $95 per acre, what is
the value of the farm?
The solution is indicated above. The steps are:
(1) 240X180= area in square rods.
(2) Area in square rods -r - 160 = number of acres.
(3) $95 X the niunber of acres = the value in dollars.
Find the answer.
In the work of computing, cancel
whenever possible.
2. A rectangular water tank is 3^ ft. wide, 2f ft. deep,
and 12 ft. long. At 62^ lb. per cubic foot, what is the
weight of the water when the tank is completely filled?
The solution is indicated at
the right. Find the answer.
3. In problem 2, what is the
weight of the water in tons?
3ix2|xl2x62i
^X-;j-Xl2X^-
4. How many cubic yards
are there in the four-inch concrete floor of a garage 28 feet
long and 24 feet wide?
How do you find the niunber of
cubic feet? the number of cubic
yards? What is the answer?
58
28x24xixi.

Add, Subtract, Multiply, or Divide?
Indicate the solution of each problem.
Work the
problems.
1. A schoolroom is 27 feet wiae, 32 feet long, and 10^
feet high. How many cubic yards of air space are there?
2. In a room 28 feet wide, 33 feet long, and 10 feet
high there are 36 persons. How many cubic feet of air
space per person are there in this room?
3. From a field 60 rods by 120 rods, John's uncle
harvested 2560 bushels of corn. How many bushels per
acre did he get? Find answer to the nearest whole
bushel.
60X120 7
4. A farmer seeded a field 60 rods by
leo
4
120 rods, using If (f ) bushels of seed
wheat per acre. How many bushels did he use?
5. At $2.70 per square yard, what is the cost of a
cement walk 5 feet wide and 140 feet long?
6. Mr. Parsons sold a lot 80 feet by 160 feet for
$32,000. How much per squar foot did he get?
7. On a trip, we drove 496 mi. and used 32 gal. of
gasoline. At this rate, how many gallons would we use
in a season's driving of 16,000 mi.? Find answer to the
nearest gallon
Suggestion:
What
16000 -^
= 16000 X^
does ^^ represent? Explain the solution shown above.
8.Whatisthevolumeofablock10in. by8in. by
7 in.? What fraction of a cubic foot is this?
Explain the solution.
9. How many cubic yards
10X8X7
5X7
12X12X12 3X3X12
ofspacearethereinaroom30ft. by21ft.by10ft.?
59

Second Self-Test
Test in Fundamentals
Find the answers.
1. 8+9+7+4+3+5
6+2+0+4+1+8
2. 61+4 + 81+71+3
71+71+8+6^+4
3. 7|+7i+ 61 + 71+3 i
8+71+7^+71+31
4. i+i
l+i
i+i
l+l
i+i
5. f+i
i+i
i+l
f+i
f+l
6. t+i
l+A-
i+i
l+l
l+A
7.
^-i
l-i
i-i
l-l
i-i
8. f-i
|-T%
i-i
f-l
A-l
Multiply the following:
9.
8
.8
.08
.08
.08
1.2
12
.12
.4
.4
4
.4
.04
1.2
.12
1.2
10. 15
1.5
.15
.15
2.5
.25
2.5
.25
.04
.04
4
.04
6
6
.06
.6
11. 240
123
1.29
912
44.4
767
7.13
. 761
5.17
1.11
578
1.84
12.
iX2
iXi
|X| HXH 1|X3
13. 31XH 5|X2i 6|XU 21X1
12^X8
Divide the following:
14.
i-i
i-i
1-2
2-1
41^11
15. 21-11
n-21
4)1.6
. 4)1.6
61^2
.4)16
6|H-3
81^11
16.
. 4).016
4).016
17. 12)96
.12)96
1.2)9.6
60
.1 25:96"
. 12)860

Mixed Test
Find the answers.
1. 8194+316+12500+3190+77+6809+549+38
2. 7.42+573+.97+890+12.9+73.89+1. 254+6.93
3. 4 .29+.197+59.3+8.6+.86+.087+6.73+894
4. 31.92-24.6
125-34.65
700-49.94
5. 8504-8496
49.816-39 .948
5.9-4.876
Mvdtiply and check. Then round off answers to not
more than two decimal places.
6. 591
644
987
975
594
301
682
87
164
826
87
294
7. 2.19
54.7
.46
6.57
67.4
9.18
658
6.84
.89
2.86
3.18
38.2
8. 1.25
8.93
9.16
4.27
26.49
476
8.75
. 124
8.57
1.82
1.34
5.01
Divide and prove.
Then round off answers to not
more than two decimal places.
9. 31)81.76
58)438.2
39.4)18.4
22.4)56.32
>.
84)59.64
573)378
7.76)519.4
12.9)85.11
Add the following:
L.
8i
12i
9|
7i
lOi
24f
15i
91
27|
87tV
9|
32i
12|
94r
Multiply the following:
!.
3i
1\
4i
5i
8|
12i
8^
6f
151
4f
3|
61

Test in Problems without Numbers
After answering each question, iQustrate by making
and solving a problem of yom* own with numbers.^
1. If you know the number of articles bought and the
cost, how do you find the price of each article?
2. If you know the price per unit and the number of
articles bought, how do you find the total cost?
3. If you know your balance in the bank on the first of
the month and your deposits and withdrawals during the
month, how do you find your balance at the end of the
month?
4. If you know a man's wages and the per cent of
increase in his wages, how do you find the wages after the
increase?
5. If you know the weight of a can filled with milk and
the weight of the empty can, how do you find the niunber
of gallons the can will hold?
6. If you know the dimensions of an excavation in
feet, how do you find the number of cubic yards removed
in digging it?
7. If you know the dimensions of a farm in rods, how
do you find its area in acres?
8. If you know the price per ton and the number of
pounds of coal in a load, how do you find the cost?
9. If you know the number of games a team has
played and the number of games it has won, how do you
find the per cent of games it has won?
10. If you know the rate and the percentage, how do
you find the base?
11. If you know the weight in pounds of a head of
cattle and the price per 100 pounds, how do you find the
value of the animal?
62

Test in Problem Solving
1. The rent of a house was increased from $55 to $65
per month. By what per cent was the rent increased?
2. Five years later, the rent of the house in problem 1
was decreased from $65 to $55 per month. By what per
cent was the rent decreased?
3. If Mr. Stewart pays 25 cents per gallon for cherries,
at what price per quart must he sell them to make 15
cents per gallon? (Disregard any incidental expenses.)
4. On three successive days, my father drove his car
275.7 miles, 78 miles, and 114.9 miles.
What was the
average number of miles he drove per day?
5. John's uncle bought a tractor for $1260. How
many bushels of corn at 67^ a bushel must he sell to pay
for the tractor? Find answer to the nearest bushel.
6. Two pieces of cloth, one 1^ yards and the other 2^
yards, were cut from a piece 10 yards long. How many
yards were left?
7. A farmer built a fence around a rectangular lot 10
rods by 30 rods.
He set the posts 1 rod apart. If the
posts cost 65 cents apiece and the fencing $1.20 per rod,
what was the total cost of the fence?
8. John makes the following use of his time each
school day: sleep, 9 hr.; school, 5 hr.; outside study, 2 hr.;
meals, 2 hr.; and the rest for recreation. What per cent
of the 24 hr. does he use for each of these purposes?
9. If your car runs 84 miles on 6 gallons of gasoline,
how far will it run on a tankful of 20 gallons?
10.Awheatbinis18ft.by12ft.by7ft.
How many
bushels will it hold if one cubic foot holds | bu.?
\63

Units, family Budgets and Records
Planning Budgets
Before the beginning of each school year, careful con-
sideration is given to the amount of money that is to be
spent on yoiu* school during the year.
This includes
the amount spent for different purposes.
There will
be so much for teach-
ers' salaries, so much
for supphes, and so on.
Such a plan of pro-
posed expenditures is
called a budget.
1. At the right is
shown a budget for a
small school. The ac-
tual expenditures for
any item may run a
httle above or below
the amount in the
budget, but care will be taken to follow the budget as far
as possible.
What per cent of the total was budgeted
for each item, correct to the nearest per cent?
2. A budget for
a
family of four with an in-
come of $1800 a year is
shown at the right. Find
out to the nearest per
cent what per cent was
budgeted for each item.
Different families may
make different budgets.
64
Budget for Lincoln School
for the School Year
1942-1943
Teachers' salaries $31,600
Supplies
3,250
Heating
4,350
Light
480
Janitors
3,775
Total
$43,455
Budget for Family of Four
Shelter
$400
Food
480
Clothing
350
Operating
200
Advancement
216
Savings
154
Total
$1800
I

Problems
1. In a recent year the
state of Texas produced
484,527,000 barrels of oil.
What was the average
daily production?
2. In that same year
the United States pro-
duced 1,264,200,000 bar-
rels.
Round off both
these numbers to millions, and find what per cent of
the total was produced by Texas.
3. A man who has a monthly salary of $175 budgeted
$480 a year for rent, $700 for food, $300 for clothing, $200
for operating expenses, $150 for savings, and the balance
for miscellaneous items. What per cent, to the nearest
tenth, did he budget for each item?
4. A family with an income of $2800 spent 25% for
food, 22% for shelter, 15%? for clothing, and 12% for
operating. How much money was left for other items?
5. John received $2.50 a week from his father for
school expenses. He found that carfare cost him 50^,
lunches $1.10, and school suppHes 50^ a week. What
per cent did he budget for each of these items and what
per cent was left for recreation?
6. Mr. Roberts pays $2.75 a month for 65 calls on his
home telephone and 4^ for each additional call. What
was his bill last month for 87 calls?
7. Mr. Jones pays 5.5^ per kilowatt-hour (KWH) for
the first 36 KWH of electricity he uses each month, 3^ for
the next 64 KWH, and 2^ for all other KWH. What
was his biU last month for 142 KWH?
65

Family Budgets
A budget made by a family with a $3000 income is
shown below. There is a larger amount for rent in this
budget than the one given on page 64, and a sum is also
set aside for an automobile.
The per cents allowed for
food, clothing, and operating
have been reduced.
Shelter
$540
Food
600
Clothing
360
Operating
300
Advancement
440
Automobile
420
Savings
340
Shelter is only rent in the
case of families Hving in a
rented apartment.
In the
case of families hving in their
own homes, it includes various items, such as interest,
taxes, and insurance.
Food and clothing are easy to understand.
Operating includes cost of any service, heat, light,
telephone, repairs, and supplies.
Advancement includes any expenses for health,
recreation, books, magazines, newspapers, vacations,
church, and charity.
Automobile includes all the costs of running a car.
Savings may also include life insin-ance and in-
vestments.
1. In the budget above, what per cent is set aside for
each pin-pose?
2. In this family budget, what items are probably the
most difficult to budget for a year in advance?
3. Why is the per cent budgeted for food usually less
for a family with $3000 income than for a family with
$1800 income?
66

Family Budgets
Below are budgets for four small-town families with
incomes of $2400 a year.
The principal difference
between these families is in the niunber of people to be
supported from the same income.
Items of
Expenditure
Number in Family
2
3
4
5
Shelter
$300
480
240
240
420
420
300
$360
540
300
240
400
360
200
$420
600
360
240
300
300
180
$450
630
400
240
300
250
130
Food
Clothing
Operating
Advancement
Automobile
Savings
1. In the budget given above for a family of two, find
what per cent each item is of the total.
2. Find these same per cents in the budget for a
family with three members; for a family with foiu* mem-
bers; for a family with five members.
3. How much per month is set aside for rent in each
of the above budgets?
4. What reasons can you give for the different
amoimts set aside for shelter by these famiUes?
5. Discuss the amoimts set aside for advancement by
these families. How do you account for this difference?
6. Why does the larger family spend less on the car
than the smaller family?
7. Which items are more likely to increase than others
with size of family?
67

Family Records
The most difficult part of the records of a family's
financial affairs is the record of expenditm-es . But even
this need not be very difficult.
The first step is to
secure, or rule, suitable blanks. Part of such a blank is
shown on the opposite page, where a record is given for
the first ten days of the month of January.
The complete blank for January will contain one line
for each of the thirty-one days of the month, instead of
the first ten days shown here.
One of these Hnes is to be filled in each day. On
January 1, (New Year's Day) no expenditures were
made, and no item was entered. On January 2, there
were five items, on January 3 there were ten items. (On
this day the mother went shopping and also paid some
monthly bills; gas and oil for the car were bought.) On
January 4 (Sunday) there was only one item (contribu-
tion to church).
Sales sKps for purchases may be used in making
entries.
All items should be entered the day that a
purchase is made, or when monthly bills are paid.
You can see that if some orderly plan is followed, five
minutes will be quite sufficient to enter any day's ex-
penditures. The total for each day should be entered at
the time the entries in that column are made.
Practice in Fundamentals
1. Multiply
each number in
line A by each
in Hne B.
A 7.64 5.43 92.8 1.04 3.56
B 4.21 63.7
.985
. 012 5.09
2. Divide each number in line A by each in B.
68

Ten Days in January
^t
^
ADVANCEMENT
AUTOMOBILE
430
4iJ3
m
^/\7
430
t3S
4m
(T)
2 (F)
50.0LI.3S-Z
l.ll o
D£
^/./U-^l
z.n
5.nm3.£i
1.50
2M'. 3o
*
is)
J6
5 (M)
i<)
IM
Z% S.QQ
6U)
ISM
7 (W)
3^lM
he
.u
4SL
/.so
e (T)
^t
.^0
9 (F)
M\ri
10 (S)
l.' /o is: 2k'
so
IJA
1. At the bottom in the complete record for the
month, there will be a Hne for totals.
The first item in
this line will show the total for rent, the second for meat,
and so on.
What is the total for the first ten-day ex-
penditures for food of all kinds?
2. What is the total for all clothing expenditm-es?
3. What is the total for all operating expenditures?
4. What did the various advancement items total?
5. What, did the automobile cost?
6. What was the total of expenses, January 1-10?
7. By horizontal addition you can total all the ex-
penditures for each day. By adding the totals of all the
days, you find the total for the month. What are the
totals spent on each day given? How does the total for
the ten days compare with the total in problem 6?
69

Calories and Food Elements
Our bodies are like engines in that they need energy to
make them go.
In the mechanical engine, the energy
usually comes from some particular kind of fuel. The
fuel that furnishes energy for our bodies is contained in
the food that we eat.
The amount of fuel value, or
energy, derived from foods is measured in calories.
In your health studies, you have learned that our
meals should provide a sufficient number of calories to
keep our bodies strong; and also that our foods should be
selected to furnish about the following proportion of es-
sential food elements: 13% protein, 24% fat, and 63%
carbohydrates (including minerals and vitamins).
The table of food values on page 71 shows how foods
differ in food elements and also in calorie values.
1. Make a list of several foods given in the table that
have the largest calorie values.
2. Make a list of several foods that have the smallest
calorie values. Why are these foods essential?
3. Using the table, find how many calories in a poimd
of milk are protein, fat, and carbohydrates, to the nearest
whole calorie.
4. Make a table showing how many calories of pro-
tein, fat, and carbohydrates there are in each of the
following: bacon, bread, cabbage, lamb chops, peanuts.
(Find results correct to the nearest whole calorie.)
5. At 7^^ per pound, what is the cost of sugar per
1000 calories? ($.075^1814x1000 = ?)
6. At 32^ per pound, what is the cost of broiled
chicken per 1000 calories?
7. Which five foods listed on page 71 supply the most
protein? the most fat? the most carbohydrates?
70

Table of Food Values
This table gives the number of calories per pound for
certain foods, and also the per cent of these calories sup-
pHed by protein, fat, and carbohydrates.
Similar
figures given by different authorities will vary.
Carbo-
Foods
Protein
Fat
hydrate
Calories
Per Cent Per Cent
Per Cent per Pound
Apples
3
5
92
214
Bacon
13
87
3153
Bananas
5
6
89
290
Beans, lima
21
4
75
1586
Beans, string
22
7
71
189
Beef, lean
90
10
750
Beef, roast
62
38
1559
Bread, white
14
6
80
1174
Butter
1
99
3488
Cabbage
20
9
71
143
Carrots
10
5
85
159
Cheese, Ameri-
can
26
74
__
1996
Chicken, broiled
51
49
289
Eggs
36
64
_
595
Fish, salmon
45
55
__
680
Lamb chops
40
60
___
1615
Lard
100
4082
Lettuce
25
14
61
87
Milk
19
52
29
338
Oranges
7
2
91
169
Oysters
49
24
27
229
Peanuts, shelled
19
63
18
2500
Potatoes, baked
11
1
88
304
Potatoes, sweet
6
5
89
447
Raisins
3
9
88
1563
Rice
9
1
90
1591
Spinach
12
8
80
108
Sugar, white
—
100
1814
Tomatoes
21
8
71
103
Walnuts, shelled
11
82
7
3200
Watermelon
5
6
89
57
71

Calories Needed by Different Persons
The amount of
food (number of
calories)
needed
each day by a
person
depends
upon his age, his
weight, and the
amount of exer-
cise that he takes.
A large man do-
ing heavy work
may need more
than 5000 calories,
exercise may need
Calories Needed up to Age 17
Age
Boys
Girls
Under 1
1-3
3-5
5-9
9-13
13-17
300- 900
900-1200
1200-1500
1500-2000
2200-3000
2500-4000
300- 900
900-1200
1200-1500
1500-2000
1800-2400
2200-2600
while a small person taking very little
only 2000 calories.
Examples of slight exer-
cise:
reading,
writing,
sewing.
Light exercise: stand-
ing, walking slowly.
Active exercise: walk-
ing rapidly, housework,
playing tennis.
Severe exercise: play-
ing football, pitching hay.
1. A man weigh-
ing 160 lb. sleeps
8 hr.,
has slight
exercise 10 hr. , and
active exercise 6
hr.
How many
calories does he need? Finish the solution of the problem
as shown in the box above.
Calories Needed per Hour
per Pound of Body Weight
Activity
Calories
Sleeping
Slight exercise
Light exercise
Active exercise
Severe exercise
.4
.6
1.0
2.0
^
3.0
Sleep
Ax 8xl60=_
Slight exercise .6xl0xl60=_
Active exercise 2 X 6x160=
Total calories
72

Problems in Food Values
1. As a co-operative class exercise, use the headings
below and change the table of food values on page 71 to
show the approximate number of calories under protein,
fat, and carbohydrates.
Find results correct to the
nearest whole calorie.
Foods
Protein
Calories
Fat
Calories
Carbo-
hydrate
Calories
Total
Calories
Apples
6
11
197
214
2. Fred is 14 years old and weighs 135 pounds. He
needs 25 food calories per pound of his weight per day.
How many calories does he need?
3. In problem 2, how many of these calories should be
protein, fat, and carbohydrate respectively?
4. Mabel is 13 years old and weighs 96 pounds. She
sleeps 8 hours, has slight exercise 6 hours, light exercise 7
hours, and active exercise 3 hours. How many calories
per day does she need? (See page 72.)
^ 5 . A woman weighing 120 pounds sleeps 8 hours, has
slight exercise 6 hours, light exercise 8 hours, and active
exercise 2 hours Find how many calories she needs.
6. A 180-lb. working man sleeps 8 hours, has slight
exercise 8 hours, and severe exercise 8 hours. How many
calories per day does he need?
7. Find how many calories per day are required by a
180-lb. man who sleeps 8 hr., has slight exercise 6 hr.,
Ught exercise 5 hr. , and active exercise 5 hr.
8. How many of the calories required in problem 7
shoiild be protein^ fat, and carbohydrate?
73

Comparing Costs of Calories
A housekeeper may save considerable money by buy-
ing foods that cost the least for the required calories.
1. At 12^ a pound for white
bread, what is the cost per 1000
calories?
12^
1174
X 1000 = 10.2^
Sample Prices
per Pound
Bacon
34^
Bananas
9ff
Beans, string 6^
Beans, lima
12i
Beef, roast
38i^
Bread
12i
Butter
39^
Cabbage
2i
Cheese,
American
28^
Fish, salmon 25^
Potatoes
3^
Rice
10^
Raisins
10^
2. At 38^ per pound for
roast beef, what is the cost per
1000 calories?
^X 1000 = 24.4^
3. Using the prices given at
the right, find the cost per 1000
calories when buying bananas,
lima beans, string beans, butter,
cabbage, cheese, salmon, pota-
toes, rice, and raisins.
Use the
table of values on page 71.
4. Secure the local prices for 12 or more kinds of foods
hsted in the table on page 71. Make a table showing the
cost of 1000 calories for each of these different foods.
5. At 6^ per pound for apples, what is the cost of 1000
calories?
6. When apples sell at 7 lb. for 25 ji, what is the cost
of 1000 calories?
7. When English walnuts (shelled) sell at Qbi per
pound, what is the cost of 1000 calories?
8. When spinach sells at 10 f^ per poimd, what is the
cost of 1000 calories?
74

Buying Food in Smaller or in Larger Containers
Many food products are packed in containers of dif-
ferent sizes, on which the net weight of the contents are
usually stated. The price per ounce or pint is often con-
siderably lower when bought in the larger container.
1. In one store a 1-pound package of soda crackers
costs 16(^ while a 7-ounce package costs 10^.
Find the
price per ounce for each package. What per cent is saved
by buying the larger package?
The divisions at the right show
that the prices are 1^ and 1.43^ per
ounce.
.01
16).16
.01428 = .0143
7).1000
Buying by the pound saves .43^
per ounce. Hence, .43 -^ 1.43 = .3, or
30%. We can save 30% of the higher price by buying the
1 -pound package.
2-9. For each example below, find what per cent is
saved by buying the larger container:
Larger
Smaller
Foods
Container
Container
2. Flour, wheat
24i lb. for 96^ 5 lb. for 25^
3. Wheat, cereal
26 oz. for21^ 14 oz. for 13^
4. Oatmeal
55 oz. for 23^ 20 oz. for 10^
5. Canned milk
14^oz.for 8^ 6 oz.for 4i
6. Canned corn
20oz.for13^11 oz.for 8^
7. Canned salmon 16 oz. for45^ 7| oz. for 26^
8. Walnut meats
8 oz. for 42^
3 oz. for 20^
9. Peanut butter
1 lb. for 23^
5 oz. for 10^
10. Make a Hst of local prices for foods in different
sized containers. Find what per cent is saved by buying
a larger package.
75

Unit 6. Home Problems
Installment Buying
In most stores it is possible to buy an article by pay-
ing part of the price at the time the article is bought and
the remainder in equal monthly or weekly payments.
A washing machine is marked to be sold for $100. It
can, however, be bought by paying $10 in cash and then
paying $10 a month for 10 months. The extra $10 is
called a carrying charge or dollar cost of the credit.
Buying on this plan is called buying on the install-
ment plan. Such remarks, as "sold on time," "pay as
you go," *'pay as you earn," and many other similar
expressions — all mean that the goods may be bought on
the installment plan.
Furniture, household equipment
of many kinds, automobiles, farm machinery, and even
articles of clothing are sold by this plan.
In most cases, it is said that a certain amount is added
as a carrying charge, but in some cases it is claimed that
absolutely nothing extra is charged for credit. Such
statements may be intended to mislead the buyer.
If
you go into a store running this kind of advertisement,
you may find that, if you offer to pay the whole in cash,
you will get a substantial reduction.
1. What was the real dollar cost of the credit for the
washing machine described above, if a cash discoimt of
5% was also given?
2. Look in the papers for advertisements announcing
installment-plan selling of different articles.
What is
the carrying charge announced in the advertisements?
76

Dollar Cost of Credit
Sometimes the actual
dollar cost of the credit is
concealed. In one case it
was found that a $100
article could be bought for
cash at a reduction of 2%,
that is, for $98, while the
installment cost was $110.
Hence, the dollar cost of
the credit was really $12.
1. A motion-picture projector marked $87.50 was
sold for $25 down and seven monthly installments of $10
each. What was the total cost of the projector?
Find the dollar cost of the credit in the following:
2. A used typewriter marked $65 can be bought for
$10 down and six monthly $10-payments. For cash the
marked price wiU be reduced by 10%.
3. A used automobile is marked for sale at $450.
This is sold to a responsible buyer for $100 cash and four
monthly $100-payments.
4. If the seller is anxious to sell the car in problem 3
for cash, he may be willing to reduce the cash price by
5%. What would be the doUar cost of the credit under
these conditions?
5. A car marked for sale at $450 was sold to a man
with doubtful credit for $150 down and eight monthly
$50-payments.
Why did this man pay more for the
credit than the man in probleni 3?
6. A set of furniture marked $185 was sold for a $25
down payment, and nine monthly $20-payments. For
cash the $185 would be reduced by 10%.
77

Rate of Interest
As you have learned, interest is money paid for the
use of money. If $5 is paid for the use of $100 for one
year, then the rate of interest is 5%. But if $5 is paid
for the use of $100 for six months, then the rate of in-
terest is 10%. That is, 10% of $100 would be paid for
the use of it for one year.
If $1 is paid for the use of $100 for one month, then
the rate would be 12% for one year.
When we speak of the rate of interest in general, we
mean the amount per $100 that is paid for the use for
one year.
If the loan runs for one year or less, then for
the purpose of comparing interest rates we assume that
the interest is paid at the end of the time for which the
money is borrowed.
Instead of finding only the doUar cost of the credit
when buying on the instaUment plan, we shall now find
the actual rate of interest paid for installment credit.
1. Furniture priced at $100
was bought for $10 cash and
ten monthly payments of $10
each. Find the rate of interest.
The doUar cost of the credit
was $110 -$100, or $10. The
down payment of $10 left $100
on credit for the first month,
$90 on credit for the second
month, and so on, as shown at
the right.
The sum of these
credits equaled $550 for 1 mo.
The total credit was $550 for
1 month or $45.83 for 1 year.
$10 is 21.8% of $45.83 .
Hence, the interest was at the rate of 21.8% per year.
78
$100 for 1 mo.
90for1mo.
80for1mo.
70for1mo.
60for1mo.
50for1mo.
40for1mo.
30for1mo.
20for1mo.
10for1mo.
$550 for 1 mo.
$550 -J - 12= $45.83 j

$60 for 1 mo.
50for1mo.
40for1mo.
30for1mo.
20for1mo.
10for1mo.
$210 for 1 mo.
$210^12 =$17.50
1
Installment Interest
1. A radio marked $60 was sold for $6 down and six
monthly payments of $10 each. Find the rate of interest.
As shown at the right, the
amoiuit of the credit was $210
for 1 month, or the same as
$17.50 for. 1 year.
The dollar
cost of the credit was $66 — $60,
or
$6.
Then $6 -^ $17.50 =
.3428, or 34.3%, which is the
rate of interest per year.
Find the rate of interest in each of the following:
2. Used furniture marked $50 was sold for a $10
down payment and five monthly $10-payments.
3. A used piano was offered for sale for $160 cash or
for a $20 down payment and eight monthly $20-pay-
ments.
4. A phonograph with cash price of $120 was sold for
a $10 down pajnnent and twelve monthly $10-payments,
5. A fvirnace stoker was Hsted at $250 cash or for a
$35 down payment and twelve monthly $20-payments.
6. What articles are sold on the credit plan in your
commiuiity?
7. It appears from oiu- problems that the rate of
interest on installment credit is very high. But in spite
of this the dealer would rather sell for cash than on this
kind of credit.
How do you explain this? Are such
debts troublesome to collect? Are there any losses?
8. Are there any laws which prohibit excessive rates
of interest?
79

Buying Automobiles on Time-Payments
Cost of auto $960
Cash
360
600
Insurance
48
648.00
Interest
19.44
6)$667.44
Monthly
$111.24
payments
For a number of years new automobiles have been sold
on a uniform plan of pay-
ment.
1. An automobile cost-
ing $960 is sold for $360
cash, the rest to be paid ia
six monthly payments. In-
surance on the car costs
$48.00. This makes an un-
paid total of $648.00. In-
terest is added at 6% for 6
months, which is half the
interest for one year, making a
sum of $667.44 to be paid in six
equal
monthly payments.
Each payment is $111.24.
Study all steps in this prob-
lem to make certain that you
understand them.
The total credit, including all charges, is the same as
$2336.04 for 1 mo., or $194.67 for 1 yr.
$19.44 -$194.67 = .9986, or nearly 10% interest per year.
There are separate finance companies that handle such
loans. Such a company really becomes the owner of the
car and advances the money so that the seller gets full
payment when the sale is made.
If the payments are not made, the company can take
the car; but so long as these are made, the buyer keeps
possession.
When all payments have been made, the
buyer becomes the legal owner. If, in the meantime, the
car should be wrecked, the finance company can tin-n to
the insurance company for any remaining payments.
80
$667.44 for 1 mo.
556.20 for 1 mo.
444.96 for 1 mo.
333.72 for 1 mo.
222.48 for 1 mo.
111.24 for 1 mo.
$2336.04 for 1 mo.

L
Problems
-^^
1. A handball team won 10
games and lost 4. What per cent
of the games played did the team
win? Fmd the rate to the near-
est tenth of 1%.
2. A new car was bought for
$840, of which $340 was paid in
cash and the remainder in six
equal monthly payments.
The insurance costs $42.
Make a statement like that on page 80, showing the un-
paid amount, the interest (at 6%), and the amount of the
monthly payments.
3. A car cost $1480; $500 was paid in cash, and the
rest in 4 equal monthly payrqents. The insurance cost
$76. Make an itemized statement as in problem 2.
4. Automobile tires costing $40 were sold on time for
$48. The down payment was $8; the rest was in five
equal monthly payments. What was the rate of interest?
5. A refrigerator marked at $96 was sold on time for a
$9.60 down payment and ten monthly $9.60 -payments.
What rate of interest was paid?
6. A family of four with a
yearly income of $4800 made
the budget shown here. What
per cent was set aside for sav-
ings? Find the amount in dol-
lars set aside for each purpose.
7. A family of two with an income of $2500 made a
budget setting aside $540 for shelter, $450 for food, $350
for clothing, $260 for operating, $300 for car, $300 for
advancement, and the rest for savings. What per cent
was set aside for each purpose?
81
/
Shelter
20%
Food
18%
Clothing
16%
Operating
^14%
Advancement 12% |
Car
9%
Savings
U-%

Owning a House
To find how much it really costs to live in one's own
house, a number of items must be considered.
1. Mr. Stevens bought a six-room house for $7500, on
which he figured interest at 5%. He paid for the year:
insurance, $12; taxes, $132; and repairs and main-
tenance, $82. He figured depreciation at 2% of $6500.
He bought 9 tons of coal at $8.75 a ton and paid a boy
$45 for helping with the furnace and in the yard. (Liv-
ing in an apartment, he would not have had these ex-
penses.) How much rent per month could he pay for an
apartment to equal this cost?
Note that depreciation is figiu-ed on the value of the
house only, that is, on $6500. The value of the lot, which
was $1000, did not depreciate.
2. The Conrads own their house, and their yearly ex-
penses are: interest at 5% on $9000; insin-ance, $15;
taxes, $175; repairs, $115; depreciation, 2% of $7500.
They pay $148 for fuel and $25 for help with the furnace
and lawn. How much per month could they pay for an
apartment to equal this cost?
3. Copy the following summary and fill the blanks:
Conrad's
Stevens' House
House
Interest
Insurance
Taxes
Repairs
Depreciation
Extra help
Fuel
_
_
Total
12)_
12)_
Expenses per month
82

i
Home Problems
1. Mr. Holmes pays $75 a month rent. How much
more or less is his yearly rent than Mr. Stevens' total ex-
penses for his house for the year? (See page 82.)
2. If Mr. Burton pays $85 a month rent, how much
more or less is his yearly rent than Mr. Conrad's total ex-
penses for his house for the year?
3. Mr. Ferris rented a house for $40 a month. One
year he paid $96 for coal, $24.42 for gas, and $39.86 for
electricity. What did these average per month?
4. A house cost $12,000. With interest at 6%, what
was the monthly interest charge? How much would the
charge be if interest were at the rate of 4%?
Topics for Discussion
1. If the Conrads had rented a house, what would
they have done with the $9000 paid for the house? What
income would this bring? Why is this income part of the
cost of owning the house?
2. If you are Hving in a rented house, who pays for
repairs, and who pays the taxes? After the Conrads
bought their own house, who had to bear these expenses?
3. If you are living in a rented house, who pays for
the coal and the cost of taking care of the furnace? Is this
the same as if you lived in your own house?
4. If you own a house that depreciates $200 during the
year, is your house actually worth that much less at the
end of the year? Should the depreciation be regarded as
a part of the cost of Hving in your own house?
5. If you Hve in a rented apartment, who pays for
heating? Does the owner of the apartment pay for elec-
tric current, gas, or telephone?
83

Cost of Owning and Operating an Automobile
Mr. Jackson bought a new automobile for $825 and
drove it 16,000 miles the first year.
The interest was 5% of $825 for 1 year.
1000 gallons
of gasoline cost 19 cents per gallon.
This car averaged
16 miles per gallon and so 1000 gallons were needed to go
16,000 miles. The oil was changed every 2000 miles, and
enough was added between changes to make 10 quarts
for each 2000 miles. Depreciation was figured at 25% of
$825.
16,000 mi. 24,000 mi.
Interest on $825 for lyr. at 5% $_
$_
State license
14.00
14.00
City license
5.00
5.00
Insurance
56.40
56.40
Gasoline, 16 mi. per gal. @ 19^
Oil, 10 qt. every 2000 mi. @ 25^
_
_
Greasing, $1.25 every 1000 mi.
_
Service and repairs
28.60
76.80
Garage, $3 per mo. for 1 year
Depreciation, 25% of $825, or
30% of $825
_
_
Taxes
8.25
8.25
Total cost
1. Copy the statement above and fill in the figures for
16,000 miles of driving. Do as much figuring as you can
without pencil and paper.
Find the total cost for the
year and the cost per rnile of driving.
2. Find the cost for driving 24,000 miles.
The de-
preciation is now figured at 30% and repairs at $76.80.
Enter these items in your last column.
What was the cost per mile of driving this car the
24,000 miles? How do you account for the difference in
cost per mile?
84

Automobile Problems
!• A family with an income of $4200 spends $600 a
year in operating a car.
What fractional part of the in-
come is spent on the car? What per cent of the income
is spent on the car?
2. A used car was bought for $460. During the year
expenses were: 380 gallons gas at 19^ cents; 48 quarts of
oil at 26 cents; license, $8; insurance, $36.50; service and
repairs, $21.60; depreciation, 20% of $460; interest, 6%
of $460; tax, $2.50. If this car was driven 7260 miles,
what was the cost per nule?
3. If the fanuly owning the car in problem 2 had an
income of $2100, what per cent of this income went for
the use of the car?
4. What was the cost of owning an automobile for
which the following amounts were paid last year: 6%
interest on $1250; 25% depreciation; $12 Hcense; $43 in-
surance; $9.50 taxes; $75 service and repairs; 500 gal.
gasoline @ 20^; 60 qt. oil @ 25^?
Topics for Discussion
1. Why should interest on the cost of the car be re-
garded as part of the cost of operating it? If the money
had not been used to buy the car, what might have been
done with it? Could it have been invested so as to bring
a money income?
2. If a car is worth $200 less at the end of the year
than it was at the beginning, is the value of the fanuly
property reduced by that much? Should this be charged
as a part of the cost of having a car? Do you think
people usually reahze that the items of interest and de-
preciation are really part of the cost of having a car?
85

Cost of Hiring Help
A hired helper in the home is paid a certain wage; she
occupies a room in the house, and she has her meals
there.
These items must be in-
cluded.
Wages $35.00
Room
8.00
Meals
12.00
Total $55.00
1. The budgeted cost per month
for a helper in one family is shown
at the right. The cost of food is
estimated at $12.00 per month, based on the total
monthly cost for the family. The room occupied by
the helper could be rented for about $8 a month. What
per cent is the wages of the total cost?
2. A family with a yearly income of $4800 spends $55
per month for a helper.
What per cent of the income is
spent for this purpose?
Problems
1. Mrs. Morgan found that her food costs had risen
considerably during the past year. Some of the changes
were: butter from 30^ to 42^, eggs from 32^ to 40^, milk
from 12^ to 15^, pork chops from 30^ to 38^, bread from
9^ to 10ff.
What per cent did each item increase during
this period?
2. Mr. Smith paid $4.00 a month for 80 calls on his
office telephone, 4(^ for each additional caU up to 200
total, and 3^ for each call thereafter. What was his bill
f
last month for 325 calls?
3. Mrs. Jones budgeted $185 a month for nuining her
apartment. She estimated the following items: food,
$60; rent, $50; gas and electricity, $10; wages to maid,
$30; telephone, $5; laundry, $12; and suppHes, $18.
What per cent of the whole did she use for each item?
Find answers to the nearest tenth of 1%.
86

Family Financial Statements
The best way for a family to show the net loss or gain
for a year is to make out a financial statement.
Under assets is entered the present value of all the
property of the fanuly both at the beginning and the end
of the year. Under liabilities is entered all the debts of
the family. The difference between the siun of the as-
sets and the siun of the liabiHties is the net worth. The
difference between the net worth at the beginning and
the end of the year is the net gain or the net loss.
Beginning of year
End of year
Assets:
Assets:
Cash in bank
$ 218.64
Cash in bank
$ 341.65
House, value
5800.00
House, value
5560.00
Furniture, value 1750.00
Furniture, value 1960.00
Insurance,
Insurance,
cash value
1060.00
cash value
1120.00
Car
460.00
Car
380.00
Total
$9288.64
Total
$9361.65
Liabilities:
Liabilities:
House, mortgage $1800.00
House, mortgage $1200.00
Current bills
74.60
Current bills
106.50
Total
$1874.60
Total
$1306.50
Net Worth
$7414.04
Net Worth
$8055.15
Net Gain
$ 641.11
1. Make a statement for this financial condition:
Beginning of the year.
Assets: Cash, $487.45;
securities,
$7900; furniture, $3200; insurance
policies, cash value, $4190; car, $1160.
LiabiHties: Current bills, $587.60 .
End of the year.
Assets: Cash $291.85; securities,
$14,800; furniture, $2950; insurance policies,
cash value, $4520; car, $820.
LiabiHties: Current biUs, $182.12; owe bank, $6,000.
87

Third Self'Test
Test in Fundamentals
Find the missing numbers m the following. Give the
rates per cent to the nearest tenth of 1%. Give percent-
ages and bases to two decimal places when necessary.
I
Base
Per-
Rate centage
Base Rate
Per-
centage
1. 460
5i% -
2.
-
8%
84
3. 1280
364
4. 14
5
5.
—
6%
260
6. 31
—
1i
7. 32
121
_
8. 12.8
71
Find products of the following:
9. 151X3
3fX2i
380X32^
6iX2i
0. 161X161
51x51
Divide the following:
1. 41^31
31^21
3.64X41
161^3
64|X48
48 -^1f
2. 61-Mi
260^161
12^11
27H-41
Write the following in columns and add:
13. 7 .1 +43.8+5.96+.046+2.004+31 .0+1.256
14. 1 .742+359+37.6+4286+.1276+2.9+.061
15. 9.8+5.34+5.59+.64+9.916+.0276+8.91
Write the following in columns and subtract:
16. 80 -37.86
.21 92 -.093
1.904 - .9 87
17. 406.1 -398.25
6.04-5.782
1.406- .08 97
Add the following:
18.
I
36
5|
8|
5i
9i
n
2i
7|
7|
2A
12A
6t^
5A
4i
19- H
3|
5A
lyk
251
2?
8i
8f
93^
7i
li
9|
ZJ.
II
_5i
88

Test in Solving Problems
1. On the first of the month om* school bank account
showed a balance of $123.67. At various times during the
month, we deposited $8, $6.35, $5, $10.50, and $19.40.
During the month there were withdrawals of $8.94,
$21.62,-$9.12, and $39.60. What was our balance at the
end of the month?
2. If you know how many miles a car was driven on
each of the seven days of a week, how do you find the
average munber of miles per day?
3. A family uses 212 pounds of sugar in one year. If
sugar beets contain 15.6 per cent of sugar, how many
pounds of sugar beets were required to produce this
sugar? Find the answer to the nearest pound.
4. A corn crib is 32 feet long, 6 feet wide, and 7 feet
deep. If one bushel of corn on the cob occupies 2^ cubic
feet, how many bushels will the crib hold?
5. One cubic foot of soHd spruce wood weighs 28
pounds. What is the weight of one cord of spruce wood,
with 56% soUd wood, if one cord occupies 128 cu. ft.?
6. At the beginning of a trip, there were 17 gallons of
gas in our car.
During the trip we bought 12.6 gallons,
14.2 gallons, 9.4 gallons, and 15.5 gallons. When we re-
turned, there were 7.8 gallons in the tank. How many
gallons did we use on this trip?
7. A truck loaded with coal weighed 13,860 pounds,
and the empty truck weighed 4420 pounds. At $8.85 per
ton, what was the cost of the coal?
^ 8. A carpenter builds a beam by fastening a board 1^
inches thick to a plank 2f inches thick. He uses screws
3^ inches long. By how much do the screws fail to reach
through the beam?
89

Unit /. Using Percentage
$95 $95.00
.15
14.25
4 75 $80.75
95
$14.25
Retail Discounts
1. A rug marked to sell at
$95 is sold at 15% discount.
For how much is it sold?
As you know, you take 15%
of $95 and subtract it from $95.
But you also know that, if you
subtract 15% of a nimiber, you will have
85% of it left.
Hence, to find the selling
price you may take 85% of $95. These two
ways of solving this problem are shown at
the right.
In solving a problem in discount, select
the method that appears to you the easier.
In the above problem the original price ($95.00) is
called the marking price or the regular price. The
reduced price ($80.75) is the net price, and the 15% is
the rate of discount. A discount given by a retail
dealer to a customer is called a retail discount.
2. A bill for $80 was discounted 12^%.
net amount of this bill?
What was the
3. A washing machine priced at $150 was advertised
at 16|% discoimt. What was the net price?
4. A globe priced at $50 is put on sale for $35,
is the rate per cent discount?
What
5. A dealer bought tablets at 60 cents a dozen with
50% discount. What was the net price per tablet?
90

Trade Discounts
Wholesale dealers use discounts extensively. List
prices are given in catalogs and price lists.
From these
list prices discounts are given regularly to nearly all re-
tail dealers. Such discounts are called trade discounts.
Trade discounts are given for several reasons:
(1) Many articles are advertised nationally, and
prices are given at which the articles are to be sold in the
retail stores.
A certain watch is advertised at $45. This
is the price at which the retail dealer will sell this watch.
To enable the retail dealer to carry on his business, the
manufacturer or wholesale dealer will give him a discount
on this watch, possibly 40%.
(2) Market prices will often change during the "life"
of a catalog or hst. Different discounts are then given
from time to time.
"Prices are down," writes the whole-
sale dealer, "and we are giving longer (larger) discounts."
(3) Special discounts may be given for large orders,
for cash payments, and for other reasons.
(4) Several different discounts may be given.
One
may be given as a regular trade discount, another dis-
count may be given because of a large order, and still
another for cash payment. In this way we get a series of
discounts, or a discount series.
If there are two discounts, the first discount is a cer-
tain per cent of the gross amount of the bill. The next
discount is a certain per cent of what remains after the
first discount is taken off.
That is, discounts of 30%
and 10% are not the same as one discount of 40%.
1. What is the net amoimt of a biU for $100 with dis-
counts of 30% and 10%?
2. What is the net amoimt of a biQ for $100 with a
discount of 40%?
91

Problems in Trade Discount
1. Find the net amount of
a bill for $260 with discounts
of 30% and 10%.
30% of $260 can be found
by horizontal multipHcation,
and 10% of $182.00 can be
found by moving the decimal point
2. Find the net price if the
list price is $385.00 with dis-
counts of 35% and 2%.
Instead of finding 35% of
$385 and subtracting, we may
find 65% of $385.
To find 2% of $250.25 we think 1% equals $2.5025, and
then multiply by 2, which gives $5,005, or $5.01.
Such per cents as 10%, 20%j, 30%^, 40%), and 50% can
be found at sight by multiplying horizontally. Use
separate paper, if pencil and paper are needed for com-
puting. The work should be shown as above.
Find the net prices below to the nearest cent:
Gross amt. $260.00
30% off
78.00
182.00
10% off
18.20
Net amt.
oint
$163.80
Gross amt. $385.00
35% oflF
134.75
250.25
2% off
5.01
Net price
$245.24
]List Price Discounts
List Price Discounts
3. $120
30%, 10% ^
$680
35%, 3%
4. $750
25%, 10%
$800
30%, 4%
5. $480
30%, 5%
$546
25%, 10%
6. $275
20%, 2%
$960
20%, 10%
7. $500
10%, 10%
$640
25%, 5%
8. $150
15%, 5%
$875
10%, 2%
9. Discuss the reasons for retail discounts, for trade
discounts, and for discount series.
92

Order of Discounts
List price $100
50
It is an interesting fact that the order in which a series
of discounts is taken does not affect the answer.
The following problems explain this fact:
1. Find the net price if the list
price is $100 with discounts of 50%
and 10%.
2. Find the net price in prob-
lem 1 if the discounts are taken in
the order 10% and 50%.
You would expect that the total
discount would be greater if the
larger one were taken first.
But
this is not so.
Less 50%
Less 10%
Net price $45
50
5
List price $100
Less 10% 10^
90
45
Less 50%
Net price $45
Take discoimts 25%, 10%, and
5% from 1000. The solution is indicated below: To
discoimt 25% multiply by .75; to discount 10% multiply
by .90; and to discount this
result by 5% multiply by
.95.
1000 X.75 X.90 X.95
We know that the order of the factors makes no dif-
ference in the product. Hence these discounts can be
taken in any order.
Sight Work
1. Find the net amount of a biQ for $100 with dis-
coimts of 20%, 10%, and 5%.
2. Find the net amount of the bill for $100 if the dis-
counts are deducted in the order 5%, 10%, 20%.
3. Find the net amount of the same bill for $100 if the
discoimts are deducted in the order 10%, 5%, 20%.
93

Problems
1. A bill of goods carries discounts of 25% and 10%. I
Is this the same as a discount of 35%? Illustrate with
the case of a bill for $100, and find the discounts.
2. What is the net price of merchandise Usted at $2400
with discounts of 25%, 10%, and 2%?
3. What is the net amount of a biU for $1680 with dis-
counts of 20%, 10%, and 3%?
4. One dealer offers a radio at $85 with discoimts of
35% and 10%, and another dealer offers the same radio
for $80 with discounts of 30% and 5%. Which is the bet-
ter offer and what is the difference?
5. Find the cost of 2000 feet of rubber hose listed at
5^ cents per foot, with discounts of 30% and 5%.
6. Discounts of 30% and 15% are equal to what single
discount? Find the net price for a bill for $100 with this
discount. What per cent of $100 is this discount? Sub-
tract this per cent from 100.
7. Discounts of 20%, 10%, and 2% are equal to what
single discount? Find the answer to the nearest tenth of
1%.
8. A dealer bought 36 refrigerators for a total list cost
of $4050. The bill was subject to a trade discount of
25%, an additional quantity discount of 5%, and a cash
discount of 2%. What was the net amount of the bill?
What was the average cost of these refrigerators?
9. A dealer bought 260 pairs of shoes at a list price
of $5.50 per pair.
His trade discount was 28%, and his
discount for cash payment was 5%. Transportation cost
$18.60 . What was the total cost of these shoes when
they were delivered to the dealer's store?
94

Practice in Discounts
Find the net prices below to the nearest cent:
List Price Discounts
List Price
Discounts
1. $336 333%, 2%
$360 20%, 5%, 3%
2. $185 25%, 10%
$720 25%, 10%, 2%
3. $145
12i%, 5%
$900 33i%, 5%, 2%
4. $290 40%, 6%
$780 25%, 10%, 2%
5. $290 30%, 10%
$864 25%, 6%, 3%
6. $860 20%, 6%
$750 33i%, 10%, 4%
7. $500 15%, 2%
$800 15%, 5%, 2%
8. $600 37i%, 5%
$500 12i%, 5%, 3%
9. $900 16|%, 4%
$360 16|%, ^%, 2%
Problems
1. By paying $25 cash and the balance at $15 per
month, how long will it take to pay for a fur coat costing
$185?
2. A bill for $100 was reduced 25%. What was the
amoiuit of the bill after the reduction?
3. Mrs. Roberts bought 6 dining-room chairs for $50,
a dining-room table for $45, and a cabinet for $18 at a
sale.
She received a discount of 15%. What was her
net bin?
4. A merchant bought 9 traveling bags at $3.50
apiece, 6 suitcases at $4.50 apiece, and 5 trunks at $8.50
apiece. His trade discoimt was 30% and he received 2%
for cash. What was his net bUl?
5. A farmer bought 2 sets of harness at $34.50 each,
2 farm wagons at $36.50 each, 4 horse coUars at $2.50
each, and 4 horse blankets at $1.85 each. He received
discoimts of 20% and 5%. What was his net biU?
95

Interest on Borrowed Money
In our business life there is a considerable amount of
borrowing and lending. You already know many of the
purposes for which money is borrowed. The following
are some more typical examples:
A manufacturer of straw hats, which have a seasonal
sale, borrows money to pay for his new materials.
A farmer borrows to pay expenses of running his farm
until crops are ready to be sold.
A man who is building a house borrows part of the cost
of building.
A school district borrows to put up a new school build-
ing.
The national government sells bonds to its citizens to
carry on the expenses of operating the government.
On all borrowed money, interest is paid. You know
that interest is money paid for the use of money. If
$1000 is borrowed for one year at 5%, 5% of $1000, or
$50, is paid at the end of the year for the use of this
money.
1. Name some other piu-poses for which money is
borrowed.
96

Principal and Interest
The amount loaned and drawing interest is called the
principal. The rate of interest per year is always
stated as a per cent of the principal.
To find the interest for one year, multiply the princi-
pal by the rate expressed as a decimal.
If the time is less than a year, express the time as a
fraction of a year and multiply the interest for one year
by this fraction. Before multiplying, reduce the fraction
of a year to the lowest terms. Thus:
1mo. - 1^2yr.
5 mo. =Ayr.
9 mo. =|yr.
2 mo. =iyr.
6 mo. =iyr.
10 mo. = |yr.
3 mo. =iyr.
7mo. -
\z yr-
11 mo. =iiyr
4 mo. =*yr.
8 mo. =|yr.
12 mo. = lyr.
In figiu-ing interest 30 da. = 1 mo.,
60da. =2mo., 90da. =
3 mo.
1. Find the interest on $1960 at
6J% for 5 months.
The interest for one year is
$127.40. The time is t% of a year.
So we multiply $127.40 by ^,
Find the interest for each of the
following amounts:
Principal Time Rate
$1960
.06^
980
117 60
$127.40
5
12) $637.00
$53.08
Principal Time
Rate
2. $1200 4 mo.
6%
$1970
90 da.
4i-%
3. $840
lyr.
5%
$790
60 da.
5i%
4. $9300 3 mo.
8%
$2460
30 da.
4%
5. $8150 8 mo.
4%
$7950
5 da.
5%
6. $5000
10 mo. 4%
$4800
7 mo.
4i%
97

Bank Discount
I
When money is borrowed from a bank, a note is often
made bearing no interest. The banker figures the inter-
est on the amount of the loan ahd deducts it, giving the
customer credit for the balance. The amount left after
interest has been deducted, is called the proceeds or
net proceeds, of the note. The amount deducted by
the banker is called bank discount.
The following is a note made out by Mr. Haydon when
he borrowed from his local bank:
U^^ yK^7{tH<<Iy
,
after, date for value
received, I promise to pay to the order of
THE FIRST NATIONAL BANK
<=/lyt//A^U^X^My ^^yi^^Apy/y/^^y^Jy^/^ DOLLARS
Due
1. Find the proceeds of this note, discounted at 4^- %.
A statement is made
like the one at the right.
The discount is found on
separate paper or by using
an interest table. Finding
the discount is exactly the same as finding the interest on
$2500 at 4^% for 6 months
Face of note
Discount
Proceeds
$2500.00
56.25
$2443.75
To find the interest or
bank discount when the
time is given in days, ex-
press the time as a fraction
of a year. See the examples
at the right.
15da. =
3^0 yr. =
2V y^
20da.=^^oyr. =
iVyr
40da. =
3Voyr.= \ yr
45da. = 3^^yr
. ..-
Ayr-
80da. =
3«^oyr. =
f yr.
75da. =
3Voyr
98

Practice in Discounting Notes
Find the bank discount and the proceeds below:
Face of Note
Time
Rate Bank Discount Proceeds
1. $600
30 da.
5%
2. $200
45 da.
6%
3. $240
75 da.
6%
4. $1800
60 da.
4%
5. $810
80 da.
5%
6. $350
90 da.
5%
Notes such as the one shown on the opposite page are
called promissory notes. The amount stated in the
note is called the face, or the principal, of the note.
The one who signs it is the maker of the note. The note
is said to be drawn in favor of the person or institution
to which the note states a promise to pay. The date due
is called the date of maturity.
The face of this note is $2500; the maker is Leslie
Haydon; the note is in favor of the First National Bank.
A promissory note should show the following:
(1) The date when the note is made.
(2) The date and place where it is to be paid. The
date of payment may be indicated by stating how long
the note is to run, or by saying it is due on demand.
(3) The definite sum to be paid. This should be
written both in figures and in words.
(4) The fact that the note is given for something
valuable (for value received).
(5) The signature of the one making the note (the one
making the promise to pay).
(6) Any interest to be paid with the note. If the note
says nothing about interest, only the face of the note is
to be paid at maturity.
99

Selling a Promissory Note
In the note on page 98, there is a promise to pay "to
the order of" the bank. If the banker writes his name
on the back of the note, this constitutes his order to pay,
and anyone who has the note may then collect it.
But the banker may write "pay to the order of Tom
Jones" and then sign his name. In this case Tom Jones
or anyone to whom he may assign it may collect the note.
In either case the banker sells the note. The possibility
of doing this is indicated by calling a note a negotiable
instrument.
1. Describe all the items that are necessary to go into
a promissory note, regarding (1) the definite amount,
(2) the time of payment, (3) the item *'for value re-
ceived," (4) the signature, (5) the rate of interest, and
(6) the one to whom the note is payable.
2. If a note contains no statement about interest,
what rate of interest, if any, must be paid?
3. How does bank discount differ from ordinary
interest?
4. What is meant by "face of note," "date of ma-
tiu-ity," and "proceeds"?
5. What do we mean by saying that a note is dis-
counted at the bank?
6. If you know the face of a note, the rate of discount,
and the time at which it is due, how do you find the pro-
ceeds of the note?
7. When interest is computed on a loan, what is meant
by the "principal"?
8. How would you find the interest on a given sum for
6 months? for 4 months? for 3 months?
100

Problems of Discount
Find the bank discount and the proceeds for the
following notes:
Face of Note
Time
Rate
Bank
Discount Proceeds
1. $15,000
60 da.
^%
2. $25,000
90 da.
4i%
—
—
3. $12,500
30 da.
5%
—
—
4. $35,000
15 da.
4%
5. $18,000
45 da.
4i%
—
—
6. $ 8,500
120 da.
6%
—
—
7. $ 7,650
75 da.
6%
—
—
8. $10,000
80 da.
•5%
—
—
Topics for Discussion
1. A merchant wishes to secm-e cash so that he may
buy a stock of goods that he expects to sell in the next
few months. He borrows the money from his bank by
discounting his own note. Why does it pay him to bor-
row the money? May he get the goods enough cheaper
by paying cash?
2. A contractor puts up a large building and must pay
for material and labor. The payments he will receive on
the building do not come for several months. Is he likely
to borrow from the bank?
3. Amanhasasumofmoneyduetohim,butthepay-
ment comes later than he has expected. In the mean-
time his taxes fall due. Is he Hkely to borrow from the
. , bank to pay his taxes? Do you think it would be sensible
for him to borrow?
101

I
I
Unit 8. Interest, Profit and Loss
Different Rates of Interest
There are great differences in the rates of interest that
are being paid. Yoiu" school board may be able to borrow
money for a new building at less than 3%, possibly nearly
2%. At the same time some banks are making small
short-term loans at 6%, or even more.
The general level of interest rates changes from time to
time. At present, rates of interest are about two thirds
of what they were in 1929. What are the effects of such
changes in interest rates? This is a difficult question,
and we are far from being in a position to attempt a com-
plete answer. But the study of some simple problems
will help you to understand the effects of interest rates
and their changes. You will meet such questions often
in the course of your life.
When a family is deciding whether to build a house of
its own or to continue living in a rented apartment, in-
terest is figured on the total investment in the new house.
This must be done whether the family has its own money
to buy or build, or whether the family borrows some of
this money.
1. A new house is acquired at a cost
of $9800. At 6%, what is the monthly
cost of living in this house?
As shown at the right, the answer is
$49.00 .
2. What would be this monthly cost if the rate of in-
terest were 4%? What is the difference per month due to
the lower rate of interest?
102
$9800
.06
12) $588.00
$49.00

Interest Problems
1. The Hudson family bought a building lot for $800
and put up a house on it costing $7500. Figuring interest
at 4% on the whole investment, what is the yearly in-
terest charge?
2. The house in problem 1 depreciates 3% a year.
What is the yearly depreciation? (The house only, not
the lot, depreciates.)
3. The tax on the house in problems 1 and 2 is
$108.50. What is the sum of the interest, depreciation,
and taxes? What does this amount to per month?
4. How much greater would be the monthly cost
found in problem 3, if the rate of interest were 6%?
Could you find the answer by taking 2% of $8300 and
then dividing by 12?
5. A house costing $12,500 is built on a lot costing
$1200. Depreciation of the house is figured at 2^%. If
the rate of interest is 5%, what is the sum of the interest
and the depreciation for one year? How much per
month is this?
6. If the rate of interest were 4%, by how much per
month would the cost of Kving in the house in problem 5
be reduced?
?• If the rate of interest is reduced from 7% to 5% (an
actual case in one community), what would be the effect
on the cost of living in one's own house?
8. What is the effect of lowering interest rates on the
rent charged on old houses and on apartments?
9. If interest rates go up, what will be the effect on the
building of new houses? What will be the effect on the
rents that will have to be paid?
103

Interest on Manufacturing Plants
It is said that in our great automobile factories from
$7000 to $10,000 has been invested in the plant for every
person that works in them
1. If $8500 is invested in an automobile factory for
each person employed, and if interest of 6% is to be paid
on this investment, how much interest must be paid in
one year on the building, machinery, and other equip-
ment used by each employee? How much per day is this
if the plant runs 280 days per year?
The computation at the right
shows that this is $1.82.
$8500
.06
280 )$510.00
$1.82
2. For the factory of problem 1,
it is figured that the plant decreases
in value each year by one-twelfth,
or 8^%, of its value when new.
What is the amount of the annual
depreciation per worker?
3. How much is the depreciation
of the factory ($8500) per day?
4. What is the sum of the daily
interest and depreciation on the
factory?
Finding depreciation is, in practice, quite complicated.
Parts of the plant, such as the machinery, depreciate
very rapidly. These are figured separately; then an
average is taken.
104
$8500
28.33
680 00
280)$708.33
$2.53

Interest and Depreciation
1. If in problem 1 on the opposite page the interest
charge is reduced from 6% to 3%, by how much is the
amount reduced that must be charged daily against the
product of each worker?
2. If through rapid changes in styles, and through in-
ventions, the depreciation in problem 2 should be
changed from 8^% to 12^%, by how much would that
increase the amount that must be charged daily against
the product of each worker?
3. In one factory, which manufactures shoes that
change very little in style, the average depreciation is
figured at 8% a year; while in another factory the depre-
ciation is figured at 25% a year. What is the difference
in depreciation of the two factories, each valued at
$450,000 when new?
4. In a new enterprise involving much risk, there may
be expected an earning of 20% in order to get people to
invest money in it; while in a weU-established business
money may be had at 3^%. For an investment of
$250,000, what would be the difference in expected
earnings for these two businesses?
5. Twelve years ago a certain automobile was sold for
$2500. Now a much better automobile is bought for
$1200. To which of these factors was this change due:
(1) to more skilled workmen? (2) to lower wages?
(3) to new inventions and better management? (4) to
lower rates of interest on the investment?
105

Effects of Low Interest Rates
During the last ten years a great university had its
yearly income reduced by $1,500,000 because of reduced
rates of incomes from its investments.
The total amount deposited in our savings banks is
about 20 billion dollars ($20,000,000,000). The income
from these deposits has been reduced from about 3% to
about 1^%.
Ten years ago a certain family had a yearly income of
$50 per $1000 on money saved and invested. Now this
income is $30.
Life insurance companies have large assets (now about
29 billion dollars). This money is invested. As the
income from investments goes down, the cost of in-
surance goes up.
1. When the income from its endowment goes down,
how will a privately endowed university obtain money
to carry on its work? Which of these results do you
think will follow? (1) Will higher txiition be charged?
(2) Will salaries be cut? (3) Will the work of the institu-
tion be decreased?
2. If the income from savings deposits are decreased
from 3% to 11%, how much less wiU the depositors re-
ceive m% of $20,000,000,000 is how much?) Are these
depositors wealthy people?
3. If the income of insurance companies is decreased
by 2% of the total assets (2% of $29,000,000,000), how
much per year will the policy holders lose?
4. As incomes decrease, what will be the effects on
the total income tax that can be collected?
106

Problem Practice
1. If one ton of a certain grade of coal occupies 39
cubic feet, how many tons wiQ a bin hold if it is 13 feet
long, 9 feet wide, and 5 feet deep? Indicate the solution
and then find the answer.
2. A pile of boards, each one | of an inch thick, is
45^ inches high. How many boards are piled one on
top of the other?
3. A volley-baU team won 13 games and lost 15 games.
What per cent of the games played did the team win?
Find answer to the nearest per cent.
4. What is the change from $5 for 3^ yd. of gingham
at 20^ per yard and a hat for $3.25?
5. If f yards of towehng are used in making one towel,
how many towels can be made from 12 yards?
6. Count from 12^ to 100 taking 12^ at each step.
Write the numbers.
7. How many rods of fence wire are required to make
a five-wire fence around a field 80 rods long and 60 rods
wide?
8. An automobile used 20 gallons of gasoline in going
280 miles . At this rate, how many gallons wiQ be re-
quired for a year's driving of 9400 miles?
9. On a certain map 1 in. represents 200 mi. What
distance is represented by a Hne that is 2^ in. long?
10. I have a pictinre measiu*ing 5^ in. by lOf in. which
is mounted on a mat that extends 1^ in. beyond the pic-
ture on all sides.
How many square inches of the mat
are not covered by the picture?
11. How many tons are there in a 200-bushel load of
wheat (1 bu. wheat = 60 lb.)
107

Margin and Profit
Cost at factory
$13.50
Wholesaler's profit
2.50
Transportation
.50
$16.50
Retailer's margin
7.00
Retail price
$23.50
There is a consider-
able difference between
the manufacturer's price
and the retail price.
The box at the right
explains this condition.
The wholesaler must
have some margin, and the retailer must have more be-
cause his expenses are greater.
We use margin to represent the difference between
the cost of the goods and the price at which they are sold.
The word profit wiQ be used with a different meaning,
to represent the money left as a retin-n on investment,
after all expenses are paid.
It is clear that to continue in business a merchant must
sell goods for more than he pays for them. That is, he
must have a ihargin.
This should include some profit.
Sales
$98,650
Cost
69,330
Margin $29,320
Overhead 23,930
Profit
$—
1. A man who keeps a shoe
store found that in one year he
had sold shoes for $98,650, and
that these had cost him $69,330.
This gave him a margin of
$29,320. What was his actual
profit?
The storekeeper had heavy expenses during the year.
He paid rent, wages, taxes, and other items. Light, heat,
advertising, and delivery cost him a good deal of money.
Altogether his expenses, including a salary of $4,000 for
himself, amounted to $23,930.
These expenses which constitute his overhead, or
cost of doing business, must be paid out of the margin.
What is then left is called profit.
108

Overhead and Loss
Sales — cost = margin
Margin —overhead = profit
Overhead — margin = loss
In case the overhead
is greater than the mar-
gin, there is a loss.
For the merchant the
rate per cent overhead is important. This rate is ex-
plained in the following problem:
1. The total sales in a
. 243
$98650)$23930.000
shoe department were
$98,650 and the over-
head was $23,930. Find
the rate, to the nearest whole per cent.
When the rate of overhead is known, it is easy to find
how much overhead is to be charged against each article.
Thus the overhead on a pair of shoes selling for $7.50 is
24% of $7.50 or $1.80 .
Copy the following and supply missing numbers:
Selling Per Cent
Profit
Cost
Price Overhead Overhead or Loss
2. $120
$200
30%
—
3. $400
$600
25%
4. $300
$400
31%
5. $488
$800
33%
—
6. $640
$960
25%
7. $434
$700
30%
^8. $400
$600
$180
9. $650
$800
$200
10. $500
$700
$210
^12.
$200
$250
20%
$280
$400
25%
$100
"
J
$20

Rate Per Cent Cost, Margin, and Overhead
The merchant finds what per cent the cost is of the
selling price.
In the same way he finds what per cent
the margin is of the selHng price, and also the overhead
and the profit. Using the figures given for the shoe store
on page 108, we get
the statement shown
at the right. The steps
are:
Step 1.
Find the
rate per cent of cost.
Step 2. Find the rate per cent margin. This can be
fomid by subtracting 70.3% from 100%. Why?
Sales
$98,650 100%
Cost
69,330 70.3%
Margin
29,320 29.7%
Overhead 23,930 24.3%
Profit
5 390 5.4%
Step 3. Find the rate per cent
overhead. This is done by carry-
ing out the division at the right.
$98650)$23930
Step 4. Find the rate per cent profit. This may be
done by subtracting 24.3% from 29.7%. Why?
1. In one year a merchant sold goods for $175,000, for
which he had paid $128,640. His overhead was $42,000.
Make a statement like the one above.
2. Mr. Ewing bought goods for $9962 and sold them
for $14,650. His overhead was 20%. What was his per
cent profit?
3. A dealer bought a piece of furnitvire for $40 and
marked it 50% above liis cost. His margin will be what
per cent of the selling price?
4. One year Mr. Hill's sales were $48,000. He had
paid $37,680 for these goods. His overhead was $12,165.
Find his rate per cent profit or loss.
no

(^XC
\
lyIo
Problems without Numbers
1. Things that change rapidly
iQ style, and so are in danger of
becoming nearly worthless in a
short time, must be sold at a high
margin. Name a number of such
articles, as women's hats in ex-
treme styles.
2. If you know a merchant's cost of an article and the
price at which he sells it, how do you find his margin?
3. If you know the selling price and the margin, how
do you find the rate per cent of margin?
4. Describe the method that the merchant uses to
find his total overhead for a year, and the rate per cent
overhead. What is used as the base for finding the rate
per cent overhead?
5. If you know the rate per cent margin and the rate
per cent overhead, how do you find the rate per cent
profit?
6. If you know the margin and the overhead, how
can you find whether there has been a profit or a loss?
1. Name all the items that you can, that form part of
the merchant's overhead.
Is cost of delivery part of
overhead? When goods are bought on approval and then
returned, does this make additional expense? Is this
part of overhead?
8. If by increasing service to his customers the nier-
chant increases his overhead, how does that affect the
price of his goods?
9. Things that are very stable in form can be sold at
a lower margin. Name a number of such articles.
Ill

Setting the Selling Price
A dealer decides that if he is to remain in business,
he must have at least a certain average profit from year
to year, such as 3% or 4%. To this he adds his known
rate of overhead, which gives the rate of margin that he
feels he must have. This gives him a basis for marking
the goods that he puts on his shelves.
1. A chair is bought for $12. The dealer estimates his
overhead at 32% of his sales and wishes to set his profit
at 10% of the sales.
The margin must then
be 42% of the sales. The
cost is 58% of the sales.
Then the problem is:
$12 is 58% of what
amount? As shown at
the right, the answer is
$20.69. He then marks
the chair at some figure
near this, such as $20.50, or $20.75, or possibly $20.00
or $21.00 .
Sight Work
1. If the cost is $4.00 and the margin is 33^^%, what
is the selling price? (4 is f of what number?)
2. The cost is $1.50 and the margin is 25%. What is
the seUing price?
3. A fine table is bought by the dealer for $75. If
the margin is 50%, what is the selling price?
4. A pair of shoes is bought for $3.20. The overhead
is 30% and the profit is to be 6%. What must be the
seUing price?
112
32%
10%
42%
$20.68 9
• 58)$12.00 00
116
100%
42%
58%
40
348
520
464
56

Problem Practice
1. A merchant whose rate of overhead is 25% wants to
make a net profit of 7%. What must be the rate of his
margin?
2. In problem 1, the cost wiQ be what per cent of the
selling price? (cost = selling price — margin)
3. A set of dishes bought for $55 is marked to sell at
$100. This price is then reduced 20%. What is the
margin on this sale? What is the rate of margin?
4. A pair of shoes is bought by the dealer for $4.50.
The overhead is 26% and the profit is to be 5%. What
must be the selling price? First find the exact answer
and then tell at what price the dealer might mark these
shoes.
5. Mr. Chandler sold a moving picture projector at a
price that allowed him a margin of $28.50 . His overhead
was $21.75. What was his profit? What additional in-
formation must you have to be able to find his rate per
cent profit?
6. Opera glasses that cost $45 were sold for $15.00
more than the cost.
If the overhead was 22% of the
selling price, what was the profit? Make a statement
like the one in the box on page 110.
7. George paid $17 for a bicycle.
He paid $4.50 for
repairs and $3.25 for a new tire.
Then he sold it for
$22.00 . What was his per cent loss? Use the selling
price as the base.
8. A hardware dealer bought a furnace for $250 and
marked it to sell for $375. Then he sold it at a reduction
of 25%. What was his margin?
113

Unit 9. Business Problems, formulas
Selling on Commission
Mr. Ward owns some building lots that he wants to
seii.
So he asks the Bishop Agency to find buyers for
hini. The agency finds a buyer for one lot that is sold
for $1200. For this service Mr. Ward pays the agency
five per cent of the selling price.
The agency does not become the owner of the lot. It
simply tries to sell Mr. Ward's property. If the agency
fails to find a buyer, it gets nothing for its work; but
if it does find a buyer, it gets a certain per cent of the
amount of the sale.
The pay for such work is called a
commission. The rate of commission is agreed upon
between the agency and the owner. Real estate (land
and buildings) is often sold on commission.
In the larger cities there are commission houses, which
sell farm products on commission. Books and subscrip-
tions to magazines are sold on commission by agents who
go to the individual buyers. There are also commission
men in the rural districts who buy cattle, hay, sheep,
wool, and grain on commission for the large city buyers.
All these receive as their pay a certain per cent of the
amount involved in the transaction, whether it \s selling
or buying.
Wlien a commission man makes a sale, he deducts his
conniiission and any expenses agreed upon, and the
owner gets the rest. What the owner gets is called the
proceeds of the sale.
1 . Name other ways in which people earn commission
for selling various articles.
114

Problem Practice
1. An agent sold a farm for $12,000 and received 4%
for selling. WTiat were the net proceeds?
2. A real estate dealer sold a house and lot for $8000
and was paid 5% commission. How much did the owner
receive from this sale?
3. An agent sold goods for $6240 at a commission of
4%. What was his commission? What were the owner's
net proceeds?
4. If Mr. Wilson received 10% commission on his
monthly sales above $2500, what commission did he
receive for January when his sales were $6890?
5. An agent received a salary of $250 a month and 8%
on monthly sales above $2800. What was his income in
February when his sales were $4924.60?
6. What were the net proceeds from a sale of $1600
after a commission of 5%, freight $12, storage $4.50,
and dray age $3.75 were deducted?
7. A commission merchant sold 500 boxes of apples at
90 cents a box, with commission at 5%. He deducted $19
for freight and drayage. How much did he remit?
8. Mr. W. C . Hart owned a city house valued at
$14,500 on which there was a debt (mortgage) of $5,500.
He sold this house for $14,500 at 5% commission, and
paid off the mortgage.
How much did he have left?
9. An agent sold goods for $235 and sent the owner
$199.75. What was the agent's rate per cent commis-
sion?
10. Mr. White received a commission of $187.50 lor
selling a house for $7500. What was his rate per cent
commission?
115

Discounting Notes at the Bank
1. The Brown Implement Company sold farm ma-
chinery to R. M . Smith
for $430.00 . Inpayment
Mr. Smith gave his note
due October 1 carrying
no interest. The com-
pany took Mr. Smith's
note to the bank 75 days
before it was due and dis-
755
$430
360 24
.06
$25.80
$430
5
5.38 24)$i29.00
|
$424.62
$5.3^ 8
J
counted it at 6%. What were the proceeds?
By taking a note, the company could get money from
the bank when needed. The company signed the note on
the back and this made them liable to the bank.
2. The Brown Implement Company had a note for
$280, carrying interest at 7%, due in three months. They
discounted the note at once at 6%. What were the
proceeds?
Step 1, Find interest at
7% for 3 months and add
to the face of the note.
This gives amount of the
note when it is due.
Step 2, Discount the amount ($284.90) at 6% for 3
months. Why are the proceeds greater than the face?
116
Face of note
$280.00
Interest
4.90
Amount of note 284.90
Discount
4.27
Proceeds
$280.63

Problems on Bank Discounts
1. A note for $1520 with interest at 5% is dated May 1
and due December 1. On October 1 it is discounted at
4%. What are the proceeds?
(1) What is the rate of
Face of note
$1520
Interest, 7 mo.
44.33
Amount of note $1564.33
Discount, 2 mo.
10.43
Proceeds
$1553.90
interest? For how many
months is it computed?
(2) How is the amount
of the note found?
(3) How is the dis-
count found? What is the time for which the note is
discounted?
Note in particular that the amoimt of the note, not the
face of it, is the base (principal) on which the discount is
computed.
2. A merchant takes a note from a customer for $160
due in 4 months. The note bears no interest. Three
months before it is due this note is discounted at 5%,
What are the proceeds?
3. A note for $3250 bearing interest at 6% due in 6
months is discounted at once at the bank at 6%. Are the
proceeds more or less than the face of the note? Why
should the proceeds be different from the face of the
note?
4. A note for $700 dated September 15 and due in 3
months, bears interest at 8%, On October 15 it is dis-
counted at 5%. What are the proceeds? Why do you
think the note bears such a high rate of interest while the
bank discounts it at a much lower rate?
5. A dealer sells farm machinery for $1480 and takes a
6 month's note bearing 7% interest. Two months later
he discoimts it at 5%. What are the proceeds?
117

Trade Acceptances
Instead of promissory notes, merchants often use
trade acceptances. The following example will il-
lustrate:
L. T. Floyd and Company of Chicago are wholesale
dealers in men's clothing. They sell a bill of goods for
$1460 on 90 days credit to Warren Barton of Meadville,
Colorado, a retail merchant. When the goods are
shipped, a trade acceptance is sent to Mr. Barton, who
accepts it by writing across the face of it, as shown. The
acceptance then becomes in effect Mr. Barton's promis-
sory note, and L. T. Floyd and Company may discount
it at their bank. Short-term notes, given to pay for
merchandise, and trade acceptances are usually referred
to as commercial short-term paper.
Chicago, Tninm«,^^>V^ /W/ #^%9
^//y<^.^f ter Ja^ pay t^he ^r of AYyA^f/zM'J
/
(^^7^i<^/J^^^//tn^7i^/:ht^t!<^^<^
DOLLARS
The obligation of this acce;
from the drawer
ice
TT
v-
of the purchase of goods
1. The acceptance of Warren Barton was discounted
at 6% Nov. 21, 1941. Find the proceeds.
The time from
Nov. 21, 1941 to
Feb. 1, 1942 is 72
days. (Count Nov. 21, but not Feb. 1 .)
Face of acceptance $1460.00
Discount
17.52
Proceeds
$1442.48
292
$146&X:^X T§o = $292 X t o
5-
118
$17.52

I
Computing Interest between Given Dates
To find interest from July 8 to November 20, for
example, the first step is to find the actual number of
days between these dates.
We include the first date,
July 8, but not November 20. The time rims 24 days
in July (31—7=24), 31 days in August, and so on
as shown at the right. The time is 135
days, or ^-|^ =
fofayear.
Tables are
printed that give help in finding the
number of days between any two dates,
but the process indicated here is very
simple and does not require much time.
Note in particular that the process of finding interest
for a given time or between given dates is exactly the
same for ordinary interest, for bank discount, or for
finding proceeds of a trade acceptance.
Copy the following and supply the niunbers missing:
Principal Rate
Time
Proceeds
July 24
Aug. 31
Sept. 30
Oct. 31
Nov. 19
135
1. $790
6%
May 8 to Sept. 21
2. $1940
5%
Mar. 3 to Oct. 15
3. $186
7%
July 27 to Nov. 12
4. $450
6%
June 1 to Sept. 12
5. $2900
^%
Aug. 12 to Dec. 15
6. $4160
4%
Nov. 1
to Jan. 28
7. $740
5i%
Dec. 7 to Feb. 23
8. $1320
5%
Oct. 15 to Jan. 31
9. A note for $2180 dated Oct. 3 , 1941 and due in 90
days bears interest at 6%. On Dec. 1 it is discounted at
5%. What are the proceeds? (On what date is tliis note
due?)
119

Formulas and Their Uses
We shall now bring together in one place the formulas
you have used and add some that are new. By this means
you will make clear how few and simple the ideas are
that run through all of them. When you really imder-
stand one of these formulas, you understand a good deal
about all of them. In addition, this will review much of
the arithmetic that you have studied.
Sight Work
1. Let m = minuend, s = subtrahend,
r = remainder.
Then formula (1) represents sub-
traction.
How is (2) obtained from
(1)? State (2) in words as a rule.
For
what purpose have you used this rule?
2. Let Z)= dividend, c/ = divisor, q
=
quotient.
Then (1) represents division.
How is
(2) obtained from (1)? State (2) in
words as a rule.
For what purpose have
you used this rule?
3. In A (area of rectangle) =^lw what
is represented by A, Z, wl How are (2)
and (3) obtained from (1)? For what
purpose have you used these formulas?
4. In d = st^ what is represented by
d, s, f> How are (2) and (3) obtained
from (1)? If speed is given as so many
miles per hour, in what imits wiU the
distance be foimd?
120
(1) m-
(2)m =
5=r
(2) D-.= qd
(1) A^
(2) 1=
(3)ii; =
A
~
w
A
^
I
a)d-
(2)s=
(3) <
=
d
t
_d
~
s

\
Sight Work
State the formula for solving each problem below:
1. If in an example in subtraction the subtrahend is
37 and the remainder is 13, what is the minuend?
2. If the area of a rectangle is 128 square feet, and its
width is 8 feet, what is its length?
3. If the area of a rectangle is 168 square inches and
its length is 21 inches, what is its width?
4. If in an example in division the quotient is 7 and
the divisor is 15, what is the dividend?
5. If the dividend is 360 and the quotient is 30, what
is the divisor?
6. If in a problem involving time, speed, and distance
the time is 6 hours and the speed is 50 miles per hour,
what is the distance?
7. If the distance is 480 miles and the time is 8 hours,
what is the speed?
8. If the distance is 240 miles and the speed is 40
miles per hour, what is the time?
9. If the dimensions of a rectangle are given in feet,
how do you find the area in square yards?
10. If the dimensions of a field are given in rods, how
do you find the area in acres?
11. If the weight of an ojiject is given in ounces, how
do you find its weight in poiuids?
12. If ^ is the number of gallons in a tank, how do you
represent the number of quarts?
13. If an airplane goes 318 miles
in 1^ hoxirs, how far will it go in
4^ hours? Study the indicated
solution at the right.
121
318 V J.1
—
A36 w
IJ^^2"3
-^

Working with Formulas
(1)c=
(2)n =
(3)^
=
np
(1)^
=
(2)T=
(3) b=
br
1. Write formula (1) for the state-
ment, cost = number X price.
Complete
formulas (2) and (3) at the right. State
each of the three formulas as a rule.
2. Express the statement, percent-
age = base X rate as a formula.
Com-
plete formulas (2) and (3). How are
(2) and (3) obtained from (1)?
Many problems in percentage deal with three nimi-
bers, base, rate, and percentage, two of which are given,
and the third is to be found.
State the formula for solving each problem below:
3. The price of a $45-chair was reduced 30%. What
was the amount of the discount?
4. A basketball team won 4 out of 7 games it played.
What per cent of its games did the team win?
5. What amount must be invested at 5% interest to
earn an annual income of $250?
6. Express the statement for finding
volume.
In V = lwd, what is repre-
sented by V, Z, w, d? How do you find
the missing number in the equation:
_^X3X4 = 24? How are (2^ (3), and
(4) obtained from (1)?
7. In i (interest) =pj% what is rep-
resented by i, p, r, t?
Complete for-
mulas (2), (3), and (4). How is (2)
obtained from (1)? How is (3) ob-
tained from (1)? How is (4) obtained
from (1)?
122
(1) V=
- Iwd
(2) /=
V
wd
(3) w=
V
'id
(4)c?=
V
'
Iw
(1)1=
- prt
(2) P=-
(3)r=:
(4) t==

I
I
Using Formulas
State the formula for each problem; then solve.
1. A farm containing 140 acres was sold for $10,500.
What was the price per acre?
2. At 7% commission, what is the commission on
sales amomiting to $3500?
3. On sales of $2000, the commission was $180. What
was the rate of commission?
4. A box is 16 in. long and 8 in. wide. How deep must
it be to contain 576 cu. in.?
5. Find the interest on $1460 at 5J% interest for 90
days.
6. When a bill for $125 is discounted 20%, what is the
amount of the discount?
7. When a bill for $36 is discounted $6, what is the
rate of discount?
8. When the commission is $50 and the rate of com-
mission is 8%, what is the amount of the sales?
9. Mr. Wilson earned $3600 last year and saved $500
of it.
What per cent of his earnings did he save?
10. How much money must be invested at 4^% to
produce a yearly income of $1800?
11. At what rate of interest must $24,000 be invested
to earn $1200 yearly?
12. A $50 suit was sold at 12-^ -% off. What was the
amount of the reduction?
13. In a school of 1876 pupils, there were 1015 girls.
What per cent of the pupils were girls?
123

Finding Interest
As a review of the subject of interest, we shall now use
a method that works smoothly, no matter how many
days a month the interest is to run. It is also the shortest
method in the case of less usual interest periods such as
37 days or 68 days.
We use 360 days as one year. Since the rate of interest
is given for one year, we must express the time as a
fraction of a year.
1. Find the interest on
$480 at 7% for 37 days.
The interest is indicated
in the second line at the
right. This is reduced by
cancellation as shown. We
then
have
4 XjwX-^3^.
The number 4 can be can-
celed into 100, but it is
better to leave the 100 in the denominator,
to divide by 100 than by 25.
$480 X^X^
4
$4S€rx
$1036
300
JL.V -2Z.
-
1Q36
100 ^J^%(f 300
$3,453
It is easier
Now find the product 4x7x37 =1036 and divide by
300. To divide by 300, divide by 3 and point off two
decimal places.
The interest is $3.45.
2. Find the interest on $1360
at 6^% for 68 days.
To indicate the solution, 6^%
is changed to 2^-
Cancel as
shown.
$1360 X^X^
34
13
34
$i3e€rx^^X^^
100
9
To find the answer, first
multiply 34 X 13 X 34. To divide
by 100X9, divide by 9 and move the decimal point
two places to the left.
124

The Cancellation Method for Finding Interest
The method used on the opposite page is the cancel-
lation method for computing interest.
It is a direct
appUcation of the formula, i =prt.
Find the interest below correct to the nearest cent:
Principal Time
Rate Principal Time
Rate
1. $860
43 da.
6% $960
47 da.
7%
2. $750
27 da.
7%
$1290
83 da.
^%
3. $380
32 da.
6% $640
93 da.
6%
4. $940
54^a.
5% $1540
76 da.
4%
5. $1530
62 da.
4% $1800
69 da.
^%
6. $240
17 da.
6% $3400
56 da.
4i%
Problem Practice
1. A truck loaded with coal weighed 11,850 lb. , and
the empty truck weighed 4250 lb.
At $7.40 per ton,
what was the cost of the coal?
2. Last year the Lincoln School had an enrollment of
976 pupils.
This year the enrollment is 1048 pupils.
Wliat is the per cent of increase?
3. A man borrowed $1600 from the bank for 90 days.
The discount rate was 6f%. How much money did he
receive from the bank?
4. A salesman received a monthly salary of $100 and
6% on all monthly sales above $2000. One month his
sales were $5794.60 . What was his income that month?
5. An agent sold 780 boxes of apples at $1.25. After
deducting a commission of 4% and paying $17.85 for
freight, how much did he send the owner?
125

fourth Self-Test
Test in Fundamentals
Perform the indicated operations below:
1. 7 .9+541 +0.988+87.03+.554+.064+89
2. 6 .91 +0.I3+89.6+402.6+89.40+3.92+.086
3. 1.94+5.613+.692+.687+8.04+.295+.64
4.
. 282+48.7+.054+0.96+4.32+83.2+8.06
5. 64.01 +1.95+8.4+547+0.973+643+13.21
6.
4.97-2 .98
32.4 -6 .704
.356 -.097
7.
700-349.86
4020-2376
79.31-68.87
8. 5.309 -4.788
1.04-0.987 ' 13.45-12.874
9.
8.4 X. 72
. 18X96
5.74X896
10. 64.01X82.7
4.67X38.2
31.97X542
11.
.78X2.85
. 734X269
. 74X5.64
Find quotient below correct to two decimal places:
12. 8 .9)41.72
37.2)519.7
.741)^947"
19)247
13. 25.3)1498
4.72)39.84
5.64)1937
126)78
Add the following:
14. 541
3f
8t%
41
1
51
2i
6i
5i
5|
6|
3f
3f
3i
81
2-1
5i
If
2i
W-.
5i
5i
8i
M5!
Subtract the following:
15. A\
18|
6i
151
8|
4i
n
5|
4|
71
51
21
Multiply the following:
16. 2iX7| 81X61 5| X6i 8|X6|
8X3|
Divide the following:
17. 2|^7i 26-^41
6^ -5| 8|-
-171 21^8-i
126

Test in Solving Problems
1. From A=lw derive two other formulas. State each
formula in words as a rule.
2. How miany tons of coal are there in a load weighing
12,600 pounds?
3. How many days are there in 12 days 3 hours?
4. At 8^ cents per can, what is the cost of one dozen
cans of hominy?
5. A grain box has a contents of 20 cubic feet.
At
f bushels to the cubic foot, how many bushels will this
grain box hold?
6. A plank 14 feet long is cut into 6 equal pieces.
How many feet and inches long is each piece?
7. John is 5 feet 2 inches tall; James is 5 feet 5 inches
tall; and Robert is 4 feet 11 inches tall.
What is the
average height of the three boys?
8. At $32 per thousand, what is the cost of 13,400
bricks?
9. At $12 per ton, what is the cost of 3500 pounds of
hard coal?
10. At $9.80 per hundredweight, what is the value of a
steer weighing 1180 pounds?
11. How many acres are there in a field 40 rods wide
and 80 rods long?
12. A building is to be 60 feet wide. How long must it
be to cover 7200 square feet of ground?
13. A picture 6^ inches wide is put on a mat that
extends 1| inches beyond the picture on both sides.
What is the width of the mat?
127

Problem Test
1. At $12 per square yard, what is the value of a rug 9
feet by 12 feet?
2. How many cubic feet are there in a box that is 5
feet long, 4 feet wide, and 2.5 feet deep?
3. How many cubic yards of concrete are there in a
garage floor that is 27 ft. long, 24 ft. wide, and 4 in.
(^ ft.) thick? Indicate the solution.
4. A motor boat travels 12^ miles per hour. How long
will it take this boat to go 85 miles?
5. A family with a yearly income of $3000 pays $50 a
month for rent. What per cent of the total income is
paid for rent?
6. A man bought a lot for $1200 and sold it for $1500.
His gain was what per cent of the cost?
7. A sample of sugar beets contains 15.6 per cent
sugar. How many pounds of sugar are there in a wagon-
load of these beets weighing 2580 pounds?
8. Three fourths is what per cent of 2^?
9. A suit marked $40 is reduced 10 per cent in price.
What is the new price?
10. Find the net amoimt of a bill for $1000 with dis-
counts of 25%, 10%, 5%c).
11. A biU is subject to 20% and 10% discoimts. To
what single discount is this equal?
12. A $50 suit was put on sale at $37.50. What was the
rate per cent discount?
13. How much interest would you pay in 3 years on a
loan of $700 at 6%^?
14. A dealer's margin is 33^% of the selling price. For
how much does he sell an article costing $6?
128

i
Problem Test
1. A hat costing $1.75 was sold for $3.25. The over-
head was 27 per cent. The profit was what per cent of
the seUing price? Find answer to nearest tenth of 1%.
2. A dealer marked a piece of furniture costing $40 to
sell at a margin of 33^%. Then he sold it at a discount of
10%. What was the selling price?
3. A dealer paid $54 for a radio.
His overhead was
30%. What was his selling price with a 10% profit?
4. A certain new automobile costing $1060 depre-
ciated 27% the first year.
Insurance and Hcense cost
$74.60, garage rent was $4 a month, and interest on the
amount paid for the car was figured at 6%. What was
the total of these amounts?
5. A school building costing $85,400 depreciated 2^
per cent per year. Interest on the cost was 4^ per cent.
What was the total of these items for one year?
6. A radio was priced at $80 and sold for $88 on the
installment plan.
What per cent of the cash price was
the installment price? The cash price was what per cent
of the installment price?
7. The year's sales of a department in a store were
$47,600, the cost of the goods was $31,425.50, and the
overhead was $12,450. What per cent of the sales was
each of the following: cost, margin, overhead, and profit?
Find results to nearest tenth of 1%.
8. Find the interest for 78 days on $3160 at 5%.
9. A can filled with oil weighed 24 pounds.
The
empty can weighed 2f pounds. The weight of the oil was
what per cent of the filled can? Find answer to the
nearest tenth of 1%.
129

Unit 10. Home Problems. Insurance
An Interesting Comparison
It is most interesting to compare om* way of life with
that of the Indians. They bought and sold very httle.
Nearly everything they used was produced near their
dweUings.
How differently we Hve! Our way of life depends upon
our use of tools, machines, transportation, science, and
education. When we look about, we can see that a large
part of the things we use comes from many places in our
country and from many distant countries.
AU this
results in an endless number of problems.
In this unit, we shall continue with a study of business
problems that an inteUigent person living in our kind of
civihzation will have to solve. We must not forget that
one of the reasons we have schools is to prepare the
pupils to live more efficiently in our kind of civihzation.
If we were Indians, living as the Indians did before white
people came, we would have no schools.
1. Make a hst of some conveniences which we have in
our homes and which the Indians never possessed.
130

Interest on Investment in a House
1, The Browns had owned a building lot for some
time before they decided to build a house on it.
The
value of the lot was estimated at $1000, and the cost of
the house turned out to be $9500.
To get money to build, they sold bonds that they
owned for $4500, and they borrowed the rest. They had
received 5% interest, or $225 a year, from the bonds, and
they paid 5% interest on the money that they borrowed.
The lots could have been sold for $1000 and the money
invested to earn $50.
What was the interest on
the total cost of the
house?
Lot
Bonds
Borrowed
$1000
4500
5000
Cost of house
$10500
.05
Interest
$525.00
You can see that this
interest was exactly what
they would have received
yearly had they sold the lot and continued living in a
rented house.
Interest must be figured on the total cost of a house no
matter whether it is built or bought with money that has
been saved or borrowed.
2. A house costing $7400 is built on a lot worth $800.
At 5^% what is the interest on the investment in this
house?
3. A family bought an old house for $5700. Then
they spent $3200 in remodeHng and repairing the house.
At 4f%, what is the interest on this investment?
4. A house is bought for $8500. New furniture, a re-
frigerator, a washing machine, and a stove, totaling
$1150, are purchased. What is the interest on this in-
vestment at 5%?
131

Depreciation of a House
As you have already learned, the value of a house
decreases from year to year.
The useful life of a frame
house is figured at about thirty years.
This decrease in value, or depreciation, is due not
only to the fact that the house wears out, but also to the
fact that it becomes obsolete. New houses are constantly
being improved. In a certain length of time an old house
becomes so old fashioned and so inconvenient, when com-
pared with new houses, that it is not worth as much to
hve in, even if the structure itself is entirely sound.
Decrease in value for this reason is called obsoles-
cence. Decrease in value due to actual wear and also to
obsolescence is included under the word depreciation.
A house consists of two parts, the building and the
land on which it stands. The building depreciates, but
the land does not. In fact, the land may even have an
increased sale value.
It is usual to figiu-e depreciation of a house at a certain
rate per cent of its value when new. If the useful life of a
house is figured as thirty years, then the yearly deprecia-
tion is one thirtieth, or 3^%, of its value when new.
1. A house costing $6500 is built on a lot worth $700.
At 5^% what is the interest on this investment? If the
house depreciates 3^%, what is the yearly depreciation?
What is the sum of these?
2. An old house bought for $5800 cost $9500 when
new. This house is depreciating at the rate of 4% of the
original value. What is the yearly depreciation? What
is the interest on the investment at 5%? (The invest-
ment is $5800, not the original cost.)
132

Interest Schedule on a House
The Brown house costing $9500, built on a lot worth
$1000 (page 131), had a yearly depreciation of 3^% of the
value of the house when new.
Mr. Brown made up a depreciation-interest schedule,
of which we give the first five Hues.
The first line in
this schedule shows
that at the begin-
ning of the first
year the house and
lot
were
worth
$10,500, that the
yearly depreciation
was $317, and that
the interest,
at
5%, was $525.
Notice the fol-
lowing: (1) The depreciation, 3^% of $9500, is taken to
the nearest dollar.
It is the same for every year.
(2)
The depreciation is deducted from the value of the
property each year.
At the beginning of the second
year the value is $10,183. (3) The interest for each
year is 5% of the value of the property at the beginning
of the year.
1. Continue the above depreciation-interest schedule
up to ten years.
What is the value of this property at
the beginning of the tenth year?
2. A building costing $65,000 is put up on a lot costing
$15,000. Figure depreciation on the building at 2^%,
and interest on the whole investment at 4^%. Make out
a schedule for 5 years.
133
Depreciation-Interest Schedule
Year Value
Depre-
cia-
tion
Interest
1
2
3
4
5
$10500
$10183
$9866
$9549
$9232
$317
$317
$317
$317
$317
$525
$509.15
$493.30
$477.45
$461.60

Schedule of Payments on House
8 rm. resid.: 1 hath: mtach. Karaire: If?
wooded lot 65x220: aleo 7 rm. reaid,.
i
baths; every modern feature; .hat wat«f
ht.: ihorolyinsul : well bmll; i>r , J11.750
UD. Oneo 11-7 every day; 2 tilUs. N ..
,
',,
blU. W . Glencoe R. R. sta. 310 Lincoln-aT.
GlenvieTv— 27 mlnntes to lonp.
DON'T SIGN A LEASE
Own a 4 or 5 rm. country home for leai
money monthly. 27 min trans, to loon.
1
mi. west of Evanston. Choose yours now
Make email down payment. Wnie r L.i.ier
3052 Be rteau -av..
ChicaK<
Mr. Allan saw the advertise-
ment at the right and decided he f
would investigate.
He finally
[^
bought a house for $8000, and ^^
paid $1500 in cash.
The re-
mainder he agreed to pay luider
the following conditions: (1) He
was to make monthly payments ' s j ^
of $60.
(2) Included in this
amount was ^% monthly interest on the luipaid balance.
(This means that he paid 6% interest in 1 yr.) (3) The
remainder of each payment was applied on the principal.
HAVEanew6rm.h?e.onHa<
down. S35 per mo.
Fast trana.
Address H H 403, Tribune.
Hlebland Park—30 ralnafen to looi
THRFE NEW HOMES IN
SHERWOOD FOREST y'
ROBF^x jj^oaiJeoK^fC^''
e-S.-JSO
-t
to loop. Kij
Month Unpaid
Payment Interest
Paid on
Principal
1
2
3
4
5
$6500
$6472.50
$6444.86
$6417.08
$6389.17
$60
$60
$60
$60
$60
$32.50
$32.36
$32.22
$32.09
$31.95
$27.50
$27.64
$27.78
$27.91
$28.05
1. To compute interest in this problem move the
decimal point two places to the left and divide by 2.
Explain this statement.
2. Wliy do the amounts in the interest column de-
crease from month to month?
3. If the average monthly payment on principal
($6500) is about $44.00, how many months will it take to
pay for this house? How many years is this? Can you
figiu-e out why the average monthly payment on princi-
pal is taken as $44? (Suggestion: The first payment on
principal is $27.50 and the last is nearly $60. What is
approximately the average payment on principal?)
134

Costs of Renting and Buying a House
The house studied on page 134 will be paid for in about
12f years.
The monthly payments of $60 plus the
additional costs were about the same as the $70 rent that
Mr. Allan paid before he bought the house, and the house
that he rented was about the same as the one he bought.
So it seems that by buying a house he was actually ahead
because he would own the house in twelve or thirteen
years.
But whenever we seem to get something for
nothing, we may suspect that this is not the case.
The
following problems will explain this more clearly
:
1. Mr. Allan had $1500, which he paid when he
bought the house. At 5%, what was the yearly interest
on this amount? What was this for 12| years?
2. How much rent would Mr. AUan have paid in 12^
years at $70 a month? What would have been his net
cost of renting when he subtracted his interest on $1500,
for the same period, from his rent?
3. The house valued at $7500 (the lot was worth $500)
depreciated 3% a year.
How much was this per year?
What was the total depreciation in 12^ years?
4. Mr. Allan paid taxes on an average of $70 each year
on this property. How much did he pay in 12^ years?
5. The cost of repairs and decorating averaged $40 a
year. What did this amount to in 12^ years?
6. What is the sum of the items in problems 3, 4, and 5
plus the $1500 he paid down and the $60 monthly pay-
ments for 12^ years?
7. From the total in problem 6 subtract the depreci-
ated value of the property ($8000 -$2775). This re-
mainder, then, represents the cost of owning the house.
How does this compare with the rent in problem 2?
135

Fire Insurance
If you pay a certain sum each year to a fire insurance
company, the company will pay for any damage to your
house that may be caused by fire.
A written agreement
to this effect is called a fire insurance policy.
The insured, that is, the person who owns the insured
property, pays the insurance company a certain amount
called a premium. This premium is always stated as so
much per year per $100 of insurance.
1. Mr. Allan insured his house for
$6500, paying a premium of 50 cents per
$100. What was the yearly premium?
$6500
.50
$32.50
A company wiU insure your property for thiee years, if
you pay 2^ times the yearly premium, and for five years,
if you pay 4 times the yearly premium. On out-of-the-
way properties, such as farm buildings, a five-year policy
may be had for only 3 times the yearly premiima. All
these are called long-term policies.
2. If in problem 1, Mr. Allan had
taken out a three-year poHcy, his pre-
mium for this time would have been
2iX $32.50 -$81.25.
For a five-year term, what would his
premium have been?
136

Rate of Premiums in Proportion to Risk
Rates of premiums for fire insurance differ greatly for
different kinds of buildings and also in different cities.
In the same city the rate on obe building may be a few
cents per $100 and on another many times as much per
$100. The kind of fire protection also makes a great
difference in the cost of insurance. In one city this cost
may be twice as high as in another, due to difference in
the fire protection provided by the city.
In the case of Mr. Allan's insurance, the company
agreed to pay for any damage from fire to his house up to
$6500, but no more. If the house was damaged to the
extent of $100, the company would pay that, and ff the
house burned down completely, it would pay $6500,
provided the house was worth that much at the time it
burned. In no case would the company pay more than
the actual value of the property at the time that it
burned.
Fire insurance is carried on aU kinds of property:
furniture, books, machinery, hay, grain, liunber in limi-
ber yards, goods in stores and warehouses, ships at sea,
and so on.
Find the premiums required below. Use 2^ times the
yearly premium for 3 years and 4 times the yearly
premium for 5 years.
Face of
Policy
Kind of
T
Building
ITearly Rate Prem.
per $100 1 yr.
Prem.
3 yr.
Prem.
5 yr.
1. $8000 Frame house
$.44
—
—
—
2. $6500 Farm building
$.60
—
—
—
3. $15000 Brick garage
$.30
—
—
—
4. $20000- Brick building
$.26
—
—
—
5. $5000 Frame house
$.44
—
—
—
6. $17000- Brick house
$.26
—
—
—
137

Life Insurance
Mr. Allan is considering taking out a life insurance
policy. There are foin* kinds of life insurance policies.
In all cases, the insured* must pay the insin*ance com-
pany a yearly premium. The rate of premium is so
much per $1000. The amount of insurance taken out
and written in the poHcy is called the face of the poHcy.
1. Mr. Allan, who is 30 years old, may agree to pay
the company $23.50 at the beginning of each year as
long as he Hves. The company then agrees to pay $1000
when Mr. Allan dies.
This is an ordinary life poHcy.
How much would Mr. Allan pay on this poHcy in 20 yr.?
2. Or, Mr. AQan may agree to pay the company
$33.20 at the beginning of each year for twenty years, if
he Hves that long. The company then agrees to pay
$1000 when Mr. Allan dies.
Such a poHcy is called a
twenty-payment-life policy. How much would Mr.
Allan pay on this poHcy in 20 yr.?
3. Or, Mr. Allan may agree to pay the company
$48.80 at the beginning of each year for twenty years.
The company then agrees to pay $1000 at the end of
twenty years in case Mr. Allan Hves that long. If he
dies in less than twenty years, the company wiQ pay
$1000 at the time of his death. This agreement is called
an endowment poHcy. What would Mr. Allan pay on
this poHcy dining 20 yr.?
Under some circumstances Mr. AUan may insure his
life for 3, 5, or 10 years. If he dies diu'ing this time, the
face of the poHcy is paid by the company. But if he
Hves that long, the company pays nothing and he stops
paying premiums. Such a poHcy is caUed a term-in-
surance policy. The rate of premium on a term poHcy
is always low. It is often possible to change a term poHcy
into another kind of poHcy.
138

Rates of Premiums
The rates of premiums depend upon the age of the in-
sured and the kind of poHcy. The following are current
annual rates used by some large mutual companies.
In each case, the premium is given for a $1000 policy.
Age
Ordinary
20-Pay-
20-Year
10-Year
Life
ment Life Endowment Term
20
$18.50
$28.10
$47.50
$11.70
25
$20.70
$30.40
$48.10
$12.30
30
$23.50
$33.20
$48.80
$13.00
35
$27.00
$36.70
$50.00
$14.20
40
$31.70
$41.00
$51.80
$16.10
45
$38.00
$46.50
$54.80
$19.80
50
$46.60
$53.80
$59.60
$26.30
55
$58.30
$64.00
$67.60
$37.30
60
$74.60
$76.60
$78.48
$55.30
Use this table to find the annual premiimis below:
Age
Face of
Policy
Type of
Policy
Annual
Premium
1. 20
$5000
Ordinary Life
2. 30
$8000
20- Year Endowment
3. 45
$20000
20-Payment Life
4. 50
$10000
10- Year Term
5. 35
$10000
20-Payment Life
6. 50
$6000
Ordinary Life
7. 20
$12000
20- Year Endowment
Mutual life-insurance premiums are somewhat higher
than is necessary to carry on the business under ordinary
conditions. This makes the company safe in case of an
unusual epidemic causing many deaths. From year to
year the excess premiums are paid back to the policy
holder in the form of dividends.
139

Sight Work
1. On an ordinary life insurance policy, when is the
face of the policy paid? How long do premiums continue
to be paid?
2. On a twenty-payment life policy, when is the face
of the poHcy paid? How long do the premiums continue
to be paid?
3. For which kind of the poHcies in examples 1 and 2
is the premium the greater?
4. On an endowment policy, when is the face of the
poHcy paid? For how long do premiums continue?
5. On which pohcy is the premiimi higher, a twenty-
payment Ufe or a twenty-payment endowment?
6. One man at the age of thirty and another at the
age of fifty take out three-year term poHcies. Which one
do you think will pay the higher premium?
f
Topics for Discussion
1. Discuss the help that may come to a widow and
her children from insurance money (money paid by the
insurance company on an insurance policy).
2. A mutual hfe insurance company loans money on
farm mortgages. If the value of farms goes down and
the company cannot collect, who in the long run will lose
the money?
3. Do life insiwance companies ever fail to pay the
amounts due on an insurance poHcy? Have you ever
heard of such a company failing in business?
4. What are the advantages of the different kinds of
life insurance mentioned on page 138?
140

Problem Practice
1. A Persian rug is
billed to a dealer for
$350 with discounts of
30% and 10%. What
is the net price?
2.Atank7feet
wide, 11 feet long, and
4 feet deep will hold
how many gallons of
water?
3. How many pounds of milk are required to make
275 pounds of butterfat if the milk tests 4.2% butterfat?
4. Abin8feetby3^feetby5feetwiUholdhowmany
bushels of grain? (1 cu. ft.
=f bu.)
5. How many cubic yards of concrete are there ia a
garage floor 18 feet by 28 feet if it is 6 inches thick?
^. It is known that a certain automobile depreciates
in value 31 per cent the first year it is used. What is the
depreciation if the value at the beginning of the year was
$940?
^. What are the proceeds of a 6% note for $800 due in
6 months when discounted immediately at 6%?
—
9r A merchant sold farm machinery for $890 and took
a six-month note bearing interest at 7 per cent. Three
months later he discounted this note at 6 per cent.
What were the proceeds?
9. An agent sold goods for $745. His commission was
7 per cent. How much did he remit if he paid $21.75 for
freight and cartage?
10. Mr. Harris wants to invest a sinn of money at 4^%
to yield $900 per year. What amount must he invest?
141

Unit II. Lumber Measure. Compound Interest
The Meaning of Board Foot
12
,"/
^
<-6 -
Z^
f6"
7A
2'-
^2S?|
A board foot, the unit
of lumber measure,
is
equal to a piece of lumber
1 in. thick, 1 ft. wide, and
1 ft. long. A board that
is less than 1 inch thick is
considered as an inch
thick.
Each piece at the right
is one board foot (bd. ft.).
The thickness and
width of liunber are usually given in inches and the
length in, feet.
The size of a
board 1 in. thick, 10 in. wide, and
14 ft. long is written V X 10'' X 14',
read *'one by ten, 14 feet long."
The sign " means "inch" or
"inches."
The sign ' means
"foot" or "feet."
The sign X is
read "by."
1. Read the following sizes
for the drawings at the right:
2''x6''xr
r'xi2''xr
r'X6''X2'
r'X 4''X3'
2''X4''Xli'
25 pc. 2"X4''X16' means 25
pieces of linnber 2 in. thick, 4 in.
wide, and 16 ft. long. Read: "25
two by fours, 16 feet long."
3^
''h
<4^
^ QCSSPI
142

Measuring Lumber
1. Find the number of board feet
in a board 1 in. thick, 6 in. wide and
18 ft. long.
1
»
lX^X>8r=9
Change the width, 6 in., to ^ ft. and solve as shown
above.
2. Find the number of board feet in
a plank 2^'' X 10'' X 20'.
Change 10 in. to f ft.
|X|X20
To find the number of board feet in a piece of
lumber, multiply the thickness in inches by the
width in feet and by the length in feet.
3. State in words the dimensions of these pieces of
lumber: 1''X12"X12'
2"X8''X8'
4''X2"Xl6'
4. Find the nimnber of board feet in each of the pieces
described in problem 3.
5. How many board feet are there in a board ^ in. by
4 in. by 12 ft.? (Call the thickness 1 in.)
6. Oneboardis^in. by6in. by10ft., andanotheris
1in. by6in. by8ft.
Which board contains the larger
number of board feet?
Find the nimiber of board feet in each item given be-
low,
(pc. means piece or pieces.)
7.
2pc. r'Xl2''Xl2'
8. 10pc. i''X 6''X10'
9. 25 pc. VX 8'XW
10. 46pc. 2''x;iO''Xl4'
11. 16 pc. 2''X12''X12'
8pc. 2''X 6"X10^
12 pc.
V'X 9''xi6'
60 pc. 1V'X14''X14'
40 pc. 2''X16'^X18'
36 pc. 3"X12''X20'
143

Finding the Cost of Lumber
1. At $41.50 per M, what is the cost of 8 pieces of
lumber 2^ in. thick, 12 in. wide, and 16 ft. long? (Per
M means per thousand board feet.)
The solution is shown
at the right. To find the
cost, multiply $41 .50 by .32 .
Lumber of different
kinds is often bought from the same lumberyard. Find
the cost of each item and the total of the bill below:
8xf XlXl6 = 320
3204-1000= .32M
$41.50 X. 32 =$13.28
No. of
Board Price
Pieces
Dimensions
Feet per M Amount
2.
3.
4.
5.
6.
7.
8.
9.
6
1"X12"X12'
56
1"X12"X16'
24
2"X10"X18'
36
2"X10"X16'
74
2"X 4"X10'
6
4"X 6"X20'
6
4"X 6"X18'
12
4"X 4"X 8'
$34.60
-
--'
--'
\
$36.00
^c!^'^''°
$41.20
^'^^'^^
$41.20 $^^55" "^^
$32.50 V'^^7'
$28.80
'^^—
^
^
$28.80
*^7-
$34.40 ^—
1
II
10. Rule a sheet of paper as above and enter the fol-
lowing: 120 pieces, 1''X10"X14' at $46.20 per M; 75
pieces, 1" X8" X 10' at $39.50 per M; 18 pieces, 2^'^ X8" X
12' at $41.80 per M; 24 pieces, 3''
X 10'' X 14' at $46.90 per
M. Find cost of each item and the total.
144
i

Problem Practice
1. At 2^ cents per mile, what is the cost of a round-
trip railway ticket to a town 760 miles distant?
2. An empty milk can weighs 15.2 pounds.
If one
gallon of milk weighs 8.6 pounds, how much will this can
weigh when 6 gallons have been poured in?
3. At $9.45 a ton, what do 7500 lb. of coal cost?
4. At $1.65 per thousand cubic feet of gas, what is the
amount of a month's gas bill if the reading of the meter
was 37,930 cubic feet at the beginning of the month and
46,340 cubic feet at the end of the month?
5. Allowing 180 square feet for doors and windows,
find the number of square feet of surface in the walls and
ceiling of a room 36 feet long, 28 feet wide, and 9 feet
high.
6. What is the number of cubic feet in the room in
problem 5? If there are 42 persons in this room, how
many cubic feet of air space per person are there?
7. The average speed of a car in an automobile race
was 100 miles per hour. How many feet per second was
this speed?
8. Marjorie solved 19 problems correctly and failed
to solve 3 problems. What per cent of the total did she
solve? Find answer to the nearest whole per cent.
9. Goods were bought at the discount series 20%,
10%, 2%. This discount series is equal to what single
discount? (Use $100 as the gross price.)
10. Merchandise is advertised at a 35 per cent reduc-
tion.
What was the original price of a coat that is now
on sale for. $32.50?
145

Practice in Percentage
Change the following to per cents, correct to the
nearest one tenth of 1%:
-16
9
23
7
A5
13.
_9_
- •2^
TT
3T
125
64
27
47
211
14
16
1
3
2^
15
21
•
24^
~9~
43"
201
17
T4
T7
O
18
12
_8_
61
36.
.
9.
4
*>.
47"
~7"
45
303
55
113
TS
Change the following to decimals:
4. 9%
71%
^% 81% 109% 10.4%
5. i% .6%
1.1%
1|% 225% 4.25%
6. i% 5.5% 66|% .05% 575% 11.1%
Change the following to per cents:
7.
.8
.07
2.5
1.01
.002
4.15
. 018
8.4
12.3
.125
. 047
. 005
. 025
.857
Find percentage below correct to the nearest cent:
9.
5% of $9.75
13% of $12.07
4^% of $28.75
10. 17% of $8.09 6.3% of $19.45 621%, of $6750
Find what per cent
11. 60isof150
12isof5
8isof2100
12. 4.5isof18
35isof20
16isof720
13. 81isof96
25isof91
96isof24
Find the numbers missing below:
14. 36is10%oof
12 is 75%, of
19is5%,of
15. 50is4%of
42is 13%of
17is35%of
16. 9%oof87is
15 is
%of75 60 is 15%, of
17.
.5%of80is
31is40%of
7is %,of15
18. 20 is
%of16 16 is
%of20 20%of16is
19. 49is7%of_
.4%of120is_
12is.5%oof
20. 150%of6is
9is
%of5
25 is
%of30
21. 25%of25is _
12 is
%of6 48is 12%of_
146
^

Problem Practice
1. Coffee that sold last year for 24^ per pound is
selling now for 31 ff.
Find the per cent of increase.
2. A •suit that sells regularly for $55 is now on sale
for $44.50 . Find the per cent of reduction.
3. Our basketball team has won 9 of the 13 games
played. What per cent of the games has the team won?
4. Tom bought a suit on sale at 15% off for $17.
What was the regular price of the suit?
5. Helen found a $6 pair of shoes on sale at 25% off.
What was the reduced price of the shoes?
6. One year Fred raised 95 bu. of corn on an acre of
ground. The next year, his acre yielded 114 bu. What
was the per cent of increase?
7. Mr. Hill paid $1195 for his auto. After two years,
he sold it for $625. What was the per cent of decrease?
8. Eggs that sold for 49^ per dozen last winter are
now selling for 37^.
Find the per cent of decrease.
9. A realtor sold a store building for $87,250 on a
commission of 4^%. Find the amount of his commission
and of the net proceeds for the owner.
10. A dealer bought 35 overcoats listed at $48.50 each.
He received a trade discount of 25%. What was the net
cost of the overcoats?
11. A dealer paid $24 for a radio. For how much must
it be sold to aUow him a margin of 35%?
12. Find the amount due on a note for $3750 at 4^%
interest for 90 days.
13. A commission merchant received 5% commission
on the sale of 175 boxes of apples at $1.15 per box. Find
the amount of his commission and the net proceeds.
147

Interest on Savings Deposits
Perhaps you have had a savings account in a bank.
A savings account pays interest on money deposited in
it.
If this interest is not drawn out, it is added to the
principal that is drawing interest. The following prob-
lem will help you imderstand the way interest is figured:
1. $100 is deposited in a sav-
ings bank that pays 2% interest
compounded
semi-annually.
Find the amoimt due in 5 yr.
Interest at 2% computed
semi-annually means that the
bank pays 1% interest every 6
months.
The interest for the first 6
months is $1.00, which is added
to the principal making the
amount $101. Interest for the
next six months is 1% of $101,
or $1.01. This added to $101.00
makes the next amount $102.01.
Deposit
1st int.
.
$100.00
1.00
Amt
2nd int.
.
101.00
1.01
Amt
3rd int.
.
102.01
1.02
Amt.
4th int.
.
103.03
1.03
Amt
5th int.
.
104.06
1.04
Amt
6th int.
.
105.10
1.05
Amt
7th int.
.
106.15
1.06
Amt
8th int.
.
107.21
1.07
Amt
9th int.
.
.
108.28
1.08
Amt
10th int.
109.36
1.09
$110.45
The savings bank does not
pay interest on a fractional part
of a dollar.
Hence the interest
for the next 6 months is 1% of
$102.00 (not of $102.01).
Study the statement. It shows that the amount at
the end of 5 years wiQ be $110.45.
Since 2% interest on $100 for five years is $10, adding
the interest to the principal every 6 months makes a
difference of $.45 in the final amount. Interest paid by
the savings bank differs from ordinary compound interest
in that no interest is paid on fractional parts of a dollar.
148

Interest Compounded Annually
1. In a savings bank paying 1^% interest com-
pounded annually, $500 is deposited. What is the
amount at the end of 4
years?
Deposit
$500.00
Int., 1st year
7.50
Amt., 2nd year
507.50
Int., 2nd year
7.60
Amt., 3rd year
515.10
Int. , 3rd year
7.72
Amt., 4th year
522.82
Int., 4th year
7.83
Amt., end 4th yr. $530.65
Check the computa-
tions at the right. Note
that in finding the inter-
est for the second year,
the bank clerk figures
1^% of $507.50 as $7.60.
The bank does not put a
fraction of a cent on its
books, or pay interest on a fraction of a dollar.
Savings banks now pay low rates of interest—from one
to two per cent. Some years ago these rates were twice
as high as they are now.
Savings banks compute interest only on stated dates.
When interest is compounded annually, it is computed as
of January 1.
If it is compounded semiannually, the
dates are January 1 and July 1.
When compounded
quarterly, the dates are January 1, April 1, July 1, and
October 1.
These are called interest dates, and the
time intervals between them are caUed interest pe-
riods.
2. One hundred dollars is deposited in a savings bank
that pays 2% interest compounded annually. What is
the amount in 4 years?
3. Find the amount of $400 at 2% interest com-
poimded semiannually for 3 years.
4. One thousand dollars is deposited in a savings bank
paying 1^% interest compounded quarterly. What is
the amount at the end of 2 years?
149

Deposits and Withdrawals
Money may be deposited in a savings account at any
time and, in practice, it may be withdrawn at any time.
Usually there is a provision that the bank may require
notice of withdrawals a certain time in advance, but the
banks seldom enforce this provision.
The banks pay interest on the smallest amount on de-
posit during the interest period. This is illustrated in the
following problem:
Balance July 1
$396.40
Deposit July 13
84.60
Deposit Oct. 1
35.00
Balance Oct. 1
516.00
Withdrawal, Nov. 1 150.00
Balance Nov. 1
366.00
Deposit Dec. 1
240.00
Balance Dec. 1
606.00
Interest Jan. 1
3.66
Balance Jan. 1
$609.66
1. In
a
savings
bank paying 2% inter-
est compounded semi-
annually, Mr. Jones
made the deposits and
withdrawal shown at
the right.
The smallest
amount on deposit
during this period was
$366.00; 1% of this is $3.66 . Study the computation to
see if the given figures are correct.
2. Make a statement Uke the above for a bank paying
2^% compounded semiannually, using the following
figures: balance, Jan. 1 , $186.50; deposits: Feb. 1, $46.-
50; AprH 15, $110.00; June 1, $50.00; withdrawals:
March 1, $25.00; May 15, $40.00 .
3. Make a statement for the following, for a bank pay-
ing 2% compounded quarterly: balance, April 1, $743.00;
deposits: May 1, $160.00; June 10, $65.00; withdrawal:
May 15, $125.00.
4. Find the final amount in problem 3 with interest at
2% compounded annually.
150

CompQund Interest
The interest on any ordinary loan is due at the end of
each interest period and should be paid at that time. If
for any reason interest is not paid promptly when due, it
cannot be added to the principal and made to draw inter-
est unless it is definitely agreed that this may be done.
That is, a loan does not carry compound interest unless
that is agreed upon in advance.
There are many business problems, however, in which
compound interest is figured, as in the following:
1. A man bought a building
lot for $800 and sold it 4 years
later.
Figuring 4% interest on
the investment, find what this
amounted to by the time the lot
was sold.
In this case, compound inter-
est was figured since the interest
could not be collected at the end
of each year.
$800
1.04
832
1.04
865.28
1.04
899.8912
1.04
$935.886848
or $935.89
Multiplying $800 by 1.04 gives
the amount at the end of the first year.
Multiplying
$832 by 1.04 gives the amount at the end of the second
year, and so on.
2. What would be the amount in the problem above if
simple interest were used? In this case, what is the
difference in the amount at simple interest and at com-
poimd interest?
3. Six years ago I bought a timber lot for $10,000. At
3% interest compounded annually, what is the amount
of this investment now? Find answer to the nearest
cent. Find the difference in the amount at simple inter-
est and at compound interest.
151

Compound Interest Tables
In practice, compound interest tables are used in com-
puting compound interest. A part of such a table is
given on the opposite page. This table gives amounts
when the first investment is $1.00.
Let us consider the last column, which gives the
amounts when the rate of interest is 4%. The table
shows that the amount in one year will be $1.04, in two
years it will be $1.0816, in five years it will be $1.21665,
in ten years it will be $1.48024, while in twenty-five years
it wiU be $2.66584.
If we want to find the amount when the investment is
$500, for example, we multiply the amount in the table
by 500.
The best way to use this table is to regard the numbers
in the left column as the number of interest periods.
1. Using the table, find the amount of $800 with com-
pound interest at 4% for 4 years.
$1.16986
800
$935,888
or $935.89
In the table we find that the amount
of $1.00 at 4% for 4 years is $1.16986.
Multiplying by 800, we get $935,888,
or $935.89, which is the amount cor-
rect to the nearest cent. Compare this with the solution
on page 151.
2. Find the amount of $800 invested for 4 years at 4%
interest compounded semiannually.
We have 8 interest periods with 2%
for each period. In the 2% column
in the table we find that $1.00 in-
vested for 8 interest periods at 2% per
period amoimts to $1.17166.
152
$1.17166
800
$937,328
or $937.33

Compound Interest
Amount of $1 with Compound Interest
Years
i%
1%
^%
2%
3%
4%
1
1.00500 1.01000 1.01500 1.02000 1.03000 1.04000
2 1.01003 1.02010 1.03023 1.04040 1.06090 1.08160
3 1.01508 1.03030 1.04568 1.06121 1.09273 1.12486
4 1.02015 1.04060 1.06136 1.08243 1.12551 1.16986
5 1.02525 1.05101 1.07728 1.10408 1.15927 1.21665
6 1.03038 1.06152 1.09344 1.12616 1.19405 1.26532
7 1.03553 1.07214 1.10984 1.14869 1.22987 1.31593
8 1.04071 1.08286 1.12649 1.17166 1.26677 1.36857
9 1.04591 1.09369 1.14339 1.19509 1.30477 1.42331
10 1.05114 1.10462 1.16054 1.21899 1.34392 1.48024
15 1.07768 1.16097 1.25023 1.34587 1.55797 1.80094
20 1.10490 1.22019 1.34686 1.48595 1.80611 2.19112
25 1.13280 1.28243 1.45095 1.64061 2.09378 2.66584
In this table amounts are given correct to five deci-
mals. When the investment is $1000 or less, you can get
results correct to the nearest cent. When larger amounts
are involved, tables with a larger number of decimals are
used. Tables with eight places are commonly used.
1. Find the amount of $600 for 5 years at 2% com-
pounded annually.
2. Find the amount of $600 for 5 years at 2% com-
pounded semiannually.
3. Find the amount of $600 for 5 years at 2% com-
pounded quarterly. This is 20 interest periods with rate
4. Compare the amounts when $1200 is invested for
25 years at the different rates: i%, 1%, 1^%, 2%, 3%,
4%, interest being compounded annually in each case.
5. Find the amount of $1200 for 5 years at 4% com-
pounded quarterly.
153

fifth Self-fest
Test on Formulas
Complete the formulas. Solve the problems.
1. If in an example in division the divisor
is 34 and the quotient is 4, what is the divi-
dend?
2. If the area of a rectangle is 480 square
feet and the width is 10 feet, what is the
length?
3. If an airplane flies 175 miles per hour,
how long will it take to go 1400 miles?
4. An agent sold a building lot for $1200
and received $48 for selling. What was his
rate per cent commission?
5. Thevolumeofabox8in. deepand10
in. wide is 1280 cu. in.
What is the length?
6. If the principal is $400, the rate 5%,
and the interest $10, what is the time?
7. If a radio which costs $14.50 is sold
for $20, what margin does the dealer
have?
8. On an article which sold for $4.50
the margin was $1.25. What was the
cost to the dealer?
9. An article costing $9.25 was sold
for $13.75. Overhead was $2.85 . Find
the profit.
A=lw
St
p=hr
r=
V=lwd
/=_
i=prt
t=—
s = c-\-m
m=
s = c-\-m
c=
c-^o+p
10. At $12 per square yard, what is the cost of a rug 10
feet by 15 feet? Indicate the solution.
154

Test in Solving Problems
p 1. If 2 pounds of candy are divided equally among 8
girls, how many ounces does each girl get?
2. The sewing class had a piece of goods 12^ yards
long. They made 6 aprons, using f yard for each. How
many yards did they have left?
3. Mrs. Cole bought 2^ pounds of meat on Monday,
If pounds on Tuesday, 2f pounds on Thursday, and 3^
pounds on Saturday. With 4 persons in the family^ what
was the average amount per person per week?
4. Mr. Lodge bought a house for $5500 and rented it
for $55 a month. Repairs were $55 yearly; interest
charges, $275; taxes, $75; and depreciation, $135. The
net income from this house was what per cent of the cost?
5. Each pupil in a class contributed 5 cents for the
purchase of a Christmas basket, and the teacher contrib-
uted 25 cents.
The total contribution was $2. How
many pupils were there in this class?
6. At 84 cents a bushel, what was the value of a load
containing 7850 pounds of wheat?
7. A farm 240 rods by 320 rods was rented at a yearly
rate of $5.50 per acre. What was the rent per year?
8. A $24 article was sold for $4 cash and six $4
monthly payments.
What was the rate of interest?
9. At $42.50 per M, what is the cost of 144 pieces of
lumber 2'' X 12'' X 167
10. At 54 cents per $100, what is the yearly premium
on a fire insurance policy for $3500?
11. A man 25 years old took out an ordinary life in-
surance policy for $5000. If he Hves to be 75 years old,
what will be the total of his premiums, at the rate of
$20.70 per $1000?
155

Unit 12. Corporations. Stoc/cs and Bonds
Organizing a Small Corporation
Mr. Morton has been operating a furniture repair shop
and has been buying and selling household furniture.
His business has been growing, and so he needs more
space. He is now trying to organize a corporation, a
business company chartered by the state, for the purpose
of buying an adjoining lot and putting up on it the kind
of building that is needed. Mr. Morton has called in a
number of his friends to consider the forming of this
corporation.
1. They agree to form a corporation with capital stock
of $80,000, consisting of 800 shares at $100. Mr. Morton
contributes his present building valued at $40,000, and
$10,000 in cash. For this he gets 500 shares of stock.
We say that he sub-
scribes for 500 shares.
His friends subscribe
$30,000 to buy 300
shares.
Morton, property $40,000
Morton, cash
10,000
Others, cash
30,000
Total capital stock $
Application is then made to the secretary of state for
a charter.
This is granted and the corporation, called
Morton and Company, is formed. The extra money ob-
tained is used to buy the lot and to enlarge the build-
ing. What is the total capital stock of the corporation?
2. The total of the shares is called the capital stock
of the corporation. The value put on a share at the time
the corporation is formed is called the par value of the
shares.
Later, the shares may be sold for more or for
less than the par value. How many shares were there at
$100 par value?
156

Dividends on Corporation Stock
1. At the end of the first year in business, Morton and
Company find that after paying all expenses, including de-
preciation on its property, it has a profit of $5480. It
is decided that $5 per share shall be paid to the owners
of the 800 shares of stock. It is said that a dividend
of $5 per share is declared. The dividend takes 800 X $5,
or $4000, of the profit. The remaiader is called surplus,
to be put into the treasiu-y of the
corporation and used as may be
decided later.
How much was
this surplus?
Profit
$5480
Dividends 4000
Surplus $
The corporation sends an annual report to each stock-
holder showing a detailed account of its operations for
the year.
When a corporation has acciunulated a considerable
siu-plus, it may decide to pay out in dividends more than
its profit for the year.
2. Din-ing the second year, Morton and Company has
a profit of $7650. A dividend of $8 per share (an 8%
dividend) is declared. Make a statement as above
showing the amount of dividends and the surplus.
3. What is the total surplus of Morton and Company
at the end of the second year?
4. Mr. Morton receives a salary of $3600 and the
dividend from 500 shares of stock. Find his total income
for the second year.
5. During the third year in business, Morton and
Company has net earnings of $7200. At the end of the
year, a dividend of $10 (10% dividend) per share is de-
clared. What is the total of this dividend? How much
must be taken from the surplus to pay it? What is the
total surplus at the end of the third year?
157

Comparison of Partnership and Corporation
If two partners are in business together, they share
all profits and also all losses in a proportion that has been
agreed upon. Any debt of the partnership is really a
debt of each partner.
If one of the partners loses his
money, the other partners must pay all debts to the limit
of their abiHty.
One who buys a share of stock in a corporation simply
buys the right to a share of the profits it may make. He
may sell his share to anyone who will buy it, but he can-
not demand that the corporation buy it from him. The
corporation does not owe him anything, except that it
must pay him dividends as it does ether shareholders. If
there is no profit, the stockholders get nothing in return
for their investment.
If the business of the corporation fails, the stockholder
may lose what he paid for his shares, but usually he is
not liable for the debts of the corporation.
Partners in business usually conduct the business
themselves, but the stockholders of a corporation elect
oflScers of the corporation to conduct the business. The
largest stockholder of a corporation is often elected its
president.
1. A large corporation has outstanding 500,000 shares
of stock. Its profit in one year is $2,860,000. If a 4%
dividend is declared, how much does this corporation
carry to surplus?
2. What are the advantages and the disadvantages of
a corporation and of a partnership in business?
^
3. In which business organization is an owner liable
for aU debts contracted?
158

Corporation Bonds
When a corporation wants to obtain additional money
to put into its business, it may do this in several ways:
(1) The corporation may declare low dividends, thus put-
ting a large part of its earnings into surplus.
(2) Addi-
tional shares of stocgk may be issued and sold to the
public.
(3) It may issue bonds and sell them for cash.
A bond is really the promissory note of the corpora-
tion.
Such bonds usually run for a number of years
before maturity, sometimes for as much as fifty years or
more. The bond promises to pay a definite amount in
interest each year or oftener.
The owner of a bond can compel the company to pay
interest as it falls due, and to pay the face of the bond
when that is due.
If the company cannot make such
payments, it is bankrupt and may be forced out of
business.
A corporation may fail to pay dividends on stock for
any length of time and stiU not be bankrupt, but inter-
est on bonds must be paid.
1. To obtain money to expand its business fm*ther
at the end of the third year, Morton and Company sold
$50,000 in bonds bearing 5% interest. In one year its
profit was $13,360. Before paying any dividends it had
to pay $2500 interest on
Profit
$13,360
Interest on bonds 2,500
Dividend
8,000
Surplus
$
its bonds.
From the
remaining part of the
profit it then paid 10%
dividend on its 800
shares of stock. How much surplus remained after these
payments were made?
2. From problem 1 and page 157, find Morton and
Company's total surplus at the end of the fourth year.
159

Problem Practice
1. Two men rented a
pasture for $60. One man
pastured 7 horses and the
other 5 horses. How much
of the rent should each
man pay?
2. A corporation has
$100,000 in stock out-
standing. In one year it
shows a profit of $6840.
After paying a 5% dividend, how much is left to carry to
surplus?
3. In the next year the corporation in problem 2 had a
profit of $5250. If it paid 6% dividends, how much had
to be taken from surplus to pay this dividend?
4. A leather vest costing $10 is marked to sell for $15.
The overhead is $3.50. What per cent of the sale price
are the cost, the overhead, and the profit?
5. A dealer paid $225 for a used automobile. For how
much must he sell it to allow a 25% margin?
6. A retail dealer bought shoes for $42 per dozen pairs.
For how much per pair must he sell them to allow a
margin of 30%?
7. A house costing $5500 when new depreciates 3%
per year.
What will be the depreciated value of this
house when it is 15 years old?
8. Find the proceeds of a note for $1200 for 6 months
discounted at 5 per cent.
9. Find the proceeds of the note in problem 8 if it
bears interest at 6%.
160

Practice in Percentage
What per cent of 1 foot is each of the following?
1.
1 in.
6 in.
2 in.
4 in.
3 in.
8 in.
2. 9in.
5 in.
7 in.
10 in.
11 in.
18 in.
What per cent of 1 pound is each of the following?
3.8oz.
4 oz.
12 oz.
2 oz.
6 oz.
10 oz.
4.7oz.
14 oz.
1 oz.
3 oz.
5 oz.
11 oz.
5.9oz.
13 oz.
15 oz.
7^ oz.
f oz.
20 oz.
What per cent of 1 yard is each of the following?
6. 9in.
18 in.
27 in.
12 in.
24 in.
6 in.
7. 3in.
9 in.
15 in.
20 in.
30 in.
21 in.
8. 7in.
14 in.
28 in.
35 in.
8 in.
16 in.
9. 2in.
32 in.
33 in.
13 in.
17 in.
31 in.
Find the percentage in each of the following:
10.
1 80% of $965
4.9% of 1 200
^% of 600
11. 6.3% of $1 25
42i%o of 1 6.8
.5% of 750
12.
1 08% of $540
20% of 1 7.25
10% of24.5
13. 250% of $360
87^% of 5.68
12%of1.07
Change the following to per cents:
T4-2--9-7_l __5_ _8_J_9
7
-^^ '
20
10
8
16
12
25
40
TS
15 11.
OL
^l.
1J.
93.
15
11
±0.
I4
^2
'8
'5
^4
's
'3
16.
.05
.38
1.4
1.25
. 125
.625
17. .025
. 015
.0425
3.02
2.75
4.85
Find the interest on the following:
18. $640at5%for9mo.
$875 at 4^% for 6 mo.
19. $350at4%for 8mo.
$980at 3%for7mo.
20. $525 at 6% for 30 da.
$460 at 5% for 10 mo.
21. $750at2%for3yr.
$248 at 6% for 60 da.
22. $635at4%for 5mo.
$720 at 5% for 90 da.
161

Saving Money to Invest Safely
Mr. and Mrs. Howe have three children, Frank, Bob,
and Mary. They make a practice of saving from 20% to
25% of their income, because they know the importance
of saving money to be invested wisely for future use.
1. The Howes know that savings will be needed for
future needs, future emergencies, and old age.
Make a
list of other purposes for which a family should save a
part of its income.
2. Mr. Howe's salary has averaged $3600 for 10 years.
His accounts show an average saving of $750 per year.
What per cent of his earnings has been saved?
3. Frank has invested $60 in postal savings, $37.50
in a defense savings bond, and has deposits of $46.80 in a
savings bank. His total income from his allowance and
earnings for the past seven years has been $535.75. What
per cent of his income has he saved?
4. Mary invests 35^ per week in defense savings
stamps. What will be the total of her investment in two
years from now?
5. Bob has a paper and magazine route which pays
him $2.75 per week. If he saves 20% of this income, how
much will he save in one year?
6. Mr. Howe says the following offer the safest in-
vestments for savings: government bonds, savings bank
deposits, life insiu-ance, and productive land. Make a
short list of other investments which offer considerable
safety.
7. In what ways do certain forms of life insurance
help a person to save part of his income regularly?
8. Make a list of several plans which you beheve will
help people save a part of their earnings.
162

Postal Bavings Accounts
To encourage people to save money, our government
has established the postal savings system. The postal
savings accounts are handled by United States post
offices under the following regulations:
Persons 10 years old or over may open accounts.
Deposits may be made at any time by buying postal
savings certificates.
These are issued for amounts of $1,
$2, $5, $10, $50, $100, $200, and $500,
Certificates draw simple interest at 2% for each full
year. Unless caUed for earlier, this interest is paid when
deposits are withdrawn.
Deposits may be withdrawn at any time, together
with any interest payable.
Deposits by one person cannot exceed $2500.
Postal savings stamps at 10^ each may be bought
with amounts less than $1 A card to hold 10 stamps is
furnished free.
When filled, the card may be exchanged
for a $1 certificate, or for $1 cash.
You may obtain complete information on postal
savings by applying at any post office,
1. If you have $250 in a postal savings account, how
much interest will this earn in 1 year? If you add this
interest to your account, how much interest will be due at
the end of the second year?
2. Mr. and Mrs. Owen have each deposited $2500
in postal savings. Find their total yearly interest,
3. Can the Owens depQsit enough money in postal
savings to make their monthly income $10? Why?
163

United States Savings Bonds
These bonds are sold at all post offices and banks,
obtained. There are
but we shall describe
Issue
Maturity
Price
Value
$18.75
$25.00
37.50
50.00
75.00
100.00
375.00
500.00
750.00 1000.00
where full information may be
several series of savings bonds,
only the Series E bonds.
The issue prices and the ma-
turity values of this series are
shown at the right. The re-
demption values of the $100
bond are shown in the second
box and are given on every
bond.
Interest is not paid on these
bonds from year to year, but
acciunulates to increase their
value to maturity.
1. What per cent will an
investment in Series E savings
bonds increase in 10 yr.?
2. What is the maturity
value of 12 bonds costing
$37.50 each?
3. Find the cash value of
eight $50 bonds held 5^ yr.
4. If Mr. Price invests $900
in savings bonds, what is their
matiu*ity value?
5. If the maturity value of
bonds costing $900 could be
reinvested in such bonds, what
would be their matm-ity value?
What per cent would the griginal investment of $900
increase in 20 years?
164
First year $75.00
Ito ^yr. 75.50
lite 2yr. 76.00
2 to 21 yr. 76.50
2^ to
3yr. 77.00
3 to 3iyr. 78.00
3ito 4yr. 79.00
4 to 41 yr. 80.00
41 to
5yr. 81.00
5 to 5iyr. 82.00
5^ to
6yr. 83.00
6 to 6iyr. 84.00
e^to 7yr. 86.00
7 to 71 yr. 88.00
7ito 8yr. 90.00
8 to 8iyr. 92.00
8^ to
9yr. 94.00
9 to 9iyr. 96.00
91 to 10 yr. 98.00
Maturity
100.00

United States Savings Bonds
For a bond with a $25 maturity value the figures are,
of course, one fourth of those given in the table on the
opposite page; for $50 they are one half, and so on.
The problem of finding the actual rate of mterest
paid by these bonds if held to maturity (or for any other
length of time) is much too difficult for us at present.
If held to maturity, the rate of interest compounded
annually is very nearly 2.9%. The longer the bonds are
held, the higher is the rate of interest that they pay.
The government wants them to be held as close to the
ten years as possible.
Other series of these savings bonds pay interest
yearly. The rate of interest of the other series is a Httle
less than the 2.9% mentioned above, but greater than
the rate that will be paid on the Series E bonds if they
are held only five years.
1. Write a schedule like that on page 164 giving the
redemption values of a $37.50 bond.
2. Write similar schedules for bonds whose issue
prices are $18.75, $375.00, $750.00.
3. If $75 is invested at 3% compounded annually,
what is the amount in 10 years (use table, page 153)?
Compare this amount with the maturity value given in
the schedule on the opposite page. By how much does
your result differ from $100?
4. In problem 3, use 2% instead of 3%. By how much
does your result differ from $100? Can you judge from
the answers in these problems whether the rate earned
by the savings bonds is nearer 2% or 3%? Is it much
nearer one than the other? How do you know?
165

Problem Practice
1. Find the amount of $500 for 10 years at 4%
compounded annually, (Use the table on page 153.)
2. Find the amount of $500 for 10 years at 4% com-
pounded semiannually.
3. X^rhat are the net proceeds of a 60-day note for
$625 discounted at 6%?
4. Merchandise bought for $1800 is sold for $3000.
The overhead is 31%. What is the per cent of profit?
5. Find the interest on $432 for 8 months at 5%.
6. What is the net amount of a bill of goods amount-
ing to $3780, with discounts of 33^% and 5%?
7. An automobile dealer pays $920 for a car and sells
it for $1230. His overhead is $184. Find the rate of
profit to the nearest tenth of 1%.
8. A bin that holds 168 cubic feet is filled with coal
which occupies 42 cubic feet to the ton.
At $11 per ton,
what is the cost of the coal?
9. Find the total number of board feet in the follow-
ing: 10 pieces, l''XlO''Xl2'; 24 pieces, l"Xl2''Xl4';
16 pieces, 2"x8''Xl6'; 40 pieces, 2"x4"XlO'; 16 pieces,
r X6'' XlO'.
At $34.60 per M, what is the cost of this
lumber?
10. A farmer has a debt of $2500 at 6% interest on his
farm, on which he pays $300 every 6 months. Part of
each payment is for the interest on the unpaid balance
for the preceding 6 months, and the rest is to be appHed
on the principal. Write a complete schedule of pay-
ments.
11. At $31.25 per $1000, what is the annual premium
on a 20-payment life insurance poHcy for $10,000?
166

Problem Practice
1. A radio with a cash price of $70 was paid for with
a $10 down payment and seven $10 monthly payments.
What was the dollar cost of this credit? What was the
rate of interest actually paid?
2. A corporation having $200,000 outstanding stock
and $100,000 in 6% bonds made a profit of $10,460.
The balance, after paying interest on the bonds, was
carried to surplus.
How much was carried to surplus
that year? Was any dividend paid that year?
3. The next year the corporation in problem 2 had a
profit of $18,200. After paying interest on the bonds,
how much did it have left? After paying 6% dividend,
how much did it have left to carry to surplus? What
was the surplus for the two years?
4. The buildings owned by Roberts and Company
cost $65,000 when new.
At 2^%, what is the yearly
depreciation? At this rate how^ much will these build-
ings be worth when they are 20 years old?
5. Roberts and Company carried $35,000 fire in-
surance.
At 35 cents per $100, what was the yearly
premium on this insurance?
6. If Roberts and Company were to take out a
three-year policy, what would be the premiimi for the
three years? (The three-year policy was 2^ times the
yearly premium.) At this rate, what would be their
average cost per year for fire insurance?
7. By making certain changes, Roberts and Company
were able to have their fire insurance rate reduced to 30
cents per $100. How much was saved per year by mak-
ing these changes, as compared with the charges in
problem 6?
167

Unit 13. Stocks md Bonds. Graphs
The Stock Exchange
Tom Walker's father
is a practicing physician.
He has some money that
he can spare and he wants
to invest it so that it will
earn some interest.
He
can put it in the local
savings bank, which now
pays only 1%, or he can
put it in postal savings,
which pays 2%.
His banker tells Dr.
Walker that he can buy
shares of stock that have
been paying dividends for
a long time. The banker
says, **At the price this
stock is selling now, it
will make about 6%."
So Dr. Walker requests
the banker to buy some
of this stock for him.
But who has shares of this stock for sale? Where can
the banker buy it? The banker says that this stock can
be bought any business day on the stock exchange.
There are many stock exchanges in this country, but
by far the most important is the New York Stock
Exchange. The banker wires his broker in New York,
and in a few minutes the stock has been bought.
168

Buying Stocks and Bonds
Stocks and bonds can be bought on any business day.
If you have an account in a bank, the banker will
advise you and will give you the prices at which you can
buy or sell stocks and bonds. In the daily papers there
is a financial page on which are given the previous day's
prices of a large number of different stocks and bonds
on the New York Stock
Exchange.
At the right is a list
from such a page show-
ing prices of ten different
stocks.
In the news-
paper the names of the
companies are given.
The prices per share
are given in dollars and
fractions of a dollar.
The only fractions used
^^68^>T?¥>2^?8^?T?
^Ild 3^ .
Shares are not sold at $41.10 or $41.15, but at $41^,
$41^ and so on.
The smallest amount that a price per
share can change is |^ of a dollar.
Sight Work
1. What is the difference in cents between the *^igh"
and ''low" in stock (1) in the above list?
2. In the above Ust, what is the greatest difference
between the high and the low of any stock? What is
the smallest difference?
3. A man bought 100 shares of stock (1), paying the
lowest price given.
What did these shares cost him?
169
(1)
High Low Close
41|
40| 4H
(2) 154| 153f 154|
(3)
86i
85f
861
(4)
25
24i
25
(5) 158f 158
158f
(6)
57
56
56|
(7)
491
49
491
(8)
2f
2i
2f
(9)
16|
161
16|
(10)
35f
341
35|

Brokers and Brokerage
Jane Arnold's father needed some cash to build a
house. He owned stock that was selling for a good price,
and so he requested his banker to sell it for him.
Ina
few minutes the stock was sold and the proceeds of the
sale were put to the credit of Mr. Arnold in his local
bank.
The actual purchase and the sale in such transactions
are made at any of our numerous stock exchanges.
Those who do the trading on the stock exchange are
called brokers, and the pay that they get for their
work is called brokerage. The rate of brokerage has
been changing from time to time, and the complete
schedule of rates in brokerage is somewhat complicated.
In this book the brokerage to be used is stated in each
problem.
1. Find the cost of 25 shares of stock bought at 56^
($56.25 per share); the brokerage is 28 cents per share.
Explain and check
the work in the box
at the right.
Find
the
cost,
brokerage, and gross cost below:
25 shares at 56^ $1406.25
Brokerage at 28^
7.00
Gross cost
$1413.25
Number Market
Shares
Price
100
131
2. 100
861
3.
70
341
4. 100
71
1
5. 150
2U
6. 100
112|
7. 200
18i
Brokerage Broker-
Gross
Cost per Share
age
Cost
$1375 121^
$12.50 $1387.50
_
20f*
_
_
_
15!^
_
_
_
mi
_
_
_
12is^
_
_
_
25^
_
_
_
mi
_
_
170

y
Selling Stock
When sales are made on the exchange, the brokerage
is deducted to find the net proceeds.
1. Fifty shares of stock are sold at 37f ($37.62^ per
share). Th e brokerage
per share.
;t proceeds.
1
is 22 cents
Find the n(
50 shares at 37f $1881.25
Brokerage at 22^
11 .00
Explain the work at
4-1^ _
^t ~"l_ J.
Net proceeds
$1870.25
1
the right.
Find the sale, brokerag e, and net proceeds below:
Number Market
Brokerage Broker-
Net
Shares
Price
Sale per Share
age
Proceeds
2.
250
41|
_
15?;
_
_
3.
75
861
20?;
4.
50
158|
25?;
_
_
5.
150
49i
_
17?;
6.
300
2|
m_
_
Bonds are sold through the exchanges exactly Hke
stocks. Brokerage is charged at so much per $1000 par
value of the bonds.
Stocks and bonds, but more frequently stocks, are
often bought with the expectation that the prices will go
up so they can be sold at a gain.
Of course, if the price
goes down there will be a loss.
Buying stocks in the hope
of selling at a higher price is called speculation, or
quite often playing the market.
Speculators sometimes make contracts to deliver
certain stocks at a future date at a given price.
One
who makes such a contract expects that at the future
date the market price will be lower than that at which
he has agreed to sell.
171

Buying and Selling Stocks
1. A man bought 150 shares at 47f and later sold
them at 49f per share.
Allowing brokerage at 15^;^ per
share both for buying and selling, find his net gain.
Explain the work
shown at the right.
Can you think of a
shorter way of solv-
ing this problem?
Cost, 150 shares at 47| $7162.50
Brokerage at 15«f
22.50
Gross cost
$7185.00
Sale, 150 shares at 49| $7481.25
22.50
Brokerage at 15 <f
Net proceeds
Gain
$7458.75
$273.75
What was
the
gross gain per share
(49| - 47|)?
What
was the total brokerage per share?
2. Two hundred shares were bought at 87f and sold at
87f. Allowing bro-
kerage at 17^ for buy-
ing and seUing, find
the amount of gain
or loss.
Explain the work
at the right.
Cost, 200 shares at 87| $17550
Brokerage at 17^
Gross cost
34
$17584
Sale, 200 shares at 87| $17575
Brokerage at 17^
34
Loss
$17541
$43
Why was there a loss even when the speculator sold
at a higher price than he paid?
Find the gain or loss in the following:
Number Buying
Selling Brokerage Gain
Shares
Price
Price
per Share or Loss
3. 300
4H
43
4. 200
67|
68i
5. 100
86i
92J,
6.
75
16|
14i
7. 600
141|
137|
15(z!
20(i
22(4
18?;
25^
172

Sight Work
1. What is the cost of 10 shares of stock at 92?
2. What is the brokerage on 50 shares of stock at 20c
a share?
3. Disregarding brokerage, find the loss on 10 shares
bought at 78^ and sold at 57^.
4. The price of a dresser is $40. What will be the
price after an increase of 15%?
5. A camp stove costing $14 is sold at a margin of
30%. What is the seUing price?
6. What is the profit on the stove mentioned in
problem 5, at 10%? What is the overhead? What is
the per cent of overhead?
7. Goods listed at $60 are sold at discounts of 33^%
and 10%. What is the net price?
8. At $10 per ton, what is the cost of 4500 pounds of
coal? -
9. What is the amount due on a note for $500 for 8
months at 6%?
10. What are the net proceeds of a note for $500 dis-
coimted at 6% for 8 months?
11. What is the length of one side of a square court
containing 64 square yards?
12. Merchandise costing $100 is marked to sell at
100% above cost. What is the per cent of margin?
13. Mr. Hastings buys 100 shares of stock at 98:^ and
later seUs them at 95. He pays 20<li per share for buying
and also for selling. How much does he lose?
14. At $30 per M, what is the cost of 60 planks, each
2 inches thick, 12 inches wide, and 16 feet long?
173

Uses of Graphs. Business Barometer
In a recent number of Nation's Business, published
by the United States Chamber of Commerce, the follow-
ing graph appeared:
PERCENT
BAROMETER OF BUSINESS ACTIVITY per cent
1935
The level of business activity for the years 1926-1930
is taken as the base (100%). From this graph you get
a clear impression of our business activity for 1935-41 .
In a recent issue of Newsweek, the following graph
appeared. In this graph the wages in our factories are
represented in cents per horn- for the last half of 1940
and the first half of 1941.
CENTS
75
CENTS
75
70
65
FACTORY HOURLY WAGE RATES- 90 INDUSTRIES,
U. S. DEPT OF LABOR
^^*
. ^ ^ESTIMATED
70
65
JUNE JULY AUG. SEPTOCT NOV. DEC. JAN . FEB. MAR. APR. MAY JUNE
1, Make a summary of the first graph showing the
per cent at the beginning of each year, 1935 to 1941.
About what per cent was the 1941 figure of the 1935
figure?
2. Make a similar summary for the second graph.
What per cent was April, 1941, of June, 1940?
174

Changes in the Prices of Stocks
Many people speculate
in stocks and bonds.
If
there is no change in the
price of these securities,
there is neither gain nor
loss from this speculation,
except loss in the payment
of the brokerage.
Are there great changes
in the prices of stocks and
bonds? The table at the
right answers this question
for the years 1925 to 1937.
The figures given are aver-
ages on the New York Stock Exchange. Many stocks
changed much less than these averages, while others
changed a great deal
more.
Aver. Prices
Year
Stocks Bonds
1925
$62
$95
1926
70
96
1927
66
96
1928
76
98
1929
89
100
1930
57
96
1931
38
96
1932
20
95
1933
17
77
1934
26
83
1935
26
83
1936
36
91
1937
44
97
The graph repre-
sents the change in the
price of stocks.
1. Construct a
graph like the one at
the right to represent
the change in the price
of bonds for the years
1925-37.
90
80
70
6o
so
uo
30
20
lO
»0'OKeoO.O --«S«n'!»'«OOK
CNCNCN(s(Nnn<onnoncn
O'O OO OwOO« CK(>0 ooo
2. During
which
years from 1925 to
1937 was there a good chance to make money by specu-
lating on the stock market? During which years was
there great chance for loss?
175

Depreciation
1. A machine costing $10,000 when new was estimated
to depreciate 8^% (one twelfth) of its value each year.
When this machine was 10 years old, it was sold for scrap,
and a new machine put in its place. What per cent was
the scrap value of the
original cost of the ma-
chine? How much was
this in dollars?
$10,000
$ 8,000
S 6,000
S 4,000
S 2,000
The graph at the right
shows the value of this
^
'
'"
machine at any time during its use.
3456789 lO
Note that this graph is a straight line.
It is for this
reason that this method for figuring depreciation is called
straight line depreciationk
2. It is figured that a large truck depreciates each
year one sixth of its value when new. A truck is bought
for $3600. Construct a line graph representing its value
up to the time when it is 5 years old. What probably
will become of the truck then?
3. A school building costing $100,000 depreciates
each year 2^% of its value when new. Construct a line
graph representing its value up to the time when it is 30
years old.
4. Each year the board of education makes a pubUc
statement of the value of property in its care.
How do
you suppose the board determines from year to year the
value of this property?
5. Mr. Jones built a house costing $6000 on his $1000
lot.
He figured depreciation at 3% a year.
Make a
schedule of the depreciation of the house for the first ten
years, and construct a line graph showing this.
176

Family Budgets
1. A family with a yearly income of $3000 makes a
budget as shown below. To make a circle graph, we find
the per cent of the whole income devoted to each piu*-
pose. Then we know what per cent of the 360° in the
circle must be given to each item. Use a protractor.
Find the per cent of the total set aside for each pur-
pose. Since 1% of 360° is 3.6°, we multiply 3.6° by the
rates per cent. The rates should be found to the nearest
whole per cent and the angles to the nearest degree.
Per
De-
Purpose
Amt. Cent
gree
Shelter
$540 18% 65°
Food
600 20% 72°
Clothing
360 12% 43°
Operating
300 10% 36°
Advancement
450 15% 54°
Automobile
420 • 14% 50°
Savings
330 11% 40°
Food
20%
12% ^
Clothing
Shelter
l87o
[Operatin
/o%
15%
'Advance
ment
Savings
11%
Auto"
/4%
2. Construct a circle graph representing the family
budget for two persons given on page 67.
3. Construct a circle graph representing the family
budget given in problem 2 on page 64.
4. A class of 34 pupils took a test of 12 problems.
The correct answers are shown in the table below:
No. of pupils
1
3
4
7
8
5
3
2
1
Correct Answers 4
5
6
7
8
9
101112
Construct a bar graph show-
ing the distribution of grades of
these pupils.
The first part of
the graph is shown at the right.
What does this indicate?
177
T
o
'
1
11
11
111
i 23U567a9IOII

Profit and Loss
Sales
Cost
Margin
1.Inoneyeara
merchant's sales, cost,
margin, overhead, and
profit were as shown
at the right.
The
graph below explains
this division even more clearly
make this graph.
$71,480 100.0%
54,870 76.8%
16,610 23.2%
Overhead 14,130 19.8%
Profit
$ 2,480 3.4%
Tell how you would
Cost 76.8%
Overheadl9-8%
Margin
Construct a bar graph for each of the following:
Retail selling 3. Retail
4. Cash and carry
furniture:
Sales
100%
Cost
63%
Overhead 34%
Profit
_
of milk:
Sales
100%
Cost
49%
Overhead 48%
Profit
_
groceries:
Sales
100%
Cost
81%
Overhead 16%
Profit
_
5. In a small country store the sales for a year were
$9364.50, the cost of goods was $6486.50, and the over-
head was $2739.
Make a statement and a bar graph for this problem
similar to those in problems 1, 2 , 3 , and 4.
6. The number of children at-
tending school in a smaU town for 7
successive years is shown at the right.
Make a bar graph representing
this attendance.
Before construct-
ing the graph, round off each number
to tens: that is, 380, 400, 420, and so
on.
178
1934 384
1935 398
1936 416
1937 438
1938 424
1939 473
1940 451

Problems
1. An art dealer's sales
were $120,000 and his
overhead was $22,400.
His overhead was what
per cent of his sales? Find
answer to nearest tenth
of 1%.
2. The art
dealer's
goods in problem 1 cost
him $88,340. His profit
was what per cent of his sales? Make up a statement of
his rate per cent, margin, and profit.
3. Mr. Swartz sold his farm to Mr. Smith, who gave a
mortgage to secm-e a note for $16,000 bearing 5% in-
terest, payable annually. How much interest did Mr.
Smith pay each year?
4. Mr. Worden owns a city building on which there
is a debt of $45,000 with interest at 5^%. How much
does the interest amount to per month?
5. Mr. Rogers bought 50 shares of stock at 90^ and
paid 20 cents per share brokerage. Later he sold these
shares at 102f and paid 25 cents per share brokerage.
How much profit did he make?
6. Mr. Watson borrowed $35,000 at 6% interest. He
paid $500 a month to apply on the interest and principal.
There was interest each month at the rate of ^% of the
unpaid principal. Complete schedule below for 6 months:
Unpaid
Total
Payment on
Principal
Payment
Interest
Principal
\.,. fS.l k
$35,000
$34,675
$34,348.38
$500
$500
$175
$173.38
179
$325.00
$326.62

Sixth Self-Test
Test in the Four Fundamentals
Write in columns and add or subtract as indicated:
1. 58.74+3.968+534+0.096+.962+9.6+960
2. 43.7+896+.543+6.85+40.7+4.68+9.107
3. 7.194+66.93+890+.734+6953+8061 +.472
4. 400+5.981 +.495+. 068+3060+ 1.88+23.3
5. 1 .38+9.683+48.7+6.34+830+5.62+35.17
6. 5000-4871
7.49-3 .578
.31 4 -.2974
7. 143.16-89.39
.97 -.049
5050-4949
8. 7.51 -6 .788
31-21 .64
1.54 -. 098
9. Multiply 3764 by each of the numbers 56, 83, 97,
286, 513, and 694.
10. Multiply 87.9 by 17.4, .58, .0 35, and 908.
11. Divide 7549 by each of the numbers 46, 54, 282,
and 595. Give quotients and remainders.
12. Find quotients correct to two decimal places.
85.3^5.7
31 .9 H- 2.46
588^67.4
595-r- 8.9
9.87^187
6.894 h- 0.95
Add or subtract the following as indicated:
13. H+ 6|+2i
I9I+8I+7A
14. 8|+17|+9f
2|+5|+2i
15. 8I-3J
19f-17A
2f-1f
Multiply the following:
16.
41X1|
16iX2i
3iX4i
1|X1|
17. 32^X61
19iXA
42iXl|
3HX2|
Divide the following:
18.
4i-1i
5|^2i
161^11
721^ U
19. 48iH-3i
.
25^31
48fH-12
105 4-
7i
180

Test in Problems without Numbers
1. Given the number of units that are bought and the
price per unit, how do you find the cost?
2. If the cost and the number of units are given, how
do you find the price?
3. Given the speed and the time, how do you find the
distance?
4. Given the area and the width of a rectangle, how
do you find the length?
5. Given the base and the rate, how do you find the
percentage?
6. Given the rate and the percentage, how do you
find the base?
7. Given the length, width, and depth of a rectan-
gular solid, how do you find the volume?
8. Given the volume, length, and width of a rec-
tangle, how do you find the depth?
9. If principal, rate, and time are given, how do you
find the interest?
10. If the amount of a sale and the rate of commission
are given, how do you find the commission? How do
you find the net proceeds?
11. If the selling price and the cost are given, how do
you find the margin?
12. If the margin and the overhead are given, how do
you find the profit?
13. If an investment and the income from it are given,
how do you find the rate of income?
181

Problem Test
Work the following problems, doing as much of the
figuring as possible without pencil and paper.
1. At 55 bushels of corn to the acre, how many bushels
will be harvested from a field containing 70 acres?
2. At $9.75 per ton, how much did John's uncle pay
for 6000 pounds of coal?
3. A 30-acre field produced 465 bushels of wheat.
What was the average yield per acre?
4. If you buy 10 yards of muslin at 12^ cents a yard,
how much change should you receive from $2?
5. Find the total surface of a cube whose
edges are 8 inches.
Reduce this to square
feet. Is the solution indicated at the right
correct?
6X8X8
144
6. What is the perimeter (distance around) a triangle
whose sides are 2^ feet, 4f feet, and S^ feet?
7. A man drove 80 miles in 2 hours and 100 miles in 3
hours. What was his average speed for the 5 hours?
8. The fuU fare between two cities is $17.50. What is
the cost of 3 half-fare tickets between these cities?
9. James weighs 64^ pounds and Henry weighs 68^
pounds. Find their average weight.
10. How many square yards are there in a garage floor
that is 211 feet by 30 feet?
11. How many cubic yards of sand will be required to
fiUaboxthatis6feetlong,3feetwide,and1foot6
inches deep?
12. If a train travels 48 miles per hour, what fractional
part of a mile does it go in one minute?
182

Problem Test
1. A farmer sold four loads of hay weighing 2750
pounds, 2640 pounds, 2130 pounds, and 2480 pounds.
At $18 a ton, what did he get for this hay?
2. How many square yards of plastering are there in
the waUs and ceiling of a room 30 feet long, 21 feet wide,
and 9^ feet high? Deduct 16 square yards for openings
in the walls.
3. At $27.50 per M, what is the cost of 275 boards,
each 1 inch thick, 10 inches wide, and 16 feet long?
4. A farm 240 rods wide and 320 rods long was
rented at $6.25 per acre.
What was the rent for this
farm for one year?
5. Last year Robert earned $2 each week for 52
weeks.
He saved $58. The amount saved was what
per cent of the amount earned? Find answer to the
nearest whole per cent.
6. A man invests $12,500 and from it gets a yearly
income of $1000. What rate of interest does he get from
this investment?
7. A certain grade of milk contains 4.6% butterfat.
How many pounds of butterfat are there in one gallon of
this milk? Find answer to the nearest hundredth of a
pound.
8. A dealer bought a rug Hsted at $500 with discoimts
of 30% and 10%. What did he pay for the rug?
9. A table bought by the dealer for $60 was marked so
astosellatamarginof40%. Thenitwassoldata
reduction of 25% from the marked price.
For how much
was it sold?
10. Find the interest on $15,000 for 75 days at 4i%.
183
#

Unit /4. Cost of Local and State Governments
Why Taxes are Necessary
In your course in civics, you have learned that we
have three divisions of government to support: local,
state, and federal or national.
Local governments are those of the county, city or
town, and school. You have also learned that each of
these governments supplies many needs and services far
more cheaply and effectively than we could provide
them for ourselves. Governments need a vast amount of
money to pay for all of the things that they do for us.
We share the expense of these services by paying taxes.
In order to know how much money must be raised by
taxes, each government makes an annual budget, or list
of its probable expenses. This budget includes the needs
of each department for the coming year.
On the opposite page are given the annual budgets of
a county with a population of 37,000 and a city in this
county with a population of 23,000.
184

Budgets for County and City
County
City
General
$234,395.00 General
$182,941.00
Roads
98,563.00
Streets
36,095.00
Bridges
15,126.00 Library
19,804.50
Poor Fund
114,714.00 Parks
13,200.00
County fair
12,167.01 Band
2,140.00
Airport
27,830.00
Interest
Library
11,692.00
and debt
27,520.00
Interest and debt
94,246.00
Total
_
Total
—
City schools
County high school
Smaller schools
Other towns
Total
$268,530
147,820
194,600
24,890
Besides these expend-
itures,
there were ex-
penditures for the city
schools and for a county
high school, as shown at
the right.
There were
also some smaller schools outside the main city with a
total expenditure of $194,600, and other town govern-
ments costing in all, $24,890.
1. Find the totals of the budgets for the county and
city, as given above.
2. Find the sum of the cost of city schools, county
high school, smaller schools, and of other town govern-
ments. Then find the cost of all local governments.
3. Find the per capita cost of local governments in
this county. Divide the total cost by 37,000. To divide
by 37,000, point off three places in the dividend and
then diyide by 37. Find answer to the nearest cent.
4. What is the per capita cost of government for the
city given above, if the city population is 23,000? Fiad
answer to the nearest cent.
5. What per cent of the total budget in problem 2
was spent for libraries?
185

Costs of Local Governments
In a recent year, the total cost of all local governments
in the United States was about 6.6 billion dollars.
At
that time the population was 125,000,000, and so this
made the average per capita expenditure about $52.80
for local governments.
This means that if every man, woman, and child in
the United States had paid $52.80, this would have been
sufficient for all expenditures of our local government for
that year.
The more accurate cost qf local government that year
was $6,643,982,000.
1. How would you divide this figure by 125,000,000?
You round off the dividend to
,
and then divide by
Prove the quotient, $52.80, given above.
There are many ways in which governments levy
taxes to obtain the money that they need. The most
important kind of tax from which local governments get
their income, or revenue, is what is called a property-
tax. That is the only tax we shall study here.
The property tax really consists of two kinds: tax on
real estate (land and buildings), and tax on personal
property (any property other than real estate).
In each county there is an official, caUed the assessor,
whose duty it is to determine the value of the property
owned by each individual or corporation in the county.
2. Examine the illustration on page 184 and make a
list of several of the important items for which this vast
amount of money was spent. Which items do you think
were the most important?
186

The Tax Rate
The assessor furnishes a Hst of the valuation of all
taxable property, and the total of this Hst. The city
council or the county commissioners have previously
determined how much money must be raised from prop-
erty taxes.
The next step is to find the tax rate.
The following
problem will illustrate:
.0183 = 1 .83%
15,000)275.0000
1. In a small city,
with an assessed valu-
ation of $15,000,000, a tax of $275,000 is to be raised.
Find the rate to the nearest hundredth of one per cent.
We must divide 275,000 by 15,000,000. To simplify,
we omit three zeros in both divisor and dividend. The
answer is 1.83%. This rate does not include any pos-
sible loss in collection.
2. If the assessed valuation is $27,500,000 and the
property tax to be raised is $325,000, what is the rate?
Find rate to the nearest tenth of one per cent above the
actual rate found in the division.
Using the rate found in problem 2, find the tax in each
of the following:
Assessed
Assessed
Valuation
Tax
Valuation
Tax
3. $7800
_
$44500
_
4. $2400
_
$11600
'
_
5. $18000
_
$39500
_
6. A man owns a house valued by the assessor at
$5600, a small store valued at $15,000, and personal
property valued at $3400. Find his total property tax
if the tax rate is 2.3%.
187

The Tax Table
In a small town the assessor's valuation of real and
personal property was $5,840,000, and it was decided to
raise $150,000 from property taxes.
By dividing, he
found that the rate had to^ be 2.568%. To allow for
losses in collection, the rate was made 2.6%.
A tax table was then made showing how much tax
had to be paid on any whole number of dollars up to $10,
on multiples of $10 up to $100, on multiples of $100 up
to $1000, and so on.
1. Copy and complete the tax table shown below:
Tax Table with Rate 2.6%
Prop-
erty
Tax
Prop-
erty
Tax
Prop-
erty
Tax
Prop-
erty
Tax
$1
$.026 $10 $.26 $100 $2.60 $1000 $26.00
2
.052
20
.52
200
5.20
2000
52.00
3
. 078
30
300
3000
4
.104
40
400
4000
5
.130
50
500
5000
6
.156
60
600
6000
7
.1 82
70
700
7000
8
.208
80
800
8000
9
.234
90
900
9000
2. Using the completed
tax table, find the tax on an
assessed valuation totaling
$13,685.
The tax on $10,000 is not
given in the table, but is ap-
parent at sight.
3. What is the tax on an assessed valuation of $6280,
including both real estate and personal property?
188
Tax on $10,000 = $260.00
Tax on $3,000
=
78.00
Tax on $600 = 15.60
Tax on $80
2.08
Tax on $5
0.13
$355.81

Problem Practice
Using the tax table on the opposite page which you
completed, find the tax on each of the following assessed
valuations:
!• $7490
$7580
$4760
$24,630
2. $5440
$3435
$8325 .
$17,470
3. A refrigerator marked $70 for cash is sold on time
for a $10 down payment and seven $10 monthly pay-
ments. What is the dollar cost of this credit? What is
the actual rate of interest paid?
4. A note for $1500 with interest at 6% and due in 5
months is discounted at the bank at 6%. What are the
proceeds?
5. A dealer receives discounts of 25%, 10%, 5%. To
what single discount is this equivalent?
6. In a smaU store, in one year goods were sold for
$16,895.75. The goods cost $13,430, and the overhead
was $3,265. Make a statement showing margin and
profit. Each of the items, cost, margin, overhead, and
profit, was what per cent of the sales? Show the answers
in your statement.
7. A house valued at $6400 depreciates $225 each
year.
Interest is figured at 5% of the value.
Repairs
are $40 for the year, and heat costs $98.60. What is the
sum of these items? How much per month does this
amoimt to?
8. In figiu-ing the cost of operating an automobile
for one year, Mr. Thomas used the following items: de-
preciation, $240; interest, 6% of $650; taxes and Hcense,
$21.50; insurance, $37.80; repairs and new parts, $41.60;
742 gallons of gas, at 20 cents; 54 quarts of oil, at 27
cents; garage rent, $36. What is the sum of these items?
189

The State Government
The state legislature meets m the state capitol to
make laws for the whole state.
In the same building
there are a governor and many other officials who take
care of state business. There is a supreme court, which
decides cases that people bring before it.
State governments build and maintain higher schools
such as universities and normal schools and colleges.
Highways are built and kept in good condition.
There
are prisons for criminals, hospitals for the insane, and
institutions for the subnormal, for the aged poor, for the
blind, and for children whose parents cannot take care of
them.
There are many bureaus and boards which perform a
multitude of duties.
1. Make a list of some important services and needs
suppHed by your state,
2. Find out what part of the funds for elementary
and high schools is supplied by your state.
190

Cost of State Government
In the table below are shown the totals of the state ex-
penditures for var-
ious purposes in a
recent year, given in
millions of dollars.
State Expenditures, in Millions
General administration 151 5.7%
Protection of persons
and property
106 —
Health
36—
Conservation and de-
velopment of natural
resources
78—
Highways
458 —
Charities
612 —
Hospital for handi-
capped, correction.
.
.
249 —
Education
830 —
All others
109
2629
—
It is interesting
to note that these
very large numbers
can be handled just
as easily as if the
amounts were given
in doUars.
This
table is no more
difficult than is a
budget for a family
whose yearly income is $2629. For the purpose of under-
standing many pubUc questions, it is very important
that we learn to work with large niunbers.
1. Copy the above table and fill in the missing per
cents.
Thus 106 is what per cent of 2629? Find each
rate correct to the nearest tenth of 1%.
2. Construct a bar graph representing the per cents
found in problem 1.
3. The item ''general administration" includes the
salaries of governors and many other executives, salaries
of supreme court judges, the cost of legislatures, and
many other items.
Does 5.7% of the whole for these
purposes appear to you to be high or low?
4. Discuss the per cent of the whole that is devoted
to each of the other purposes. Which seem low? high?
5. Why are the total costs of state government so
much less than the costs of local governments (page 186)?
191

State Taxes
The expenditures of the state must come from taxes.
If a state borrows for some unusual emergency, interest
must be paid on the money that is borrowed, and in time
the principal must be repaid. The kinds of taxes from
which all states derived income in a recent year are shown
at the right.
State Taxes, in Millions
|
Property
371 13.2%
Income
245
Inheritance
115
—
Severance
95—
Gasoline
649 —
General sales 431
—
Special sales
208 —
Business
305 —
Motor vehicles 309
—
All others
74
—
2802
—
Property taxes
are
from the same source as
the taxes for local govern-
ments.
Usually they are
collected by the counties
and turned over to the
state.
Income taxes, both
from individuals and from
business, are like income
taxes obtained by the federal government.
Severance taxes are paid in some states on coal or
metal mined and on timber cut, but no tax is paid on
this property before it is '^severed" from the soil.
We are familiar with gasoline taxes which are now
collected in every state.
These taxes range from 2^ per
gallon to 7^ per gallon.
The money from the gasoline
tax is usually set aside for the building of roads. There
is a general sales tax in a nvimber of the states, and
certain special sales taxes in every state.
It will be noticed that the total of the taxes is greater
than the cost of state government as given on page 191.
This is due to expenditures not given, such as payment
of interest on debt, which are not a part of the cost of the
government as an operating concern.
192

Tax Problems
1. Copy the table on the opposite page and fill in the
missing per cents.
2. Construct a bar graph showing the per cents
found in solving problem 1.
3. What was the average cost per capita of the state
governments in the United States, using the figures on
page 191, if the population was about 128 millions?
(Suggestion: Divide 2629 by 128.)
4. In the same year, what was the average per capita
amount of tax for state purposes?
5. Why do you suppose there is a sales tax on gasoline
in every state? For what especial purpose is the income
from this tax used?
6. Find out what is meant by "charities" for which
the states spent 612 millions in this year.
Was any
special work for the unemployed included in that
amoimt?
7. Find out what kinds of educational institutions are
supported by the states.
Is the school you are attending
supported by the state? Find out where the public
schools in your state get most of their support—from
local, state, or federal government.
8. From what kinds of property is the property tax
obtained? What happens if a family is unable to pay
the property tax levied on its home?
9. Is there a general sales tax in your state? Does
a general sales tax mean that you pay a few cents extra
on every article that you buy?
10. Which tax do you consider the best for the average
citizen?
193

Sight Problems
1. What was the original price of a siiit bought on
sale for $24 at a discount of 33^%?
2. What is the margin on 800 post cards bought at
$1.25 per hundred and sold at 2 for 5^?
3. How many pounds of butterfat are there in 1000
lb. of milk that tests 3.9% butterfat?
4. At $37.50 per thousand feet, what is the cost of
1500 feet of lumber?
5. An automobile costing $900 was sold for $750. The
loss was what per cent of the cost?
6. A suit costing $12 is marked to seU at 50% above
cost. What is the selling price?
7. A suit costing $12 is marked to seU at a margin
of 33^%. Find the selling price.
8. At 104 plus brokerage of $2.50, what is the cost
of a $1000 bond?
9. At $5, what is the cost of 100 shares of stock in-
cluding brokerage at 17 cents per share?
10. How many board feet are there in a plank 3 inches
thick, 12 inches wide, and 18 feet long?
11. At $35 per M, what is the cost of a lot of lumber
containing 7400 board feet?
12. A farm worth $6000 is taxed on 50% of its true
value. What is the tax if the tax rate is 2^%?
13. At $52 per $1000, what is the annual premium on a
20-year endowment poHcy for $8000?
14. At 50 cents per $100, what is the annual premium
on a fire insurance poHcy for $7500?
194

Problem Practice
1. A farm, 160 rods by 320 rods, is offered for sale for
$40,000. How much is this per acre?
2. At 480 cubic feet to the ton, how many tons are
there in a haymow 18 feet wide, 32 feet long, and 16
feet high? At $14 per ton, what is the value of this hay?
Indicate the solution before computing.
3. If a team played 26 games and lost 7, what per
cent of the games played did this team win?
4. Find the rate, correct to one tenth of 1%, if the
base is 14 and the percentage is 2^.
5. Mr. Baker estimated that, of 10 tons of coal costing
$8.50, 15 per cent was wasted through bad firing. How
many dollars' worth were wasted?
6. A contractor estimates that it will cost him $7200
to build a certain house. How much must he charge the
owner to make 10% of the contract price?
7. A merchant marked an article 100% above the cost
price.
Later he sold it at a reduction of 50% of the
marked price.
What was his margin?
8. Corn placed in a crib in the fall shrinks about 15
per cent by the following spring. A farmer wants 150
bushels of seed corn in the spring. How many bushels
must be set aside for seed in the fall? Find the answer
to the nearest whole bushel.
9. A dealer sold bookcases for $350 with a discount
of 10%. The bookcases cost $240 and the overhead was
$43. What was the rate per cent profit?
10. Mr. Welch bought 250 shares of stock at 27^ and
then sold them at 29J.
Brokerage cost 15 cents per
share for buying and for selling. What was his profit?
195

-^.
r
I
:^
Unit 15. federal Taxes. Scale drawing
The Federal Government
The government of the United States, called the
federal government, has certain powers and duties
definitely given to it by our Constitution.
The Con-
gress and the President conduct this government.
The Congress makes oxir federal laws, the Supreme
Court interprets them, and the President enforces them.
The federal government maintains an army and a navy;
it regulates commerce; it carries our mail; it takes care of
all relations with foreign governments, including making
war and peace; it regulates our system of money; and it
provides for the general welfare of the country.
In times of war, or danger of war, the federal govern-
ment has very great powers and may regulate our Hves
most closely, while in peace times it does not touch our
Uves very closely, except when it collects federal taxes
and asks that we conduct ourselves as loyal citizens.
1. Make a list of important services and needs that
are suppHed by the federal government in your state.
196

Cost of the Federal Government
During the last eighty years there has been an ahnost
constant increase in the cost of our federal government.
This increase has been much greater than the increase in
population, general wealth, or income. After two wars,
there were long periods when expenditures were lower
than during the war years.
The table at the right shows,
to the nearest dollar, the per
capita expense of the government
from 1860 to the present time. It
shows that if in 1860 every man,
woman, and child in the United
States had paid $2.00, that would
have been sufficient to pay all the
expenses of the federal govern-
ment, while in 1865 it would have
required $37.01, in 1919, $176.40,
and in 1941, $96.21.
1. What caused the sudden rise
from $2 to $37.01 from 1860 to
1865?
2. What caused the sudden rise
from $7.29 in 1916 to $176.40 in
1919?
3. How do you explain the rise
from $32.99 in 1931 to $96.21 in
1941?
4. Why was the cost several
times as much in 1920 as in 1917?
5. What were the 1941 federal expenditures in mil-
lions, when the total population was about 131,700,000?
197
Per Capita Cost
Federal Gov't.
1860
$2.00
1865
37.01
1870
5.04
to
to
1915
8.01
1916
7.29
1917
19.36
1918 122.58
1919 176.40
1920
60.84
1921
51.18
1922
29.56
to
to
1930
34.54
1931
32.99
1932
41.28
1933
40.91
1934
56.19
1935
58.00
1936
69.41
1937
62.69
1938
59.70
1939
70.65
1940
73.16
1941
96.21

Comparing Costs of Governments
The table shows the
cost in millions of dollars
of the local, state, and
federal governments in
1912, 1932, and 1937.
The cost of local govern-
ments for 1912 and 1937 are partly estimates, considered
to be as accurate as possible.
Year 1912 1932 1937
Local
2200 6645 6900
State
383 2506 2629
Federal 690 5154 8105
Totals 3273 14305 17634
As shown at the right, the loc£il
governments cost 67.2% of the total,
the state governments cost 11.7%,
and the federal government cost
21.1% of the total.
1. Make a statement similar to
that above for 1932 and also for 1937.
2. Make a circle graph for each of the years 1912,
1932, and 1937 showing the per cents foimd above.
Per Cent of Total
for 1912
Local
67.2%
State
11.7%
Federal 21.1%
Total 100.0%
Total Cost of
Year Income Govt.
Per
Cent
1912 32000
1932 39991
1937 71436
3273
14305
17634
10.2
3. The totals of aU
incomes in the United
States for the years
1912, 1932, and 1937
are shown at the right
in millions of dollars.
For each of the three years, find what per cent of all in-
comes was used for government expenditures. Copy and
fill in the table.
Keep this for reference,
4. How many cents out of each dollar of income were
used to pay the cost of government in each of the years
1912, 1932, and 1937?
5. What is the per cent of increase in the total cost
of government from 1912 to 1937?
198

Federal Taxes
Personal income tax
1418
Corporation income tax 1852
Liquor tax
820
Tobacco tax
698
Other internal revenue 2280
Customs
302
All others
237
Total
7607
Below are given in millions aU receipts of our federal
government for the year 1941 from all sources except
from borrowing.
Many of these items
are
very compH-
cated, but
some
general facts about
them will be of
value to you.
In
the years to come,
you will hear much
about these items.
Personal income taxes are now assessed against
many citizens.
These taxes are paid on aU individual
incomes of $750 or more for single persons and on $1500
or more for married persons.
The rate of income tax
varies from 10% for the smallest taxed incomes to 81%
for any incomes which are above five millions.
A credit of $400 is allowed for each dependent.
A 10% earned income credit is also allowed on the net
income before exemptions are taken.
Corporation income taxes vary from 15% to 24%,
depending on the amount of the income. There is also
an extra tax in the case of corporations, called surtax,
which varies from 6% to 7%.
Customs or import tariff are paid on many articles
imported from foreign countries, such as woolen goods,
furniture, cotton cloth, silks, and hundreds of others.
1. A single person with a net income of $100,000 paid
$53,214 in income taxes.
What per cent of his income
did he pay?
199

Tax Problems
1. Mr. Smith had an income of $3400 in 1941. He
had two small chil-
dren and claimed
the following deduc-
tions: contributions,
$50; interest, $150;
and taxes,
$125.
What was his fed-
eral income tax in
1942?
Total income
$3400
Contributions
$50
Interest
150
Taxes
125
Total deductions
325
Net income
3075
Personal exemption 1500
Credit for dependents 800 2300
Surtax net income
775
Earned income credit
307.50
Balance subject to
normal tax
467.50
Normal tax —4%
18.70
Surtax— 6%
46.50
Total tax
$65.20
The box at the
right explains the
process.
Examine
every step and be
certain that you imderstand the amounts secured.
2. A single person with a net income of $5000 paid a
federal income tax of $482.50 . What per cent of his net
income was this tax?
3. A married person with two children, having a net
income of $5000, paid an income tax of $271. What per
cent of his income was this tax?
4. A single person with a net income of $25,000 paid
$7224. What per cent of his income was this tax?
5. A tourist bought a valuable
piece of furniture in a foreign
country for $1112. After paying
a duty of 40%, how much did he
pay for the furniture?
6. On a piece of jewelry the
import duty is 72%. What is the
duty on $4680 worth of this
jewelry?
200

Problem Practice
1. Mr. Jackson bought a new automobile for $795 and
drove it 16,000 miles the first year.
Depreciation was
$275, insurance was $46.85, and interest was figured at
6%. Other expenses were: 980 gallons of gas, at 19^^
per gallon; 90 quarts of oil, at 27^; repairs, $29.80; a
new tire, $12.60; and taxes, $14.25. How much per mile
of driving did this car cost?
2. A loan of $8400 carries interest at 6%. Payments
of $60 are made each month including interest on the
balance unpaid. The rest of each payment is appHed to
the principal. Write a schedule of payments for six
months. Below are the first two Hnes:
Balance on Payment on
Interest
Total
Principal
Principal
Payment
Payment
$8400
$18
$42
$60
8382
—
—
60
3. A man bought 50 shares of stock at 38:^^ and sold
them at 38^.
Brokerage was $15. How much did he
gain or lose?
4. At $42.50 per M, what is the cost of 60 planks, each
ofwhichis 3'' X12'^X167
5. At $6.50 per cord, what is the value of a rick of
wood 4 feet wide, 5 feet high, and 210 feet long? In-
dicate the solution before computing.
6. Mr. Hines has property assessed at $2980 on which
he pays a 2.7% tax, and other property assessed at
$12,450 on which he pays 3.1%. What is his total tax?
7. Mr. Brown has an income of $2400. He is un-
married but has deductions of $100. Find his federal
income tax.
201

Scales on Maps and Drawings
In your geographies you have often seen a map on
which a scale was given.
Do you understand what this
means
•5^
A^ CLEVELAND
P^
•
.HD^ANAPOLIS ^
[scale. 320 M.LES TO I INCh] %SSM.
In the above map, one inch represents about 320 miles
of actual distance.
1. The air-Hne distance on the
map between Chicago and Boston is
3 inches.
What is the actual dis-
tance between the two cities?
3X320=960
The scale on a map is also frequently indicated by
such a line as the following:
«
I
I
I
I
I
I
I
I
I
t
O /OO 200 300 UOO 500 6oO 700 flOO 900 /GOO
Scale:
I in.=320 miles
To find the air-line distance between two cities on the
map, open a pair of dividers (compasses) so as to point to
the two cities and then put the dividers against this
scale.
You can then estimate quite closely the distance
between the cities.
(A ruler may be used for measuring.)
2. What is the approximate distance between Detroit
and Chicago?
202

Scale Practice
Using the map on the opposite page and a pair of
dividers as suggested, find the air-line distances between
the folio v^dng cities:
1. New York and St. Louis
2. Chicago and Montreal
3. Cincinnati and Toronto
4, Boston and Milwaukee
5. Washington and Boston
6. Detroit and Baltimore
7. The first figure below represents an ordinary base-
ball diamond. What is the length of its sides? Wliat is
the distance from A to C (the distance from the home
plate to second base)? What is the distance from the
pitcher's box, E, to the home plate?
D
Scale:
I in.^6o ft
Scale: Iin—Cft.
, 8 . The second figure above represents a room with a
rug in the middle.
What are the dimensions of this
room? What are the dimensions of the rug?
9. A building lot is 50 feet wide and 150 feet deep.
Make a drawing to scale of this lot.
What is a con-
venient scale?
10. A house 30 feet wide and 45 feet deep is built on the
lot in problem 9. Make a drawing to scale of the space
occupied by this house. Use the scale you used in draw
ing the lot.
203

Standard Time
You know that if the President is to speak over the
radio at 9 p.m. Eastern Standard Time, the people in the
East will have to tune in at 9 p.m., those in the Central
West at 8 p.m., those in the Mountain Belt at 7 p.m., and
those on the Pacific coast at 6 p.m .
From this it is evident that the United States is di-
vided into four time belts.
If all our clocks were exactly
right with the sun, every locality from east to west across
the country would have its own time. In the latitude of
Chicago, two places, one 40 miles east of the other,
would have a difference in time of about 4 minutes.
However, within each time belt, clocks show the same
time. When it is 10 p.m. in Washington, D.C ., the clocks
in all places in the eastern time belt show 10 p.m .
The
approximate centers of the time belts are the meridians
at 75° west, 90° west, 105° west, and 120° west longitude.
There is a fifth time belt, the Maritime or Atlantic
belt, starting in Canada east of the United States, and ex-
tending from 60° to 75° west longitude.
204

Standard Time
The time belts in this map agree with those estabhshed
by national authorities. Local use of boundaries varies.
1. Name a number of cities that are in the eastern
time belt; the central time belt; the Pacific time belt.
2. When schools are opening in San Francisco at
&*A.M ., what time is it in Denver? in Pittsburgh?
205

Time and the Rotation of the Earth
(IOBi8p''7iO"60''
%'
You have learned in geography that the earth makes a
complete turn on its axis once every 24 hours. As you
know, to make a complete turn, the earth must turn 360"^ ,
for there are 360° in a circle.
Since the earth
turns 360" in 24
hours, it turns 15°
in one hour, and 1°
in 4 minutes.
In the illustra-
tion at the right,
the meridian at 70°
east of the prime
meridian is directly
under the Sim. The
meridians shown are 10*^
apart, and it takes the earth
just 40 minutes to turn 10°.
Use the illustration in answering these questions:
1. When it is noon on the meridian 70° east, what time
is it on the meridians 55° east? 40° east? 25° east? 10°
east?
2. When it is noon on the prime meridian, what time
is it 60° west (the maritime time)? What time is it 75°
west? 90° west? 105° west? 120° west?
3. Ships at sea carry very accurate clocks, marine
chronometers, that show the time on the prime me-
ridian.
Then the sailors determine by observation just
when the sun passes the meridian on which they are.
From this they find how many degrees east or west of the
prime meridian they are.
How do you explain this?
206

Problem Practice
1. The sum of $560 is placed on interest at 2% com-
pounded semiannually. What will be the amount in
10 years?
2. In s?^ = c (commission), what is rep-
resented by s, r, c? How are (2) and (3)
derived from (1)? State these formulas in
words as rules.
3. Make and solve a problem for each
of the equations in problem 2.
4. In 1932 Mr. EUis bought at 91 a 4 per cent $1000
bond, due in 1942. How much did he pay for the bond
(disregard brokerage)? How much did he get for it
\Yhen it became due? How much interest did he get
from this bond during the ten years that he kept it?
(1) sr-= c
(2) r=
s
(3) s =_£
r
5. How many board feet are there in 260 planks, each
21 in. thick, 8 in. wide, and 14 ft. long? At $38.50 per
M, what is the cost of this limiber?
6.Inaclassof35pupils,4hadagradeofA,7had
B,16hadC,5hadD,and3hadF. Constructabar
graph showing this distribution.
Also construct a circle
graph showing the same facts.
Which graph shows the
facts more plainly?
7. The assessed valuation of all the property in a
certain city is $1,460,000,000. The tax wanted is
$45,000,000. What must be the rate? Find answer to
the nearest hundredth of 1%. Before dividing, how
many zeros can you strike out in the divisor and the
dividend?
8. If a train travels 48 miles in one hour, what frac-
tion of a mile does it travel in one minute? How many
feet does it travel in one second?
207

Seventh Self-Test
Test in Fundamentals
¥/rite in columns, and add or subtract as indicated:
1. 13.57+2.468+0.95+.0486+861 +300+1.004
2. 72+5.89+.625+1. 908+760+5.01 6+89.67
3. 231 +7.75+0.863+.5902+900+450+.398
4. 1 .19+982+5.92+358+2.807+.978+6.83
5.
.882+649+5.528+.089+7.28+5.798+1.09
6. 290-2.835
82.09-6 .892
.594 -.5863
7. 504-298.76
2.49-1 .287
.659 -.598
8. Write three formulas using h, r, p (base, rate,
percentage). Change each formula into a rule stated in
words. In using these formulas, how is the rate given?
Find the nvimbers missing below.
Find rates to the
nearest hundredth of 1%. Find unknown bases correct
to three decimals.
9. 769
17%
81%
371
10. 1269 28.7%
89.46
87Wo
11. 39
_
ls
59.8
23.6
12. 7|
-
2i
47
9860
13.
6%
845
18|
^
Perform the operat ions indicated below:
14.
3|-1|
If-
""
16
181-7^^
20|-9f
15. 37f-28| 591--36t^ 1021-8911 371- 18t^
16.
3|X1|
i|:XH
241 X6|
14X6|
17. 3HX5i 86|;X12
16|X5|
41X313,
18.
3|-1|
Il-4-31
i|--Ji.
4f-|
208

Problem Test
1. A truck loaded with coal weighs 15,600 pounds and
the empty truck weighs 5300 pounds. At $9.50 per ton,
what is the cost of this load?
2. When sugar is selling at 6^ cents per pound, what
is the cost per 1000 calories? (See page 71.) Find answer
to the nearest tenth of a cent.
3. When spring chickens sell for 32 cents a pound,
what is the cost per 1000 calories?
4. A man 30 years old takes out a 20-year endowment
poHcy for $10,000, the rate of premium being $48.80 per
$1000. If he keeps up his payments for 20 years, what
will be the sum of his premiums? What will be the dif-
ference between this sum and the $10,000?
5. A house costing $9800 when new depreciates at the
rate of 3^%. What will be the value of this house when
it is 12 years old?
6. A concrete garage floor is to be 36 feet wide, 54
feet long, and 6 inches thick. How many cubic yards of
concrete will be needed to make this floor? At $3.50
per cubic yard, what will be its cost?
7. From an assessed valuation of $57,800,000 a tax of
$158,000 is to be raised. Find the rate to the nearest
hundredth of 1%. At this rate, what is the tax on a
property assessed at $13,400?
8. At 37 cents per $100, what is the yearly cost of a
fire insurance policy for $26,000? What is the cost of a
three-year policy for this amount?
9. Find the interest on $7400 at 4^% for 7 months.
10. What are the proceeds of a note for $1675 dis-
counted at 5^% for 5 months?
209

'Utiit 16. Square Root Ratio and Proportion
Squares and Square Roots
Surveyors laying out a new road
needed to know the distance across a
bad swamp from a point A to a point
B. Since direct measuring would be
difficult, they measured from A to C,
as shown in the figiu-e.
Then they A
turned a right angle at C and measured from C to S.
From their figures, they were able to determine . the
distance from A to B. How did they do this figuring?*
They had to find squares and square roots of njimbers.
1. The table on the opposite page gives the squares of
whole numbers from 1 to 100. Find the following:
162
ig2
232
272
322
352
472
592
832
The square root of 25 is 5 because 5x5=25. The
sign for square root is V . V25 =5 is read, "the square
root of 25 is 5."
2. Find the square root of 6889.
According to the table,
83^ = 6889.
Therefore,
V6889=83.
3. Find the square root of 4734.
According to the table, the root is between ^^ and 69.
On page 212 we shall learn how to obtain this root more
closely.
210

¥
Squares and Square Roots
This table gives squares of numbers from 1 to 100:
I
No. Square
No.
26
Square
676
No.
51
Square
2601
No. Square
1
1
76 5776
2
4
27
729
52 2704
77
5929
3
9
28
784
53 2809
78 6084
4
16
29
841
54 2916
79 6241
5
25
30
900
55 3025
80 6400
6
36
31
961
56 3136
81 6561
7
49
32 1024
57 3249
82 6724
8
64
33 1089
58 3364
83 6889
9
81
34 1156
59 3481
84
7056
10
100
35 1225
60 3600
85 7225
11
121
36 1296
61 3721
86 7396
12
144
37 1369
62 3844
87 7569
13
169
38 1444
63 3969
88 7744
14
196
39 1521
64 4096
89 7921
15
225
40 1600
65 4225
90 8100
16 256
41
1681
66 4356
91 8281
17 289
42
1764
67 4489
92 8464
18 324
43
1849
68 4624
93 8649
19 361
44 1936
69 4761
94 8836
20 400
45 2025
70 4900
95 9025
21 441
46 2116
71
5041
96 9216
22 484
47 2209
72 5184
97 9409
23 529
48 2304
73 5329
98 9604
24 576
49 2401
74
5476
99 9801
25 625
50 2500
75 5625
100 10000
Find the square root of the following:
1. 1156
1849
2116
2304
9216
2. 4356
5184
5776
7225
7921
3. 8464
9216
7056
211
6241
9604

Approximate Square Roots
You will now learn a method for approximating square
roots.
1. Find the square root of
7283.
Step 1.
Find from the
table the two squares be-
tween which the given num-
ber Hes.
Step 2.
Find the differ-
ences as shown in the box.
852 = 7225
862=7396
7396
7225
171
7283
7225
58
.3 34
171)58.0
513
670
513
IS
The quotient
very nearly .34.
Hence,V7283 =85.34
Note that the first differ-
ence is the difference between
the two squares between
which the given number lies.
The second difference is the
difference between the given
number and the smaller of the two squares.
.,
Step 3.
Divide the smaller difference by the larger.
The quotient is the decimal part of the root. This
method gives correct answers to one decimal for small
numbers and to two decimals for large numbers (numbers
above 100).
By squaring 85.34 as at the right,
you obtain 7282.9156, which differs
from the given number by less than
one tenth. If you square 85.35, you
get 7284.6225, which differs from the
given number by more than 1.6 .
Hence the root you found is much
closer to the required number than
the next higher number in hun-
dredths. That is, the root is correct to
212
85.34
85.34
3 4136
25 602
426 70
6827 2
7282.9156
two decimals.

Square Roots of Decimals and of Large Numbers
1. Find the square root of
387.68 .
Step 1. From the table you
see that 387.68 is between
192 = 361 and 202 =400.
Step 2. Find the two differ-
ences, 39 and 26.68 .
Step 5. Divide 26. 68 by 3 9,
giving m. Then V387.68
=
19.68. This is correct to two
decimals.
2. Find the square root of 1.53 correct to two places
of decimals.
To simplify the work, multiply 1.53 by 100 (move the
decimal point two places to the right) and approximate
the square root of the product, 153. We find \/153 =
12.36 . Then move the decimal point one place (not two)
to the left, giving 1.236. The answer correct to two
decimals is 1.24.
20^
19^
= 400 387.68
= 361 361
39 26.68
.68
39)26.68
234
328
312
16
V1869.48 =43.23
V186948 =432.3
3. Find the square root of
186948. This number is larger
than any found in our table.
The steps are:
Step 1. Point off two decimals.
Step 2, Find the approximate root of 1869.48.
Step 3,
In the result, move the decimal point one
place to the right. The root correct to the nearest imit
is 432.
Find the approximate square roots of:
4. 8910
5. 4097
6. 8.97
7. 15,090
213

The Right Triangle
The figure at the right shows
one of the most important
facts that you know about
triangles.
The triangle ABC has one
right angle, the angle at C.
For this reason it is called a
right triangle. The side AB
opposite the right angle is
called the hypotenuse. The
two shorter sides, CB and CA, are called the legs of
the triangle.
The legs of a right triangle are also called
the sides.
If squares are constructed on the three sides of a
right triangle, then the area of the square on the
hypotenuse is equal to the sum of the areas on the
two legs.
Read and supply the niunbers missing below:
1. The legs of the triangle ABC are the
lines
and
^
2. The hypotenuse is the line
.
3. The square of the sides AC and CB
are32-_, 4'^=
4. If a, 6, c are the sides of a right triangle, c
the hypotenuse, then a^ -\ -b'^= c^f \/a^-{ -b^=c,
y/c^—o?^^}), \/c'^—h'^=a.
State each of the four formulas above.
5. Explain how this enables you to find
the distance from A to 5 in the figure on page
210.
A
214

Problem Practice
1. Find the length of the hypotenuse of a ri^ht tri-
angle having legs 8 feet and 6 feet long.
2. The hypotenuse of a right triangle is 13 inches long,
and one of the legs is 12 inches long. Find the length of
the third side.
3. Find the shortest side of a right triangle of
which two sides are 20 inches and 16 inches
long.
4. What must be the length of a ladder to
reach a height of 24 ft. on the side of a building
if the foot of the ladder is 7 ft. away?
~^
5. A ladder 24 ft. long leans against a build-
ing. The foot of the ladder stands 8 ft. from
the building. How high does the ladder reach?
Find the answer correct to a tenth of a foot.
xl 24'
7'
6. The hypotenuse of a right triangle is 42 inches,
and one leg is^2 inches. Find the length of the other leg,
correct to one decimal.
7. A baseball diamond is 90 feet square. Find, cor-
rect to the nearest tenth of a foot, the shortest distance
from first base to third base.
8. The length of one side of a square field is 40 rods.
What is the length of its diagonal? Find the answer
correct to a tenth of a rod.
9. A certain county, in the shape of a rectangle, is
28 miles wide and 36 miles long. What is the diagonal
distance from the southwest corner to the northeast
corner? Find the answer correct to the nearest hun-
dredth of a mile.
215

Diagonals of a Rectangle
y
In a rectangle, a line connecting op-
posite corners (vertices) is called a
diagonal of the rectangle. Thus, in the
^
figure at the right, AC is a diagonal.
The triangle ABC is a right triangle and you can find
the line AC if you know the sides AB and BC
1. The side AB in the figure is how long?
2. The side EC is how long?
3. The line AC is how long?
4. How long is the diagonal of a rectangle 5 feet wide
and 12 feet long?
5. Measure the length and width of a sheet of foolscap
paper.
These should be 11 inches and 8 inches.
By
computing, find the distance between opposite corners
(along a diagonal) of this sheet. Then measure to see
whether you are right.
6. In problem 2, can you measin^e the diagonal ac-
curately to within a hundredth of an inch? Can you com-
pute the distance so accurately?
•
7. Find the length of a diagonal of a rug 9 feet wide
and 12 feet long. Check your answer by measin-ing a
diagonal of such a rug.
8. A ladder known to be 24 feet long is lean-
ing against a building. The lower end is 10 feet
from the waU. How high up the wall does the
ladder reach?
24 //
9. If AC = 350 feet and C5=460 feet, find
the length of AB. (See page 210.)
216
/o^

Problem Practice
1. The day Harry was born, his uncle deposited $150
to the boy's credit in a savings bank that compounds
interest annually at 2%. When Harry is 20 years old,
what will be the amount of this deposit?
2. Harry's father took a note from one of his cus-
tomers for $380 due in 6 months. Three months later
he discounted this note at the bank at 5% interest.
What were the proceeds of this note?
3. What is the cost of two $1000 bonds selling at
103^ with brokerage of $2.75 per $1000?
4. At $39.75 per M, what is the cost of the 29,800
bricks that were used in a building?
'T
5. A farmer's livestock is valued at $21,900. The
assessed value is 33^% of the full value, and the tax
rate is 4.8% of the assessed value. What is the amoiuit
-
of the tax?
6. What is the annual premium on a 20-payment life
poHcy for $15,000 taken out by a man aged 25? For
,
rate, see page 139.
7. Mr. Waters has a house valued at $10,000, which
he insures at 80% of its value. At 24 cents per $100,
what is the annual premiimi?
8. Herbert lives 6 blocks north and 5 blocks west of
the school he attends. A diagonal street runs from his
home straight to the school. What distance (in blocks)
does Herbert go in walking along this street from his
home to the school? Find answer to the nearest tenth
of a block. The blocks are approximate squares; the
width of one street is included in each dimension of a
block. Draw a map of this neighborhood.
217

The Meaning of Ratio
You will now study proportion, which is a very im-
portant tool in your work. A ratio is a part of a pro-
portion.
The ratio between two numbers is the first nmnber
divided by the second. Thus, the ratio of 2 to 3 is f, and
theratioof6to18is^,or^.
The ratio between two numbers is also indicated by
writing a colon between them. Thus, the ratio of 2 to 3
is written 2:3, and the ratio of 6 to 18 is written 6:18.
: means ^.
1. Reduce f : f to the simplest
form. As shown at the right this ratio
reduces to f| or ly^.
2. Measure these lines and find the
ratio of their lengths
:
2.3
_2
.
.3
6-8
5•8
=fxf=H
= 16:15
3M''
The lengths are 2^ in. and 3f
in.
As shown, this ratio reduces
tof.
3. The lengths of two
linesarel^ft. andlf ft. Find
the ratio of their lengths.
^|Xt*5 =1=2:3
8^-'-4
-8
-48 -^7
2
Reduce the following ratios to their simplest form:
4. H:3
3:4i
f:|
^:^
5.
4:101
1|:7i
8:24i
^:7i
6. H:5i
2f:5|
3|:6i
"TO'^TO
218

Proportion
By looking at the triangles below, you can see that
they are about the same shape. If you measure, you wiQ
find that the sides of the larger triangle are twice the
sides of the smaller one. The rectangles are also about
the same shape.
B A'Z.
/c
D'
/D
L
/B'A
BA'
In referring to these figures, A' is read ''A-prime," B^
is read "5-prime," and so on.
In the triangle ABC and A'B'C, AB and A'B' are
said to be corresponding sides, as are also BC and
- B'e^ and CA and C'A\
.
In the rectangles ABCD and A'B'CD\ AB and A'B'
are corresponding sides, as are also BC and B'C\ and CD
and CD', and DA and D'A'.
By measuring the sides of the triangles, you can find
the ratios.
AB:A'B\ BC:BV\ CA:CA' are aU in the
ratio of 1:2.
By measuring the sides of the rectangles, you find the
ratios AB:A'B\ BC:B'C\ CD:CD\ and DAiD'A' aU
equal to 3:4. Writing thf» ratios as fractions we have:
ABBCCA
A'B'
AB
B'C
BC
CA
CD
,
for the triangles, and
,
for the rectangles.
A'B' B'C CD' D'A
Two equal ratios form a proportion,
AB BC
That is,
jj^^
=
-g^,
is a proportion.
219

Uses for Proportion
In every proportion, four numbers are involved. Thus,
in the proportion, f =^, you have 2, 5, 6, 15. f =t% is
read,2isto5as6isto15,or2-^5=6-t-15,or2over5
equals 6 over 15.
The usefulness of a proportion in solving problems
comes from the fact that, when three of these numbers
are given, you can find the fourth number by solving the
proportion as an equation.
When a proportion is used in solving a problem, you
indicate the unknown number (the number you are to
find) by some letter, as x.
Usually, you can write the
proportion so that x is the numerator in the first fraction.
Finding the value of the unknown number in a pro-
portion is solving the proportion,
1. Solve|=^.
Since 6 is one half of 12, we know
that X must be one half of 7. That
IS, X
^^=
<J'2^»
A more direct way is to multiply both members of
equation (1) by 6. This gives
equation (2).
2. Solve
I=|.
o
o
Multiply both members by 5
and reduce to \\,
X3
68
Proof: 1q"^^=q
Solve the following equations and prove the answers:
3.
-^=
X
4
510
2X
918
X15
824
X
15
83
:c
12
318
X18
816
X15
12 36
X36
,7~4
4.
-S-=7^
220

Proportion
1. A fanner raised 265 bushels of potatoes on 3 acres.
At this rate, how many bushels wiQ he raise on 11 acres?
You can easily solve this prob-
lem by methods you have already
learned. At the right, a solution
using proportion is shown.
^^
265 ^
11
3
(2)x=265x
11
The ratio of the amounts raised must be the same as
the ratio of the areas.
Hence, you have the proportion
stated in equation (1). Multiplying both members of
(1) by 265, you have (2). Notice that the second mem-
ber of (2) is an indicated solution.
2. Last year a farmer had 36 cows and used 84 tons
of hay. This year he has 54 cows. How many tons of
hay will be used?
Explain the equation at the right.
Then reduce t^ to ^ and solve 7^ =:^
36
2
842
for:3C.
X
84
54
36
3. In 4 hours a motorboat traveled 45 miles,
rate, how long will it take to travel 118 nules?
At this
4. Last week John worked 19 hours and earned $4.85 .
At this rate, how much should he earn this week if he
works 31 hours?
5. A city lot 45 feet by 110 feet was sold for $1500.
At this rate, how much should another lot
cost if it is 82 feet by 140?
~
Notice that the ratio of the areas is as
shown at the right.
82X140
45X110
6. The cost of the walk 4 feet by 86 feet was $124.00.
At this rate, what would be the cost of a walk 5 feet by
140 feet?
221

Unit 17. Similar Triangles. Areas and Volumes
Measuring by Similar Triangles
Triangles with the same shape are said to be sitmlar.
The two triangles in each of these pairs are similar.
Triangles that are similar may be very different in size,
but one is a small copy of the other.
How do you know whether two triangles are similar?
The simplest test is that if
in two triangles the angles
of one are equal respec-
tively to the angles of the
other, then the triangles
are similar.
Thus, if in the two triangles above, AA=- Z .A\
ZB= ZB\ ZC= ZC\ then the triangles are similar.
Since the sum of the angles of any triangle is 180°,
it follows that if two pairs of angles are equal, then the
third pair are equal. Hence, if ZA= ZA\ ZB= ZB\
then you know that the triangles are similar.
Hence you have the rule:
To find whether two triangles are similar, find
whether two angles in one are equal respectively
to two angles of the other.
222

Proportions in Similar Triangles
The two triangles at
the right are similar. Us-
ing the lengths of the sides
of these triangles, you can
state several proportions.
1. Using the lengths of
the sides of the triangles,
check the proportions in the box.
2. Study the equations at the right.
How many more proportions can you
write from them? Write these pro-
portions.
_ 3 . Using the lengths of the
side^rof the triangles, check the
proportions found in the second
^^ AC A'C
AB^A'B'
^^
BC B'C
w' box.
ABBCCA
A'B' B'C CA'
In similar triangles, sides opposite to the equal
angles are called corresponding sides.
In the triangles ABC and A'B'C, sides AB and A'B',
BC and B'C\ and CA and CA' are corresponding sides.
In similar triangles, corresponding sides form a
proportion.
4. In the similar tri-
angles ABC and A'B'C,
AB^ll, BC = 21, and
A'jB'=28, FindJ5'C'.
Explain the equation:
^=Tn'
Find value of x.
223

Finding a Distance without Measuring It
1. A tree is casting a
shadow 93 feet long, and
at the same time a vertical
stick 7 feet long casts a 9-
foot shadow. How tall is
the tree?
,7'
y
B' A.
y
93'
The line AB represents the shadow of the tree and the
Anes B'C and A^B' represent the
stick and its shadow.
93
9
x=7x^=72^
The triangles ABC and A'B'C
are similar. Hence, if x is the height
BC, you have the proportion at the
right. Check the solution.
2. To find the distance from the point A to a point B
on the other side of a river, two boys proceeded as
follows:
Step 1,
the river.
They measured a line AC along their side of
AB
Step 2,
They measured the
angle ACB (ZC) and then laid
off angle ADE equal to ZC.
Step 3.
Since the triangles
ACB and ADE are similar, they
wrote the proportion shown at
the right.
Step 4, They measured the lines AE,
AC, and AD, and found the length ofAB.
Explain fully how these boys knew that
the triangles ADE and ACB are similar.
Which side in ACB corresponds to AD in triangle ADE?
Which side in A CB corresponds to AE in ADE?
224

Problem Practice
/9A^
1. The smokestack in the
figure at the right casts a shadow
194 feet long at the same time
that a stick 8 feet long casts a 15-
foot shadow.
How tall is the
smokestack?
2. How tall would the smokestack in problem 1 be if a
14-foot pole were casting a 12-foot shadow?
3. In the figure, ZADE= ZABC.
Then the triangles ADE and ABC are
similar. Why?
What lines must you measure to en-
able you to compute the length of the line EC?
4. Find the length of BC
from the first box.
5. Find the length of EC
from the second box.
6. In the first figure on
the opposite page, why do you think the triangles ABC
and A'B'C are similar? What kind of angles are ZB
and ZB'?
7. In the second figure on the opposite page, why do
you think ZADE and ZACB are equal? In the tri-
angles ADE and ACB, what other angles do you know
to be equal? How many angles in two triangles must
you know to be equal in order to be certain that the
triangles are similar?
8. You know that the triangles ABC and A'B'C are
similar, ZA being equal to ZA\ and ZB being equal to
ZB'.
Write as many equations as you can, using sides
of the triangles as the numbers in your proportions.
225
AD=108
AB=346
DE= 68
BC= ?
AE= 94
AC=216
DE= 54
BC= ?

Measuring Distances Indirectly
1. Two boys wanted to find the distance across a cer-
tain lake without crossing the lake.
The boys were at
point A in the diagram.
They located a pine tree at
point B on the opposite shore. Then they located points
C and D on their side of the lake to make right angles
BAC and DCA. Next they sighted from D to B and
located the point E. They concluded that the triangles
DCE and BAE were similar.
After measuring the distances DC, AE, and EC, the
boys were ready to calculate the distance AB. They
found that DC was 35 yards long, AE was 30 yards long,
and EC was 10 yards long. What was the distance AB?
AB_AE
DC EC'
Find the width of the lake if the lines were as given
below:
DCAEEC
DC
AE EC
2. 20yd.90yd.15yd.
3. 32yd. 66yd. 11yd.
4. 18yd.75yd.15yd.
5. 16yd.126yd. 9yd.
6. 50yd.40yd.10yd.
7. 75yd. 60yd.15yd,
226

Practice
Solve the following proportions for x:
^*
12~27
9~3
3~20
4~20
o
JL—
1
JL—
A
^—
^
^_^
7:5~3
15~36
6~28
25~3
^
a:_35
^_1
f?_
^
x_16
8~56
9~4
5~30
7~28
^6
X _2\_
^_36
:x:_5
T8~24
25"35
T6~64
48~20
Solve the following equations:
5. jc+18 = 25
x-9 =19
3x+7 = 22
6. 4x-37 = 63
2jc+8 = 62
e+4=9
7. i-6
=2
1+16 = 21
1-5 =3
Problems
1. Find the area and the circumference of a circle
whose diameter is 56 feet.
2. Find the net amoimt of a bill of $1800 with dis-
coimts of 25%, 10%, and 2%.
3. Find the length of the hypotenuse of a right tri-
angle having legs 9 feet and 12 feet long.
4. Find the length of the hypotenuse of a right tri-
angle having legs 48 yards and 64 feet long.
5. The hypotenuse of a right triangle is 20 feet long,
and one side is 16 feet long. Find the length of the other
side.
6. What are the square roots of: 25, 49, 121, 225 ?
1. What are the squares of: 6, 25, 57, 8.5, 4| ?
227

A
case
hh=A
Areas
You know the rules for finding
the areas of rectangles and tri-
angles. You hav used I and w to
denote the dimensions of the rec-
tangle,
but h (base) and h
(height, or altitude) are also used, as is usually the
for the triangle.
A parallelogram is a four-
sided figure with both pairs of
opposite sides parallel.
Ina
parallelogram, opposite sides AB
and CD, and also EC and DA are
parallel.
A trapezoid differs from a
parallelogram in that only two
opposite sides are parallel.
In
a±fc^^_^
the trapezoid ABCD, the sides
AB and CD are parallel, while AD and BC are not paral-
lel. The two parallel sides of a trapezoid are called the
bases of the trapezoid.
In the figure of the trapezoid above AB and CD are the
bases. The lengths of these are denoted by a and b. The
distance between the bases is called the altitude, and
the length is denoted by h.
By drawing the diagonal, AC, for the parallelogram
and the trapezoid above, dividing them into triangles,
you can have other rules for finding their areas.
A formula is given with each of the figures above.
1. Translate ~^
Xh=A into a rule stated in words.
2. If, inatrapezoid,a =18,6 =12,andh=10,whatis
the area?
228

Circumference of a Circle
You have already learned the rule for finding the area
of a circle.
You square the radius and then multiply by
a certain number that is represented by t, (pi). This
number cannot be expressed exactly either as a common
fraction or as a decimal. The value 34^ is often used. The
value 3.1416 is correct to four decimal places.
The number represented by tt is the number by which
the diameter of a circle is multipHed to find the length
of its circumference. If d represents the diameter, r the
radius, and c the circumference, then 7rd = c and 27rr = c .
If you draw radii (plural of radius) close
together, you divide the circle into parts
that are very nearly triangular, the differ-
etice being that the bases are somewhat
curved.
From the rule for finding the area of a
triangle, you then find the rule for find-
ing the area of the circle.
You multiply
each little base by the altitude, which is
very nearly the radius of the circle, and
add the products. The result is that irr^
is very nearly the area.
As you make the triangles
smaller and smaller, the area comes more and more
nearly to the exact area irr^,
1. Find the circumference and the area of a circle, the
radius of which is 5. Use w = 3.1416.
2. Find the area of the circle in problem 1, using
TT = 34^.
Reduce the result to a four-place decimal. Com-
pare this answer with the answer found in problem 1.
3. Find the circumference and the area of a circle, the
radius of which is 14. Use 7r =
229

Rectangular Solids and Cylinders
You often think of a rectangular solid as standing on a
base. The area of the base of the rectangular soHd in
the figure below is Iw, and its volume is Iwh. That is,
the volume is the product
of the area of the base and
the altitude.
This idea helps you to
understand the rule for
the volume of a cylinder.
A
f
kJ[
d;
vv
//
/
/
3
h
The volume of a cylinder is the product of the
area of the base multiplied by the altitude. For-
mula: V = Trr^h.
The base of an ordinary cylinder is a circle, whose
radius you denote by r.
Hence, the area of the base is
7rr^ and the volume is Trr%, h
being the altitude, or height.
The formula for finding the
volume of a cylinder is very im-
portant.
The amount that a
small cylinder, such as a can, will
hold can be found by pouring Kq-
uid into it from a quart measure.
But it would not be practical
to find in this way how much a large oil tank will hold.
Nevertheless, it is known quite accurately how much
such a tank will hold, even if it is large enough to hold
many thousands of gallons.
Such volumes are always
determined by using the rule you are now learning.
1. Name several products which are sometimes stored
in large cylinders.
Why is it necessary to know the
volumes of such cyUnders?
230

Area of a Cylinder
2ift.
6 ft.
7 ft.
81ft.
12^ ft.
24 ft.
To find the volume of any can, tank, or silo, in the
shape of a cylinder, measure the diameter and the length
(or height) and then use the formula. The radius is, of
course, half the diameter.
Find the volume of cylinders with dimensions below:
Radius
Height
Radius
Height
1. 10 in.
1ipin.
2.
9 in.
'•Vin.
3.
4 ft.
10 ft.
It is sometimes important to find the total surface of
a cylinder.
This is really very simple.
The top and
bottom (the two bases) are ordi-
nary circles.
You can think of
the curved surface as a flat piece
wrapped around the cylinder.
If the radius of the cyhnder
is r, then you know that the dis-
tance around it, or circumfer-
ence, is 2 wr. Hence a rectangular
wrapper, h wide and 2 irr long, will completely cover the
curved surface of the cylinder.
4. Find the total surface
of a cyhnder with radius 3 and
altitude 6.
Curved surface =2 xr/i
= 113i
Top and bottom =2Trr^
=
56^
Total
169f
User=3andh=6inthe
first formula at the right. Use
7r = 34^.
This gives the curved
surface.
Then find the area of two circles the radius of
each of which is 3.
5. Find the total surface of each of the cyhnders in
problems 1, 2 , and 3 above.
231

Volume of a Pyramid or a Cone
^
If a rectangular solid and a pyramid have equal bases
and equal altitudes, then the volumepf the pyramid is
one third that of the rectangular solid. If a cyHnder
and a cone have equal bases and equal altitudes, then
the volume of the cone is one third that of the cylinder.
The rule is expressed as follows:
The volume of a pyramid or a cone is one third
the product of the altitude and the area of the base.
1. A receptacle for holding gravel is
in the shape of an inverted pyramid. If
the base (opening at the top) is a square
whose sides are 5^ feet and if the alti-
tude is 6 feet, how many cubic feet of
gravel wiU this receptacle hold?
2. A conical tepee is 10 ft. in diameter
at the bottom and its height is 9 ft. How
many cubic feet of air wiU it hold?
3. What is the volume of hay in a
conical haystack 8 feet high and 6 feet
in diameter at the base?
4. A large funnel used for pouring oil into an auto-
mobile is 12 inches in diameter and 10 inches high. If
231 cu. in. = 1 gal., how many pints of oil will the funnel
hold (to the tenth of a pint)?
232

Surface and Volume of a Sphere
The rules for finding the surface and the voliune of a
sphere are also important.
A circle whose radius is the same
as that of a sphere is called a great
circle of the sphere.
Ifyoucuta
sphere into two equal parts by cut-
ting it through the center, the cut
wiU be a circle.
The surface of the sphere is equal to four great circles
Hence, you have the formula at the right,
in which s is the total siu^face.
47rr2 = s
To find the volume of a sphere multiply the cube of
its radius by tt and the product by f .
r'=V
(To find the cube of a number use it as
a factor three times. Thus 4^ =4X4X4= 64.
)
^
Problems
1. What is the volume of a cyHnder whose radius is 1
and altitude 2? Use 7r = 3|.
2. What is the volume of a sphere whose radius is 1?
Use 7r = 34r.
3. Divide the answer problem 2 by the answer in
problem 1. What is this ratio?
4. Find the volimies of two spheres, one with radius 2
and one with radius 4.
What is the ratio of these
volumes?
5. If you double the radius of a sphere, you multiply
its volume by 8. Can you verify this statement from the
answers in problem 4?
233

Unit 18. The Metric System. Review
Metric Units
The metric system of weights and measiu-es is ex-
ceedingly easy to learn and to remember. It was first
worked out ana adopted in France a Httle before the year
1800. Since then it has spread gradually until now it is in
almost exclusive use in every civihzed country except the
United States and the British Empire.
For scientific
work and some engineering work, the metric system is
used in these countries also.
The fimdamental unit of the metric system is the unit
of length, the meter. The meter was originally designed
to be one ten-millionth of the distance on the earth's
sin-face from the equator to the North Pole.
The "world's'' meter is now determined from a metal
bar kept in Paris, which differs a Httle from that origi-
nally planned. The metric system used in the United
States is based on a meter that is fixed by law as equal
to 39.37 inches.
There is a metal bar of this length in
Washington, D. C, which is used as the standard meter
for aU our country.
The luiits of this system are arranged on the decimal
system. That is, each imit of length, for example, is ten
times the next smaller unit, as follows:
The Units of Length
1 kilometer (km.) =1000 m.
1 decimeter (dm.) =^ m.
1 hectometer (hm.) =100 m. 1 centimeter (cm.) =^^k ni.
1 decameter (dcm.) =10 m.
1 millimeter (mm.)
=y^q-q m.
1 meter (m.), the principal unit
234

Use of Units of Weight, Capacity, and Length
The principal unit of weight is the gram (g.)? and the
principal unit of capacity is the liter (L).
The prefixes kilo, hecto, deca, meaning thousand,
hundred, ten; and deci, centi, milli, meaning tenth,
hundredth, thousandth, are used as in the table on page
234.
That is,
kilogram, hectogram, decagram,
decigram, centigram, milligram, and gram are
units of weight.
In measuring length the meter is used in place of the
yard, the kilometer is used in place of the mile, and the
centimeter is used in place of the inch br foot.
The
millimeter is used for very small or very accurate meas-
urements.
1. Find the number of feet in 1 km.
Since 1 m. = 39.37 in., 1 km. = 39370
in.
Hence, the kilometer is approxi-
mately 3281 ft. as against 5280 ft. in a
mile. By division we now find that 1 mi. = 1 .61 km., and
1km. = .62mi.
3280.8
12)39370
39.37-36 = 1 .094
2. By what number must a
number of meters be multi-
plied to get the number of yards?
The answer is 1.094, approximately.
In the Olympic Games the meter is used instead of the
yard and the mile. Thus Olympic records are given for
runs of 100 meters, 200 meters, 400 meters, 800 meters,
1500 meters, 5000 meters, 10,000 meters, and 50,000
meters.
3. A champion skier made a jump of 67^ meters. How
many feet was this?
235

Sight Work
Length
1mm. =.001m.
1 cm.
=.01m.
1 dm.
=.1 m.
1dcm. =10m.
1 hm.
=100m.
1 km.
= 1000 m.
Read and supply the missing numbers. Use tables
at the right for reference.
1. Tell what is meant by the
prefixes milli, centi, deci, deca,
hecto, kilo.
2. Give a complete table of
weights with the gram as the prin-
cipal unit.
3. Give a complete table of capacity with the liter as
the principal unit.
4. Reduce 1 km.,
6 hm.,
9 dcm., and 8 m. to meters.
You should be able to read the
answer at once.
5* Reduce 4 km., 4 hm.,
and 7 m. to meters.
6. 4286 m.=_
dcm. =_
.
cm.
14m. =
cm. =
dm.
100 km. =
mi.
101.=_qt.
10 m. =_yd.
1cu.cm.=
cu. mm.
1cu.dm.=
cu. cm.
13. One liter is 1 cu. dm. How many Hters are there
in one cubic meter?
14. One kg. = 2.2 lb. 10 kg. = 1 myriagram. 10 myria-
grams = 1 quintal. Change 1 quintal to poimds.
236
Km.
7. 7km.=
m.
=
8.8m.=
yd.
9. 10yd. =
m.
10. 10qt. =
1.
11. 1cm.=
mm
12. 1dm.=
cm.
Convenient Equivalents |
Im.
= 39.37 in.
Im.
= 1.094 yd.
1 km.
= .621 mi.
1kg.
= 2.2 lb.
1 quintal = 220 lb.
Imi.
= 1.609 km.
1yd.
= .9144 m.
11.
= 1.056 qt.
Iqt.
= .946 1.

Problems
1. The winner of the
high jump at the Olympic
Games in 1936 cleared the
bar at 2.03 meters. How
many feet and inches (to
the nearest inch) is this?
2. How many yards
are run in a 100-meter
race?
3. What is the differ-
ence in yards between an 800-meter and a half-mile race?
4. The distance from New York to San Francisco is
3173 miles. How many kilometers is this? (Find answer
to the nearest tenth of a kilometer.)
5. The distance from Paris to Berlin is 1067 km. How
many miles is this, to the nearest tenth of a mile?
6. A rectangular tank is 3.2 meters long, 1.7 meters
wide, and .5 meter deep. How many cubic decimeters
does it hold? how many cubic meters?
7. A cylindrical tank is 2.8 meters long and 1 meter in
diameter. How many Kters will it hold?
8. How many liters of oil, to the nearest tenth of a
liter, are there in a barrel of 31^ gallons?
9. My desk is 52 inches wide. How many centimeters
wide is it, to the nearest centimeter?
10. The airplane distance from Chicago to New York is
given as 749 miles. How many kilometers is this?
11. How many kilometers per hour is 60 mi. per hour?
12. An airplane goes 275 miles per hour. How many
kilometers per hour does it go?
237

Relations among Metric Units
The principal units of capacity and weight (the hter
and gram) are made to depend upon the meter.
One Hter is one cubic decimeter. Since 1 decimeter is
3.937 in. (1 meter = 39.37 in.), you can find by multiply-
ing that one liter (1 cu. dm.) equals approximately 61.023
cu. in.
By further computation you find that approxi-
mately 1 qt. = .95 1. and 11.= 1.06 qt.
The kilogram, which is 1000 grams, is defined as fol-
lows: One liter of water near the freezing point (or about
39° Fahrenheit) weighs one kilogram. One kUogram is
very nearly 2.2 pounds.
That is, 1 kg. =2.2 lb. and
lib. =.454 kg.
The unit for measuring land where you use the acre
is the hectare, which is 10,000 square meters. 1 hectare =
2.47 acres and 1 acre = .405 hec. Farmers in France and
Germany speak of their farms as containing so many
hectares.
1. A gallon of milk contains how many liters?
2. Ten pounds of butter is how many kilograms?
3. Tom weighs 120 pounds. How many kilograms
does he weigh?
4. A field is 400 meters wide and 600 meters long.
How many hectares are theice in this field?
5. A bushel of wheat weighs how many kilograms?
(1 bu. of wheat =60 lb.)
6. A ton of coal is how many kilograms of coal?
7. A horse weighing 1500 pounds weighs how many
kilograms?
238

Problem Practice
1. At 75^ per bushel, what is the value of the wheat
in a bin 18 feet long, 15 feet wide, and 8 feet deep? (1
cubic foot =f bu.)
2. My father owns property having a cash value of
$10,000. The assessed value for taxation is 40% of the
cash value, and the tax rate is 6.25%. What is the
amount of my father's taxes?
3. Allowing 490 pounds per cubic foot, what is the
weight of a steel ball 12 inches in diameter?
4. How many bushels of wheat are there in a conical
pile 14 feet in diameter and 9 feet high?
5. What is the volimie of a pyramid having a base 8
inches square and a height of 12 inches?
6. How many tons of silage will fill a silo 14 ft. in
diameter and 50 ft. high? Allow 50 cu. ft. per ton.
7. Find the volume of a pyramid having a height of
8 feet and a base 10 feet square.
8. How many gallons of water will a hot- water tank
hold that is 6 feet high and 14 inches in diameter?
9. Find the interest on $15,000 for 55 days at 5^%.
10. The diameter of a cylindrical tank is 1 meter, and
its altitude is 1^ meters.
How many Hters will it hold?
11. A conical pile of gravel is 2.8 meters high and 3
meters in diameter. How many cubic meters are there in
this pile?
12. A sphere is 30 centimeters in diameter. How many
square centimeters are there in its surface?
13. How many cubic centimeters are there in the
sphere in problem 12?
239

Special Practice in Decimals
Write in columns and add the following:
1. $75.96+$8.04+$719+$56+$83.69+$7.89
2. $2.68+$45.93+$372.80+$709.64+$7.92
3. $2.80+$5.82+$37.18+$.81 +$6.93+$794
4. $8.48+$37.59+$684.73+$9.45+$.92+$7.84
5. $8.73+$1 .79+$59.29+$6.94+$0.92+$6.60
6. $88.35+$9.71 +$48.45+$7.92+$0.68+$297
7. 1.348+807+95.2+378+86.8+20.5+.93
8.
.736+70.6+8.199+.76+84+62.9+54.9
9. 3 .78+16.9+379+8.483+.759+6.84+817
Write in columns and subtract the following:
10. 76.84-18.99
3.739-2 .502
7886-35.25
11.
8.07-3.918
48.2 -3 .97
927.5-48.41
12.
9.71-4.88
80.35-66.92
4.96-2.99
13.
597-13.78
487-37.94
6.29-4.937
14. 81.63-79.98
84.37-59.68
4.81-3 .728
Multiply the following:
15. 7 .59X60.8
47.1x.956
.836X.97
16.
.89X26
8.45X93.7
28.07X9.06
17. 8.17X32.8
,50.8X271
. 82X9.74
18. 89 .2X68
4.59X362
8.07X90
19. 6.79X.63
865X.91
.7 4x80.6
Divide.
Find quotients correct to three decimals.
20. 4 .8)67:9
18.6)7i06
37.3)95:28
21. 48.3)28.62
97.5)48.41
71.9)3.38
22. 66.2)904
29.9)49.8
7.84)87,49
240

Practice in Fractions
Find the sum of each of the following pairs:
1.
1
2
i
ii
i1
1
2i
1
2
3.
4
1
2
1
8
iA
2.
1
2
i
ii1i
i1
i1iif
1
T2
3.1i
ii
if
ii
1
2f
iiitV
4.11
ii
1i
if
f1
ii fA
5.11
if
11
2
"3
i
3.
4i
1iitV
6.fA
ii
f^
i111
i
1
8
1Vs
7. Find the difference between the larger and the
smaller fraction in each of the preceding pairs.
8. Find the products of the pairs of fractions in exer-
cises 1-6. Give each product in the lowest terms.
9. Divide the first fraction by the second fraction in
each pair in exercises 1-6 .
Add the following:
10. ^
7i
^
12i 6| 8f
12i
18|
3i
5i
3i
7i5iH
9i
5^
Zi
6i
6i
5,V
7^
9|
7t% Ji
11. 16i 50i 7i
14i 5i
104i
7| 9f
9|mH7f9|
9i 24| 7|
1|
2i 5i 15tV
7A191JlM
Subtract the following:
12. 18i
6i
8J
12f
311 14i 47|
191
9f
Si' 4|
9i
9f
9i
29i
121
13. 21i 9i
101
15A 6| 16|
141
m
n2iJi9i41
51
51 181
241

Practice in Fractions and Decimals
Find the product of each of the following pairs of num-
bers.
Give each answer in the simplest form.
1. 11H
16iH H 21
121 3
4i33
2. 9|2|
10131
25 41
36i 11
8i1i
3. 2i4
15141
12| 11
121 8
3|4|
4. 322i
64111
48 21
18^31
51 48
5. 102|
52111
361 21
42|6i
57 2f
6. In the preceding pairs of numbers, divide the first
by the second and reduce each result to simplest form.
For each of the following, make up a cash account.
Rule paper for putting the account in the proper form.
Exactly the same form may be used for a statement of
bank balance.
Find the final balance in each case.
Supply dates within the same month for each item.
7. Balance: $15.80 . Receipts (deposits): $1.50, %.^b,
$2.50, $3.15. Paid out (drew checks): $1.80, $2.30, $1.15,
$.75 .
8. Balance: $150.60. Receipts (deposits): $250.00,
$25.00, $37.50 . Paid out (drew checks): $40, $17.80,
$35.50, $7.15, $65.
9. Balance: $280.32. Receipts (deposits): $300, $15.
Paid out (drew checks): $3.15, $75, $1.20, $9.75, $12.40,
$39.60.
Supply the nimibers missing below. Find rates to the
nearest tenth of 1%. Find bases to the nearest tenth.
Base
Rate Percentage
Base
Rate Percentage
10.
875
4^%
—
17
—
6
11.
47
—
24
—
31%
480
12.
—
6%
260
340
4i%
-
13. 1560
5i%
—
151
—
78
242

Practice in Percentage
Write the following as fractions in lowest terms:
1.
25%
2.
80%
3. m%
4. 9tV%
5.
12%
75%
30%
62i%
44|%
55%
10%
90%
87i%
33-5 -%
1
50%
40%
1H%
45%
Write the following as decimals:
6.
9% 4.3%
5i%
2|%
7.
1% 5.16% 3.05% 25i%
8.
1% 21% 110% 250%
9. H% 42.4% 5.55% 83.6%
Write the following as per cents:
10.
.6
.17
1.04
1.20
11. .0125
.0275
.125
1.8
12. 3.5
.35
.035
3
13. .0025
.0075
.0 01
. 105
Change the following to per cents:
14.
15.
16.
17.
18.
19.
20. ^
21. ^
9
3-"
20
1
TO
A
1
25
11
14
29
14
7
1
4
25
9
17
12
31
tV
7
16
7
20
4
19
13
34
"1
1
3
1
7
12
1
50
8
21
41
21
20%
60%
6i%
66|%
186%
1.L»/0
10.5%
125%
240%
.124
.107
.01
1.05
X
6
1
12
T^
1
40
12
23
19
53
1%
2%
6%
5%
.75%
1.1%
200%
400%
. 055
. 005
1.01
.275
_5
12
1
16
9
1
1
20
1
30
15
26
23
64
243

Practice in Percentage
Find the net proceeds of each of the following commis-
sion sales:
Sales Com.
]Exp. Paid
Sales Com. Exp. Paid
1. $149
8%-^
$4.80
$1200
5% $14.76
2.
490.60 7% 12.65
527.80
7%
9.81
3.
87.40 9%
5.20
5800.00
4% 19.24
4.
593.50 2% 21.60
657.20
8% 47.40
5, 1840.00 5% 12.45
8400.00 4% 27.62
Find the net amount in each of the following:
Gross Price
Discounts
Gross Price
Discounts
6.
$18.40
20%, 10%, 5%
$940.00
50%, 5%. 2%
7.
360.00
25%, 5%, 2%
2740.00
35%, 5%, 1%
8.
216.80
30%, 10%
•3580.00
25%, 15%, 5%
ST.
1560.00
40%, 5%, 2%
150.00
20%, 20%, 2%
10.
845.00
27%, 10%, 3%
487.50
^5%, 20%, 16%
Find interest and amount of the following:
Principal Rate
Time
Principal
Rate
Time
11. $740
6%
4 mo.
$450
6% 105 da.
12. 4200
5i%
3 mo.
1675
5%
50 da.
13. 6500
4^%
5 mo.
950
5i%
120 da.
14. 850
51% 45 da.
2500
4|%
72 da.
ItB. 8900
H% 75 da.
1725
5%
85 da.
Find amounts below at compound interest, each being
compounded annually:
Principal Rate
Time
Principal Rate
Time
16. $500
3%
5 yr.
$2000
i%
10 yr.
17. 350
2%
8yr.
390
1i%
15 yr.
18.
225
4% 10 yr.
720
2%
20 yr.
19.
800
H% 7yr.
2150
3%
25 yr.
20^ 1200
1% 20 yr.
1500
4%
Syr.
244

The Great Pyramid
1. The Great Pyramid
(before
its
dimensions
were reduced by weather-
ing) was 481 feet high and
its base was 756 feet
square.
Find how many
acres were covered by the
base, correct to the near-
est tenth.
2. What fraction of a
mile was the perimeter of the base of this pyramid?
3. Find the volume of the Great Pyramid in cubic
yards, correct to the nearest yard.
4. Originally, each one of the four triangular sides of
the pyramid was smooth and had a slant height of about
600 feet. Find the area of the four sides in square yards;
in acres, correct to the nearest tenth.
5. It has been estimated that the Great Pyramid
weighed 6,848,000 tons and that it contained 2,300,000
blocks of stone.
Find the average weight of these
blocks.
6. The present height of the Great Pyramid is 451
feet.
What per cent of the height has been lost by
weathering? (It was built about 3000 B. C .)
7. Find the volume of a pyramid with an altitude of
20 inches and a base 25 inches square.
8. The radius of the base of a cone is 28 inches and the
altitude is 40 inches.
Find its volume.
9. A can 14 inches in diameter and 12 inches high will
hold how many gallons of milk?
245

Eighth Self-Test
Testing What You Have Learned
The purpose of this last self-test is to enable you to
learn whether you can really solve all the different kinds
of problems that you have studied during the year.
If
you find that you can plan the solutions of these prob-
lems without too much diflSculty and if you can perform
all the fundamental processes reasonably well, then you
may feel that you have done good work in arithmetic in
your whole elementary school course.
1. On an automobile trip of 500 miles, 25 gallons of
gasoline were used. At this rate, how many gallons have
been used in a car which has gone 38,400 miles?
2. A beet sugar factory has brought in 147,000 tons
of sugar beets.
How many tons of sugar are there in
these beets if they contain 16.5% of sugar? How many
100-pound sacks of sugar will this make?
3. At 48 cents a bushel, what is the value of a load of
oats weighing 5680 pounds? (1 bu. oats =32 lb.)
4. At $10.40 per ton, what is the value of a load of
coal weighing 12,740 pounds?
5. A schoolroom is 28 feet wide and 30 feet long. How
many square feet of floor space per pupil are there in this
room if there are 35 pupils?
6. If the room in problem 5 is 9^ feet high, how many
cubic feet of air space per pupil does it contain?
7. How many square yards of plastering are there in
the waUs and ceiling of a room 30 feet long, 21 feet wide,
and 9 feet high? Deduct 18 square yards for openings.
8. At 42 cubic feet per ton, how many tons wiU a bin
hold that is 18 feet long, 5 feet wide, and 7 feet deep?
246

Problem Test
1. A very fast steamship averaged 31.5 miles per hour
for 75 hours and then, on account of fog, traveled the
rest of its journey at 18 miles per hour for 28 hours.
What was its average speed in miles per hour for the
whole journey?
2. A load weighing 9450 pounds is put on a truck that
weighs 4780 pounds when empty. The load is what per
cent of the weight of the loaded truck? The load is
called the ''Hve load."
This question is then asked:
**What per cent of the weight is the live load?"
3. Five years ago a building lot was worth $800, but
it now sells at $2000. What per cent has the lot increased
in value?
4. Ten years ago a house was worth $8600; now it has
depreciated to $6020. What per cent has it decreased in
value?
5. A farmer knows that his seed corn will shrink 16
per cent from harvest time until he needs to use it in the
spring. If he needs 125 bushels in the spring, how many
bushels must be set aside for seed in the fall? Find
answer to the nearest bushel.
6. Mr. Coleman has just finished building a new
house. The lot cost $700 and the house $6500. In find-
ing the cost of living in this house, the Colemans figured
interest at 5^% on the total cost, depreciation at 3% of
the cost of the house, taxes $85, 8^ tons of coal at $9.75
per ton.
How much do these items taken together
amount to per month?
7. A merchant bought a refrigerator for $65 and
marked it for sale at $110. Later he sold it at a discount
of 15%. What was his margin? If the overhead was $25,
what was his net profit?
247

Problem Test
1. A dealer marked a coat costing $24 to allow a mar-
gin of 25% of the selling price.
What was the selling
price of the coat?
2. The cash price of a bed is $35 and the installment
price is $10 down and 9 monthly payments of $5 each.
How much more is the installment price than the cash
price?
3. An article bought for $3.50 was marked 60 per cent
above cost. Then it was sold at a discount of 20 per cent.
What was the margin?
4. Mr. Hill bought a washing machine for $62 and
sold it for $95. His overhead was $28. The cost, margin,
overhead, and profit were each what per cent of the sell-
ing price?
5. Find the interest on $1740 for 90 days at 5%.
6. Find the interest at 5^% on $2100 for 105 days.
7. A note for $1150 due in 4 months was discounted at
the bank at 6%. What were the proceeds?
8. Mr. White borrowed $5000 at 5 per cent interest.
In 6 months he paid $1000, part of which was interest
for the 6 months. How much was paid on principal?
9. A merchant bought goods listed at $3140 with
discounts 30%, 5%, and 2%. What was the net amount
of the bill?
10. Tom Moore takes a three-year term fire insurance
poHcy for $8000, the rate being 42 cents per $100. What
is the premiimi, if it is 2^ times the regular one-year
premium?
11. Four hundred shares of stock were bought at 37f,
brokerage 15 cents. What was the total cost?
248
1

Problem Test
1. Mr. Ward borrowed $10,000 at 5%, with an agree-
ment that he was to pay $500 every 6 months. Out of
this amount interest was to be paid on that part of the
principal that was unpaid and drawing interest during
the preceding six months. The remainder was to be ap-
pHed on the principal. Write a schedule of this loan for
5 years.
2. Find correct to one tenth of a foot the lengfh of a
diagonal of a rug that is 11 ft. wide and 15 ft. long.
3. Conrad Orr, age 25, took out a $10,000 twenty-
year endowment poHcy, premium $47.84 per $1000. By
how much does the sum of his premiums for twenty years
differ from the face of the policy?
4. A stick 8 ft. long put vertically in the ground casts
a shadow 11 ft. long. At the same time, a tree casts a
shadow 157 ft. long. Find the height of the tree.
5. A cylindrical oil tank is 8 feet in diameter and 14
feet high. How many gallons of oil does it hold? (1 cu.
ft.= 7tgal.)
6. Find the total surface (square feet of metal) of the
tank in problem 5.
7. In one city, schools cost $310,000 a year and the
assessed valuation is $27,800,000. What is the tax rate
for schools? Find the answer to the nearest hundredth
ofl%.
8. The assessed valuation of a family living in the
city in problem 7 is $11,400. What is the school tax of
this family?
9. Find the surface and the volume of a sphere whose
e TT-
249
diameter is 14 inches.
Use tt =^

Testing Your Readiness for Next Year's Wor/c
Addition and Subtraction
If you can do the work in the following pages wdth
reasonable speed and accuracy, you will know that you
are well prepared for mathematics in high school and also
in the practical affairs of your life.
Add the following:
1
695
43
4108
7800
209
521
74
109
835
896
8175
2347
157
7204
1802
123
356
8790
3563
137
2040
5876
248
654
9247
799
964
94
2906
293
146
2108
807
539
818
4506
Write in columns and add:
2. 70.5+21.19+.814+87.8+300+.087+4.96
3. 5 .64+98.6+52.97+4.54+91.35+4.91 +18.94
4. 50 .5+29.81 +680+.137+7.g9+8.71 +7.801
Subtract the following:
5. 8102
9000
4241
2492
4706
8975
5684
8042
2374
1678
3987
6987
6. 5042
2927
3981
2986
7204
2631
4962
3829
1894
1798
5000
4209
7. 7893
3498
6370
2981
2080
1887
5837
2695
5182
4196
1400
1204
Write in columns and subtract:
8.
42.81-16.39
50-24 .76
7.39 -4.876
9. 839 .58 -427
1.5-1 .246
9.37 -.459
250
'

Practice in Addition and Subtraction
Add and check the following:
2.
4
7
9
5
_7
_6
6
8
7
9
7
_8
6
9
J
9
8
_5
8
7
J
6
4
5
8
_8
_9
3
5
9
8
8
4
2.
_§
8
3
9
_7
9
5
6
_9
8
2
9
_4
6
7
4
_7
9
6
8
6
8
2
8
9
6
8
_8
J_
$278.56
94.68
756.95
683.74
$67.94
856.79
90.48
73.56
$438.06
87.79
865.37
74.58
$869.00
96.47
8.59
527.85
$1760
894
4800
87
ubtract and prove \ ;he followingr *
45806
37998
81096
40897
64839
57926
70002
68965
87114
36506
5. Find the missing niunbers in Mr. Walker's balance
in his bank for the four months below:
March
April
May June
Balances
$390.45
$-
%—
$—
Deposits
417.65
504.10
398.75
492.15
Checks
65.00
65.00
65.00
65.00
40.00
31.40
47.66
102.50
12.80
18.62
51.90
7.85
7.45
97.14
5.64
13.47
108.14
49.60
15.40
27.59
51.18
18.00
10.00
52.00
1.85
40.50
9.50
816.75
Totals
$-
$-
$—$
—
Balances
$~
$-
$—%
—
251

Mixed Practice
Multiply and check:
1. 14.5
36.4
5.74
39.5
9.15
2.72
46.8
57.9
18.42
. 754
9.6
263
2. 54.16
2.45
4.57
39.5
9.86
45.3
21.63
25.2
2.72
38.7
4.95
29.4
3. 1.94
876
43.8
3.47
88.9
.67
4.52
2.97
65.9
4.52
78.4
8.75
Find quotients below correct to two decimals:
4. 45.2)61.54
2.73)1592
47.8)53.9
6.84)354.6
5. 61.4)59.42
7.39)49.3
65.3)21.74
4.51)9.282
6. 8.76)2.732
3.84)823.6
74.3)48.35
46.5)29.87
Read and supply the missing words and numbers:
7. The fraction f indicates that
is to be divided
by
The numbers 7 and 8 in this fraction are called
the
of the fraction.
8. If the terms of a fraction are multiphed by the
same number, the value of the fraction
changed. If
the terms are divided by the same number, the value of
the fraction
changed. Give examples of both cases.
9. TheLed.of1I,I,I,
-^is_.
10.TheLed.ofI,I,I,I,T%is_.
11. To change ^, f , f to 12ths, multiply the terms of
^ by ,thetermsoffby^, andthetermsoffby
12.Toaddf,^and^,
reduce the fractions to
Then add the
and reduce to
form.
13. To subtract ^ from j^, reduce the fractions to —
,
subtract
from
,
and reduce to
.
252

84.1
-(4)
9.7
-(7)
588 7 28 -(1)
7569
815.77
- >(1)
Practice in Multiplication and Division
!• State the rule for plac-
ing the decimal point in niiil=
tiplying decimals.
2. Explain the check on
multiphcation shown at the
right.
3. State the rule for plac-
ing the decimal point in division.
4. Explain the
proof of division
shown at the
right.
Notice
that we prove
exactly as with
whole numbers.
5. State the
rule for finding
the last figure
(4)
4.58
5.17)23.70
20 68
- (8)
- >(3)
302
2585
4X8 =
5+7 =
=
32
=
12
-(5)
- (3)
43 50
4136
2 14 ->(7)
in rounded quotients.
^ Multiply and check the following:
6.
7.
6.28
4.07
83.9
.84
6.28
46.5
16.72
8.7
6.45
. 613
78.3
46.2
7.96
4.85
620.7
8.39
59.3
.075
69.2
8.07
48.9
34.8
.675
.493
8. Multiply each number in ]line A by each in line B.
A
675
493
825
946
875
809
B
89
74
63
25
48
409
Divide. Find quotients correct to two decimals.
9. 4 .08)92.75
7.81)645.1
253
3.72)2783
69.4)81.6

Practice in Fundamentals'
Add:
1. $197.34
$790.00
$57.50
$18.95
$40.31
26.85
1940.00
312.75
390.00
93.58
421 .56
186.50
18.94
35.75
151.79
43.21
450.75
8.70
142.61
242.55
191.65
2900.00
20.40
1.93
97.13
32.58
2160.00
356.80
70.00
175.49
203.16
740.00
87.52
4.45
801.20
Write the following in columns and add:
2. 4.76+91 .4+864+.397+.046+54.6H-12 .45
3. 65.34+4.92+65.32+550+92+354.7+64.70
4. 48.3+.049+1. 36+3.46+80.64+2.93+564.7
Add the following horizontally:
5. 8+2+6+4+6+1+5
6. 4+9+7+5+5+3
7. 2+6+4+3+4+2+9
8. 6+8+4+5+7+9
Write the following in colmnns and subtract:
9. 174.24-29.08
3040-204.6
5-3.46
10. 48-43.28
5.41-3.786
3.93-2 .976
Multiply the following:
11. 5.2
96
4.52
41.52
97
13.5
68.2
3.95
1.56
3.75
6.41
.38
J
12.
.84
9.6
.342
8.96
65
5.5
4.75
5.8
3.45
524
4.98
3.5
Find quoti ents correct to two decin
8)5734
6)2355
lals.
13. 7)8697
4)7008
7)3478
14. 9)6967
7)6780
8)4075
6)2854
9)6560
15. 7)3769
8)6873
9)7770
254
4)3915
8)7010

Rounded Numbers
1. The last census report gave the population of a
certain village as 3487. Is anyone certain that on any
given day the population was exactly this number?
Give reasons for your answer. Which number states the
nearer approximation to 3487: 3480 or 3490? 3400 or
3500?
2. In estimating the population of such a village,
wotdd you give the nimiber to the nearest unit? to the
nearest ten? to the nearest hundred? to the nearest
thousand? You might say it is between 3000 and 4000.
When you estimate the population as 4000, you would
mean it is nearer 4000 than to 3000 or 5000.
3. At the right the nimiber 3487 is
rounded to the nearest ten, to the nearest
hundred, and to the nearest thousand. State
exactly what is meant by each of these.
4. In the last census report, populations of certain
American cities were given
as shown at the right. Give
each
of
these
numbers
rounded to the nearest thou-
sand. Give each rounded
to the nearest ten thousand;
to the nearest hundred thousand.
5. How would you estimate the present population of
Buffalo? To make a good estimate, what would you
want to know about the recent history of Buffalo?
6. Look up the population of your own state as given
by the last census. Then estimate the present popula-
tion to the nearest million; the nearest hundred thousand.
7. Look up the populations of the three largest cities
in the coimtry rounded to the nearest hundred thousand.
255
Buffalo
575,901
Minneapolis 492,370
Seattle
368,301
St. Paul
287,736
New Haven 160,605

Mixed Practice
By horizontal multiplication find these products:
1. 4X$2.17 8X$24.36 2X$19.60
5X$4.96
2. 7X$9.35
9X$81.40
3 X $81 47.60
6X$41.92
3. Supply the numbers missing in the following ac-
count that a farmer kept of his hay field:
Expenditures
Use of land, 42 acres
at $5.50
Irrigating
Cutting and stack-
ing
Use of machinery
Interest
Total expenditures
$53
153
29
9
70
25
60
40
Receipts
98 tons of hay at
$9.20
Pasture
Total receipts
Total expenditures
Gain
$21 00
$_—
$——
$_—
4. The daily attendance in each of ten schools in a
city is given below.
Find (a) the daily totals for all
schools and (b) the weekly total for each school. Then
find (c) the average daily attendance in each school for
the week and (d) in all schools for the week.
School Monday Tuesday Wednesday Thursday Friday Totals
1
763
784
752
791
780
2
391
401
398
392
389
^^_
3
1262
1243
1286
1271
1262
..^_
4
913
898
924
902
908
_^
5
593
612
604
598
591
,_^
6
814
832
817
824
809
7
1102
1124
1133
1098
1116
_^_
8
1467
1502
1487
1492
1490
^^_
947
959
949
971
967
_
10
1202
1192
1187
1209
1212
_
256

Working with Fractions
Change these fractions to lowest terms:
1_8__9_J_0 _6 _JL5 12
14
15
--•10
12
15
16
18
20
21
24
9J_0i_8 2_4J_2I_4
15
20
18
-^^
25
30
27
18
16
20
24
32
q2_54_83 _62_5J_6
5
12
21
*^*
40
60
48
45
24
15
30
35
Change to whole or mixed numbers:
A1±
9.JL3I_4
9.
8
12
12
^•3
425683
4
P;2j42_52J_i _2
65
34
20
12
*^'8
6
5
10"
15
8
6
9
Change these mixed numbers to improper fractions:
6. 4|
6|
2t
7|
31
41
9f
7 fvL
?7
OS
47
RA
^4
97
Add the Hke fractions below:
Q32253753
*^'4
3
5
6
8
9
12
16
3
2
4
5
7
5
11
7
- i._J._L _6_8._9.J_2
16.
941 05
Q_7_
'^Z
f\7
45
17
•
^
^8
*^10
^8
^12
^
'10
£6.
2^
^1
£8.
Qi2
^8
'^l
Subtract the like fractions below:
1A3 5
7
8
9
11
13
1±
^^'
46 8 9 T0T2"r5
16
113 5
3
5
8
7
3__L
J_
9
TO
T2
T5
T6
11. ^
51
3|
61
5f
3i
8t^
95^
43.
-11
Q5
94
92.
R3
12. 5
4
2
6
5
8
9
2|
3i
If
3i
21
4|
Tj^
13. 4|-|
H-l
12-111
51-li
17
20
411
ft7_49
75_47
1U 19
^TO
^T6 ^T6
'12 ^12
'24
24

Addition and Subtraction of Fractions
Write the sum of each pair of fractions:
1
2
i
i1
ii
i1
ii
i1
ii
1
2
f
ii
i1
i
1
4
i1
2
4
1
3
2
4
1
1
6
1
3
1
4
1
6
3.
4
i
i1
fi
i
1
5
11
i1
fi
1
1
16
5-8 . In each of the above pair of fractions, subtract
the smaller from the larger.
Add. To check, go over the work again.
9. 11
3|
5i
2i 3i
171
14i
2i
1
8|
5|
4|
211
13i
3|
4i
7i
61 3| 131
17i
If
9|
51
5^^
7i%
6t%
7t^
0.
11
2i
H6i
StV
3|
If
2i 5i
3|
7i
4|
2i
6|
3iH
2i
6|
2|
4i
7f
4iV
8i
7f
3|
8i
6.^
91
1. 4|
9| 31
7f
9i
8i
5f
6i
5|
9|
5i
7f
n
7i
2i
6in
4| 8i
5i
91
li
7t%
5|
2t^
3i
6|
3|
2.3|2i5t%
8i
1
4i
6i
2tV
5t%
1
9i
2i
6|
7|
1
9|8|7i
9f
i
3|
4|
7| 3| 84r
5^
4t^
8t^
258
J

Subtraction of Fractions
Subtract. To prove, add subtrahend and remainder.
1.i
1
t
1
i
f
1
1
1
2_
i
i
i
i
i
i
i
2.1
1
1
f
T%
ii
13
1
i
i
i
i
i
±3.
4
i
3. 8f
7|
16|
9t^
3f
14A 231
li
3i
4|
2|
li
,8i
191
4. 9i
4|
7|
8i
12| 24|
59t%
li
2i
5i
11
7t%
12f
411
5.4
6
8|
10
7
8i
6i
2|
Ji
*
2i
5tV
2i
6. 8i
6f
5t^
n7i
4i
3i
HM2|
4t^
3A 21
1t^
7. 5|
7f
9|
6|
4i
8f
5t%
M!i
5.%
3|
li
5|
11
8. 4|
IOt^s
6^
7i
9i
5f
8i
31
5f
2f
5^
6t\
2,«o
Zii
9. 2i
8i
3|
8i
5ii
7f 16|
li
Mm.
2il
4|
2i%,
9|
10. 5|--T%
7--Wo 5f-2A 6|- 4i\
9|-i
11. 7i --H
6-
-m 3|-2^ 8|-3f
9^-§
259

Problem Practice
1. From a bolt of cloth containing 25^ yards, pieces
4^ yards, 3f yards, and 2^ yards were sold. How many
yards long should the remaining piece be?
2. A pictm-e is 14^ inches wide and 18f inches high.
Find its area in square inches.
3. What is the cost of a 6f pound ham at 32^ cents
per pound?
4. At 39 cents a pound, what is the cost of 3 pounds
and 10 ounces of round steak?
5. If I buy 9 gallons of gasoline at 19.3 cents per gal-
lon, what is my change from $2?
6. Fred caught 3 trout weighing If lb. , 3| lb., and 2^
lb. Find the average weight of the trout.
7. I drove 212 mi. in 4 hr. 30 min. What was my aver-
age speed? (Find answer correct to a tenth of a mile.)
8.Aroomis18ft.6in.longand14ft.3in.wide.
What is its area?
9. On a floor 15 ft. wide and 21 ft. long, there is a
rug9ft,6in.by13ft.4in.
What is the area of that
part of the floor not covered by the rug?
10. A piece of glass 49 in. by 56 in. was sold for $21.75.
What was the price per square foot, correct to the nearest
cent?
11. At $3.25 per square yard, what is the cost of a walk
3^ feet wide and 140 feet long?
12. By what number must 37^ be multiplied to make
the product 1800?
13. Add Si to the product of 4| and 6|.
260

Multiplication of Fractions
1.
ix|
|X|
|X|
fx-^
fxi^
2.
fxi
|Xt%
tXT%
AXA |X|
3.
fXlO
|X12
|X15
fxis |X25
4. 12X|f
15X|-
32XH 18Xf 35XA
5.
iX2i
fXH
^X3|
JX3i |X2|
6. 3fXf
71 XI
4iX|i UXt^ ^y<H
7. 2iX3|
2fX2|
4fXli
3iX2f 2fX3i
8. 5iX4i 12iXlH 4iX4i
3|X2| 8iX4i
9. 7^X4,^
3iX3i
4fX2f| 2T%X54r 4|X4|
10. 2|X1| 2fXH 3AX1I
3iX2i 41X41
Division of Fractions
1.
l-t
l-f
l-l
1-1
l-i
2.
1^1
i^-i
T%-A
f-l
l-l
3.
I^A f-H
i-l
l-i
l-A
4.
5-1
6^1
4^A
9--M
8^1
5.
7-1
9^1
6-1%
5^1
10^1
6.
8^3^
6-2|
5-6f
9^4i
6-MI
7.
5-6| 8^H
7^2f
6H-2i
4-Hl|
8. 6i-^4
6|-8
9i^7
5^4-11
3|-3
9. 5f-|
2|-|
4i-i
3|-f
3|-|
10. 3i-H 6i^2i 2|^6i
2i-4i 61^51
11. 4i-3i 8|-2i 6|-1|
6|-6| 4f-3f
12. 9i^5i 6i-4i 2|-3^ 1i-1| H-2|
13. H^2| 9J :4| 1|-H
3|-5| H-1|
14. 8i^|
4f-|
3|-|
3I-1J 9|^2|
261

Equations
Solve each equation below:
1.
4a;=48
6a--= 42
3a;=10
12y=60
2.
7a;=51
8b-- = 96
5y=45
15a; = 75
3.
i=«
b
6''= 11
^12
l,"'"
4.
fe'"
X
35'
= 100
1^
=54
1=30
5.
x+3=11
a;+4.5 = 7.5
y-9 =72
6.
x-3=^^
a+13 = 25
6+8=23
7. 2a:+5 = 15
3x-4 =8
6a+3 = 75
8.
1+4=13
1+7=14
1+12 = 24
9.
1-7
=20
^-6=2
1-4 =
5
0. y+4=10
1-5.3
2x
~+3a; = 25
Solve the following problems using equations:
11. In 2 years from now Florence will be 20 years old.
How old is she now?
12. If 13 is added to a certain number, the siun is 25.
What is the nimiber?
13. Four times a number added to 8 equals 40. What is
the number?
14. If 17 is subtracted from one third of a number,
the remainder is 8. Find the number.
15. Four times a number increased by 9 equals 37.
What is the number?
16. Six times a nimaber less 7 equals 47. What is the
number?
262
\

Percentage
Change these fractions to per cents:
-•
1
4
2
8
3
12
20
^5
9_3 _3.
3.
5.
7
J.
5.
7
-^•10
4
8
8
8
6
6
10
Q_9_2._!_ _5 _J.2.
3.
4
^•10
340 12
5
5
5
5
Change the following fractions to decimals; then to per
cents, correct to 1 tenth of 1%.
A
4
8
7
3
M
12
13
16
^•TT
13
12
16
15
17
TT
T9
P;_7_I _9JL3_8 _J _31_L
15.
31
*^'
22
24
25
26
27
30
32
40
Change the following decimals to per cents:
6.
.9
.06
.48
.045
. 005
. 015
7.
.8 07
. 03i
.06^
.33^
1.08
1.75
8.
.105
.0625
. 4275
. 625
. 125
. 875
Change the per cents below to decimals:
9. 6%
28%. 4i% 3i% 20|% 8.5%
10. 5 .6%
.5%
1.2% 12^% 6i%
.15%
11. 105% 150% 325% 110%) 200% 301%.
12. Find 15% of $200; then name the base, the rate,
and the percentage.
13. Find what per cent $45 is of $360; then name the
base, the rate, and the percentage.
14. $3.50 is 20% of what number? Find the number;
then name the base, the rate, and the percentage.
15. State each of the following formulas as a rule in
yourownwords:br=p |= '^
-
=6.
16. State the formula to be used in solving each of
problems 12, 13, and 14.
263

Problem Practice
1. In a recent bond election in a certain city, tliere
were 3485 qualified voters.
In order to make the vote
valid, it was necessary that at least 40 per cent of these
vote at the election.
However, 1297 actually voted, of
whom 1127 were in favor of the bond issue.
Was the
vote sufficient for the bonds to be sold?
2. The weight of a certain grade of hogs is reduced
about 31 per cent in butchering. At this rate, how much
will a 250-pound hog weigh when butchered?
3. A certain hog weighing 280 pounds weighed 198
pounds after it was butchered. What per cent did its
weight decrease?
4. Carl bought a young turkey weighing 8.5 pounds
and kept it until it weighed 15 pounds. What per cent
did the turkey increase in weight?
5. A used automobile was bought for $560. At the
end of one year, it was sold for $400. What per cent did
it decrease in value?
6. In one month a farmer deHvered 7460 pounds of
milk to the creamery. This milk averaged 4.7 per cent
butterfat. At 36 cents per pound, what was the value
of this butterfat?
7. In a small store, the sales for one year totaled
$21,426.25. The cost of the goods sold was $13,670,
and the overhead was $7040. What was the profit?
What per cent of the sales was the cost? the overhead?
the profit? Find each correct to one tenth of 1 per cent.
Add these per cents.
How do you explain the sum?
8. A board 12 inches wide when cut, shrank to 11.7
inches wide, when seasoned. What per cent did this
board shrink in width?
264
i

Practice in Percentage
Given the base and rate below, find the percentage:
1. 5%of$1.75
25% of $49
106% of $48.65
2.
.5% of 1250
4.5% of 964
12^% of 1700
3.
1%of6500
31% of 5000
1 6|% of 2500
4.
.8% of 3600
21% of 7860
6^% of 7200
5.
.25% of 490
22.5% of 425 87^% of 480
6. 250% of 330
6.4% of 940
66|% of 1 500
7.
1i%of4500
11^%of81
371% of 4400
8.
.95% of $4.50
20% of $80
62i%of1265
9. 10% of $135
6|%of900
75% of 9600
Given the base and percentage below, find the rate:
10.
12is_%of24.
24is—%of12.
11. 45is_%of135.
800 is _% of 640.
12. 6 is _%, of 1200.
40 is _%, of 8000.
13. 51is_%of17.
190is_%of7600.
14. $3.50 is _% of $50.
$600 is _% of $960.
15. $47 is^_% of $225.
7.48 is _%o of 39.8 .
16. 39 is _%, of180.
749 is _%, of 625.
17. 130 is _%, of 780.
85.3 is _% of 1050.
18. 8.2 is _%, of 25.6.
1440is_%of960.
Given the rate and percentage below, find the base:
19. $9is25%oof_.
$62.50 is 1121%, of __ .
20. 24is15%of_.
1200 is 150% of __.
21. 45is75%oof
208 is 26%o of
22. 75is331%of__
$960 is 1
6f% of
265
*

Problems
1. At $7.95 per hundred pounds, what is the value of a
carload of cattle weighing 27,830 pounds?
2. At $34.70 per M, what is the cost of 11,950 bricks?
3. At $10.50 per ton, what is the value of 19,400
pounds of hay?
4. The year's budget
Teachers' salaries $19360.00
„
nil.
Supplies
2,450.00
for a smaU school is
Heating
2,950.00
shown at the right.
Light
26O.00
Find the total of this
Janitors
2,400.00
budget and the per cent
'^^*^^
"~
of this total set aside for
'
each purpose. Find per cents to one tenth of 1 per cent
and add them. The sum should be 100%.
5. A family with an income
of $3250 made up the budget
shown at the right. How much
was set aside for savings?
What per cent of the total
income was set aside for each
purpose? Check as in prob-
lem 4.
6. Using the table on page 71, find the cost per 1000
calories of the foods listed below:
Bacon, 42^ per lb.
Cheese, American, 29^ per lb.
Rice, 9^ per lb.
Lamb chops, 48^ per lb.
Lard, 27^ per lb.
Lean beef, 30^ per lb.
7. Find the nimiber of calories per day needed by a
man weighing 170 poimds who sleeps 8 hr. ,
has shght
exercise 6 hr., active exercise 8 hr., and severe exercise
2hr. (See page 72.)
266
Shelter
$600.00
Food
720.00
Clothing
400.00
Operating
250.00
Advancement 450.00
Automobile
400.00
Savings
Total
—
—

Problems
1. A used car was offered for sale at $450 cash. It
was sold on time for $200 cash and 6 monthly payments
of $50 each. What was the dollar cost of this credit?
2. A car costing $850 is bought for $250 cash, the
remainder being paid in 8 equal monthly payments.
The insui'ance is $45 and the rate of interest is 6 per
cent. These are charged as described on page 80. What
is each monthly payment?
3. What is the rate per cent interest paid for the
credit on the car in problem 1?
4. A piece of furniture marked $100 is sold for a $10
down payment and 5 monthly $20-payments. What is
the dollar cost of this credit? What is the rate per cent
interest paid for this credit? (See pages 77 and 78.)
5. Mr. Chatland bought a home (house and lot) for
$9800 on which he figures interest at 5%. Insurance
cost $15 per year, taxes $145, and repairs $95. He
figured depreciation at 2^% on $8000. Heat and water
cost $120 for the year. Figuring all these expenses, how
much per month did it cost the Chatland family to live
in this house? (For form of statement, see page 82.)
6. The Chatlands included the following items in
figuring the yearly cost of their automobile: interest, 5%
on $750; Hcense and tax, $23; insm^ance, $46; gasoline,
980 gal. at 21^; oil, 75 qt. at 25^; greasing, 15 times at
$1.25; service and repairs, $65; garage, $36; depreciation,
$250. Find the cost per mile of driving this car 15,800
miles.
7. What would have been the cost per mile of driving
the car described in problem 6 for 22,500 mi., with gas,
oil, greasing, and repairs increased 40%?
267

Problem Practice
1. The Stewart family had the following facts from
which to make a financial statement for the beginning
and the end of the year.
Make a statement like that
on page 87 to show net gain or loss for the year.
.
Beginning of year.
Assets: cash, $324.60; value of
house, $8650; furniture, $2460; insurance poHcies, $3250;
car, $750; securities, $5000.
Liabilities: current bills,
$196.40; mortgage, $2500.
End of year.
Assets: cash, $427.20; value of house,
$8400; furniture, $2600; insurance pohcies, $3600; car,
$575; securities, $5800. LiabiHties: current bills, $147.20;
mortgage on house, $2000.
2. A piano marked $360 was sold at 15 per cent dis-
count. What was the selling price?
3. A set of furniture with list price $275 was sold with
discounts of 30% and 10%. What was the selling price?
The total discount was what per cent of the Hst price?
4. A dealer bought 30 suits of clothes Hsted to sell at
$37.50 each. His discounts were 25% and 15%. What
was the total cost of these suits, with $18.60 included
for transportation?
5. At 5%, what is the interest on $3750 for 4 months?
(4 mo. is what fraction of a year?)
6. A note for $200 with no interest, payable in 3 mo.,
was discounted at 6%. Find the proceeds.
7. A promissory note for $4000, due in 6 months from
date, bears interest at 6%. Three months later it is
discounted at 5%. What are the proceeds of this note?
8. A city having a debt of $47,000, bearing 4^%
interest, borrowed this amount at 2|% interest and paid
the old debt. How much per year did the city save?
268

Miscellaneous Problems
1. What does a merchant mean by total sales? by the
cost of goods? by margin? by overhead? by profit?
2. If the margin is greater than the overhead, does
the merchant have a profit or a loss? If margin is less
than overhead, what is the result?
3. If the rate of interest goes down, what is the effect
upon the income from an investment? Ten years ago a
man had $1500 in a savings bank paying 4%. Now the
same bank pays 1^%. How much less per year does the
man receive from his savings?
4. How many rods of fence wire are needed to put a
six-wire fence around a field 36 rods wide and 60 rods
long?
5. If posts are placed f of a rod apart, how many posts
are required for the fence in problem 4?
6. A piece of furniture bought for $40 was marked to
seU for $72. At a sale this price was reduced by 16f per
cent.
What was the reduced price? What was the
dealer's margin?
7. A hardware dealer bought a furnace for $250 and
marked it to sell for $375. Then he sold it at a reduc-
tion of 25 per cent. What was his margin? What per
cent of the selling price was this margin?
8. An automobile goes 297 miles on 16^ gallons of
gasoline. At this rate, how far wiU it go on 480 gallons?
9. The printed part of a certain page is 4 inches wide
and 6f inches high. The width is what per cent of the
height? Find answer to one tenth of 1 per cent.
10. A bill of goods for $1860 is sold at discounts of
20%, 10%, and 5%. Find the net amount.
269

Problems
1. If the cost of a pair of shoes is $3 and the margin
is 40%, what is the selling price? (Is the margin figured
on sales or on cost?)
2. A merchant whose overhead is 23% wants to make
a profit of 4%. What must be the rate of his margin?
3. A chair is bought by the dealer for $12. The over-
head is 35 per cent and the profit is to be 10 per cent.
What must be the selling price? First give the exact
answer and then give a price at which the dealer may
mark the chair. Give two answers.
4. A radio costing the dealer $55 was sold at a margin
of $35. If his overhead was $30, find his profit. Then
find the rate per cent of margin, overhead, cost, and
profit. Make a statement Hke that on page 108.
5. An agent was paid 8 per cent commission on aU
monthly sales above $1500. What was his commission
for one month when his sales were $9365.50?
6. An agent received a monthly salary of $175 in
addition to a commission of 12 per cent on all sales above
$15,000 for the year.
What was his income for a year
when his total sales were $31,380?
7. What were the net proceeds from the sale of beef
cattle weighing 17,850 pounds at $8.45. The commission
was 2^ per cent and other expenses were $499.50 . (What
is meant by giving the price of cattle at $8.45?)
8. Mr. R. C. Porter sells road machinery. On April 1
he took a six-months note for $2750 bearing interest at
6%. On July 1 he discounted this note at the bank at
5%. What was the amount of this note when due? What
were the proceeds when discounting it?
270

Problem Practice
1. Find the number of days from March 15 to July 1;
from May 8 to July 26; from June 6 to November 17.
Copy the following and supply the numbers missing:
Principal Rate
^
Time
Interest Amount
2. $860 5i%
May1toOct. 1
__
_
3. $1250
5%
May 12 to Sept. 6
_
_
4. $300
7%
Jan.6toMay15
Principal Rate
Time
Discount Proceeds
5. $460
6%
Mar. 1 to July 15
6o $1750
5%
AprH 27 to Oct. 6
_
_
7- $2400
3%
May14toDec.4
8. A note for $5400 dated Nov. 7 and due in 4 months
bears interest at 6 per cent. On Dec. 3 it is discounted
at 4 per cent. What are the proceeds?
9. A trade acceptance for $12,500 is dated Jime 17
and is due in four months. It is discounted August 24
at 5%. Find the proceeds. Note that this acceptance
bears no interest.
10. Mr. Aitkin has a debt of $6000 on his farm. He
agrees to pay $500 at the end of each year, part of which
is for
Unpaid
Prin.
Int.
5% interest on
the unpaid part of the
principal, the rest to
be appHed on the prin-
cipal.
Write a ten-
year schedule for this
debt. The first three lines of this schedule are given
above.
1st yr.
2nd3rr.
3rdyr.
$6000 $300.
5800 290.
5590 279.50
Paid on
Prin.
$200.
210.
220.50
271

Problems
!• A building costing $45,000 is built on a lot valued
at $15,000. At 4^ per cent, what is the interest on this
investment?
2. On a lot worth $1800, a house costing $12,000
was built ten years ago. At 3% of the value of the house
when new, what is the yearly depreciation? (The lot
does not depreciate.) What is the value of the house
after 10 years?
Depreciation-Interest Schedule
Value j Depr.
Int.
1st yr.
$13800 $360 $690
2ndyr.
13440 360 672
3rd yr.
13080 360 654
3. In the schedule
begun at the right, the
rate of interest is 5%,
figured on the value of
the property at the be-
ginning of the year.
The yearly depreciation is 3% of the house when new.
Continue the schedule for ten years.
4. Using 2^% as the rate of depreciation and 4^%
interest, write a 10-year depreciation-interest schedule
for the property described in problem 1.
5. Mr. Ward bought a house costing $9000, on which
he paid $2000 down. He agreed to pay $65 a month,
from which ^% of the unpaid principal was to be de-
ducted and the rest was to be appHed to the principal.
The schedule for the first three months is shown at
the right. Copy
this
schedule
and continue it
for 12 months.
A schedule like
this is made for
every transaction of this kind. It must be continued
until the final payment is made.
272
Paid on
Unpaid Payt. Int.
Prin.
1st mo. $7000
$65 $35
$30
2nd mo. 6970
65 34.85 30.15
3rd mo. 6939 .85 65 34.70 30.30

Corporation Problems
1. Describe briefly how a corporation is organized.
What is meant by capital stock? dividends? surplus?
2. What are the main differences between a partner-
ship and a corporation?
3. What is a corporation bond? What are the main
differences between a bond and a share of stock? What
happens if a corporation fails to pay dividends on its
stock? Can the owner of a share of stock compel the
corporation to pay dividends on it? Can the owner of
a bond compel the corporation to pay interest on it?
4. A corporation has 1000 shares of stock outstanding.
In one year its net earnings are $7500. After paying a
dividend of $5 per share, how much has the corporation
left to carry to surplus?
5. One company has 5000 shares of stock outstanding
and also $100,000 in bonds paying 5% interest. From a
net earning of $34,800, the corporation pays the interest
on its bonds and a dividend of $4 per share. How much
has the company left to carry to surplus?
6. A city (also called a municipal corporation) sells
bonds to the amount of $250,000 to extend its water-
works system. At 2^ per cent interest, how much must
the city pay yearly on these bonds?
7. Mr. Moore bought 100 shares of stock at 47f. How
much did these shares cost him? Notice that he must
pay a small additional amount for brokerage, which is
not included here.
8. If you buy a $750 Series E United States savings
bond, how much will this bond be worth in 5 years? in
10 years? (See page 164.)
273

Miscellaneous Problems
Pieces Dimensions
3.
4.
5.
20
150
60
I"xl2"xl6'
2"x4"xl2'
2 x8 xl4'
1. What is meant by a board foot? What is meant by
1''?
by V? How many board feet are there in a board
1 in. thick, 12 in. wide, and 12 ft. long?
«
2. Find the number of board feet in each of these
pieces:Vx12''x16', VxS"x12', 2"x6"x10', 3"x10"
xl6'.
3-5. Find the nimiber
of board feet in each of the
items listed at the right.
6. How many board feet
are required for a floor 32 ft. by 48 ft. if it is made of one-
inch flooring? Add one sixth of the area for waste. At
$56 per M board feet, what is the cost?
7. Goods were bought at the series discount of 20%,
6%, and 2%. This series discount is equal to what single
discount?
8. At $1.45 per thousand cubic feet of gas, what is
the amount of a month's gas bill if the readings at the
beginning and the end of a month were 49,600 and 53,900
respectively?
9. A coat is advertised at 33^^ per cent discount.
What was the original price if the present price is $36?
(Remember that 33^ per cent =^ .)
10. A can filled with nulk weighs 104 pounds, while the
empty can weighs 16.2 pounds. How many quarts of
milk does it hold if one quart weighs 2.15 pounds? Find
answer to the nearest quart.
11. How many square feet are there in the walls and
ceiling of a room that is 16 feet wide, 22 feet long, and 9
feet high. Allow 150 square feet for doors and windows.
274

Solving a Proportion
1. The proportion a: is to 7 as 20 is to 35 may be stated
X20
in two ways, = = —; , or x:7 = 20:35. State the proportion
/
oo
.r isto14as15isto42intwoways.
2. Solve the proportion
x_20
7 35*
(l)x=^xT=4
(2)x
4
5
=4
(3)35jc=140
x=4
A proportion may be solved
IQ three different
ways,
as
shown at the right. You have
used the first plan and can easily
see the similarity of the second.
To obtain 35x = 140 in the
third solution, multiply x by 35 and 20 by 7. Then find
the value of x.
In the proportion 4:7 =20:35, the first and last num-
bers, 4 and 35, are called the extremes; the second and
third numbers, 7 and 20, are called the means.
In the proportion q =yR, 3 and 12 are the extremes and
9 and 4 are the means.
In a proportion, the product of the extremes equals
the product of the means, hence, in 4:7=20:35, the
productof4X35=7X20.
Solve the following proportions:
"*•
14 "42
X
2
243
X3
244
X8
716
21*
24~8
21 :c
277
12x
155
15X
186
.=;
28
312
X16
183J-
30X
217
28X
275

Graphs
1. Study the first graph on page 174. In a newspaper
or magazine you are Hkely to find the facts in this graph
brought down to the present date. What questions can
you answer from a study of this graph?
2. In your newspapers, find other graphs representing
changes in business conditions.
Make a collection of
such graphs and see if you can understand the stories
that they tell.
3. A machine costing $5000 depreciates at the rate of
12^ per cent yearly. Construct a bar graph showing its
value for 6 years.
4. A school building costing $180,000 when new de-
preciates 2^ per cent each year.
How much will it be
worth when it is 20 years old? Construct a bar graph
showing its value during this period.
5. A class of 29 pupils took a test consisting of 16
problems. One pupil had 6 correct answers, 4 had 8 cor-
rect answers, and so on, as shown in the table.
No. of Pupils
1
4
4
6
6
3
3
1
1
Correct Answers 6
810111213141516
Construct a bar graph showing this distribution of
grades.
(See page 177.)
6. A merchant foimd that, out of every dollar taken
in for sales of his merchandise, 61 cents went for cost of
goods, 31 cents for overhead, and that the rest was profit.
Construct a circle graph representing this distribution
of the sales dollar of this merchant.
7. Make a circle graph to show how you use the 24
hours of one day.
276

Miscellaneous Problems
1. At $41.75 per M, what is the cost of 74^0 board feet
of lumber?
2. At $47.25 per M, what is the cost of 350 planks,
each 2 inches by 12 inches and 16 feet long?
3. Mr. Williams bought 250 shares of stock at 38^5^ and
100 shares at 37|^, brokerage 15c per share.
What was
the total cost of this stock, including brokerage?
4. A building lot is 60 feet wide and 120 feet deep.
Make a drawing to scale representing this lot. Use scale:
15 feet to 1 inch.
5. On the lot in problem 4, a house is biult that is
30 feet wide and 40 feet long. Make a drawing of the
ground plan using the same scale.
6. A loan of $5500 carries interest at 5 per cent.
Every 6 months a payment of $500 is made. From this,
interest on the unpaid balance is paid, and the remainder
is applied on the
principal.
Extend
to ten lines the
schedule begun at
the right.
Unpaid
Paid on
Prin.
Int.
Prin.
1st
$5500.
$137.50 $362.50
2nd
5137.50 128.44 371.56
7. At 520 cubic feet to the ton, how many tons of hay
arethereinamow32feetby48feetifthehayis12
feet deep? Find answer to the nearest ton.
8. A merchant marked a rug costing $100 to sell at
75% above his buying price.
What was his selling price?
If he sold it at the marked price, what per cent was the
margin of the selling price?
9. When it is noon at Washington, D. C, what is the
time at Denver? at Seattle?
277

Miscellaneous Problems
1. Two sides of a right triangle are 12 inches and 5
inches. What is the length of the hypotenuse?
2. The hypotenuse of a right triangle is 20 ft. and
one side is 12 ft.
What is the length of the other side?
3. What is the length of a diagonal of a room that is
18 feet wide and 24 feet long?
4. Find the length of the hypotenuse of a right tri-
angle whose legs are 6 inches and 10 inches. Find answer
correct to two decimals.
5. Mr. Gordon has a house valued at $6500, which he
insures at 75 per cent of its value. At 35 cents per $100,
what is the cost of his insurance for one year? What is
the yearly cost if he takes out a poHcy for 3 years?
for 5 years? (See page 137.)
6. Mr. Gordon took out a $5000 ordinary life in-
surance poHcy when he was 25 years old and a $5000
twenty-payment life insurance policy when he was 35
years old. How much premium is he now paying at the
age of 50 years? (See page 139.)
•
7. A radio priced at $60 is sold on the installment
plan for $6 down and five $12 monthly payments. What
is the doUar cost of this credit? How much can be saved
by borrowing $54 at 6% interest and paying cash for
the radio?
8. Shirts costing $1.10 were sold for $1.75. What was
the rate per cent margin?
9, How many pounds of sugar are there in a load
of beets weighing 9400 lb. if the beets contain 17.2%
sugar? How many 100-pound sacks of sugar is this?
278

Problem Practice
1. Find the area and the perimeter of a lot 220 ft.
long and 180 ft. wide.
2. The length of one side of a square flower bed is
15 ft. Find the area in square yards.
3. The diameter of a circular flower bed is 15 ft.
Find its area in square yards.
4. The base of a triangular field is 48 rods and the
altitude is 32 rods. Find the area in acres.
5. The circumference of a large tree is 24 ft. 6 in.
Find its diameter in feet and inches.
6. What is the circumference of a tractor wheel whose
diameter is 56 inches?
7. A city lot is ia the shape of a trapezoid having
parallel sides of 120 ft. and 150 ft. and a width of 84 ft.
What is its area?
8. A cylindrical tank has a depth of 6 feet and a
diameter of 4 feet. How many gallons will it hold?
9. Find the volimie and the area of a sphere whose
diameter is 24 inches.
10. At 37^ per square foot, what is the value of a slate
blackboard 24 ft. 8 in. long and 4 ft. wide?
11. At 2^ per square foot, what wiU it cost to paint
the outer curved surface of a cylindrical silo which
has a diameter of 14 ft. and a height of 32 ft.?
12. The diameter of the earth is about 8000 miles.
What is the circimiference of the earth?
13. A corn crib measures 24 ft. long, 11 ft. wide, and
7^ ft. deep. Allowing 2^ cubic feet per bushel, how
many bushels of corn on the ear will it hold?
279

Miscellaneous Problems
1. Mr. Rogers owns a business building costing him
$48,000. After deducting the yearly depreciation, taxes,
insurance costs, and other expenses, his net yearly in-
come from this building is $2160. What per cent income
does he get from this investment?
2. It was found that a 24-pound bag of flour could be
bought for 65 cents while a 5-pound bag cost 19 cents.
What was the price per pound to the nearest tenth of 1
cent for each of these bags? What per cent was saved
by buying the larger amount of flour?
3. A 20-ounce can of peas cost 13 cents, while an 11-
ounce can cost 9 cents.
What per cent was saved by
buying in the larger can?
4. Mr. Potter bought a used car for $540, turning in
his old car for $200, and paying the balance in 5 equal
monthly payments. He was charged $35 for insurance
and interest at 6 per cent on the unpaid balance for 5
months. What was the amount of each payment per
month?
5. It has been found that for a certain grade of men's
suits, 26.6% of the selling price goes for retailer's over-
head and 4.8%, for retailer's profit. What per cent goes
for retailer's cost? For a suit selling for $45, how much
goes for retailer's cost? overhead? profit?
6. A co-operative gasoline station is paying its mem-
bers 3 per cent on aU purchases.
In one month, a
member bought 87 gallons of gasoline at 19 cents, 8
quarts of oil at 28 cents, and a battery for $9.80 . How
much refund did he get for his month's purchases?
7. Find the interest at 4| per cent on $4800 from
March 12 to August 28.
280

Tables of Measures
Liquid Measure
2 cups =1 pt.
2 pt.
=1 qt.
4 qt.
=1 gal.
Dry Measure
2pt. =1qt.
8qt. =1 pk.
4pk. =1bu.
Counting^
12 units =1 doz.
12 doz.
= 1 gross
20 units = 1 score
Cooking
3 tsp.
=1 tbs.
16 tbs.
=1 cup
2cups=1pt.
2 pt.
=1 qt.
Long Measure
12
3
in.
=1 ft.
ft.
=lyd.
16^ ft.
i
5^yd.[
320 rd.
5280 ft.
1760 yd.;
6080.20 ft.
=1rd.
=1mi.
Weight
16 oz.
=1 lb.
100 1b.
=lcwt,
20 cwt.^
2000 lb.
= 1T.
Square Measure
144 sq. in.
9 sq. ft.
30| sq. yd.
160 sq. rd.
640 aci
36 sq.
1 nautical mile
=1sq.ft.
=1sq.yd.
=1sq.rd.
= 1 acre (A.)
_
'
1 sq. mi.
,1 section
= 1 township
Angle Measure
360 degrees (°) =a circle
90 degrees
=a right angle
]80 degrees
=a straight angle
U, S. Money
10 mills = IC
lOOc^ =$1
Cubic Measure
1728cu. in. =1cu.ft.
27 cu. ft. =1 cu. yd.
Time Measure
60 sec.
=1min.
60 min.
=1hr.
24 hr.
-1 da.
7 da.
=1wk.
30 da.
=1mo.
365 da.
52wk.> =1yr.
12 mo.
366 da.
=1leapyr.
10 yr.
= 1 decade
100 yr.
= 1 century
Useful Facts
1 gal. =231 cu. in.
Weights per Bushel in Most States
74gal. =1 cu
3li gal.
ft.
= 1 barrel
bu.
=2150.42 cu. in.
bu. =1^ cu. ft.
.8 bu. =1 cu. ft.
TT =3.1416 or 3^^
1 Hquid qt.
^
=57.75 cu. in.
1 dry qt.
=67.2 cu. in.
1 gal. water
= about 8^ lb.
1 cu. ft. water =62.5 lb.
1 gal. milk
= about 8.6 lb
1 cord wood =128 cu. ft.
Apples, 48 lb.
Barley, 48 lb.
Beans, 60 lb.
Clover seed, 60 lb.
Coal, soft, 80 lb.
Corn, on cob, 70 lb.
Corn, shelled, 56 lb.
Oats, 32 lb.
Onions, 57 lb.
Potatoes, 60 lb.
Rye, b& lb.
Wheat, 60 lb.
Lumber
A board 1 inch or less ) thick, 1 foot
wide, and 1 foot long = 1 board foot.
Paper
24 or 25 sheets = 1 quire
20 quires
=1 ream
281

Formulas
Cost, number. price:
c==np
c
c
n=-
p=-
P
n
Speed, time, distance:
d=st
d
d
s=-
t=-
t
s
Base, rate, percentage:
P==br
b
r
Principal, rate, time, interest:
i==prt
i
i
p=—
r=
—
rt
pt
t=A
pr
Area
Volume
Circle:
Cylinder:
Parallelogram:
Rectangle:
A=7rr2
A=2xrh
A=bh
A=lw
Cone:
Cube:
Cylinder:
fV =lBh
V =|7rr%
V=e3
fV=Bh
\V=7rr%
Sphere:
A=47rr2
•
Prism:
V=Bh
Square: A=s2
Pyramid:
V=^Bh
Trapezoid: A=^(a+b)h
Rectangular
solid:
V=lwh
Triangle: A=^bh
Sphere:
The Metric System
Units of Length
10 millimeters =1 centimeter
10 centimeters =1 decimeter
10 decimeters =1 meter
10 meters
=1 decameter
10 decameters =1 hectometer
10 hectometers = 1 kilometer
Units of Weight (most used)
1000 grams
=1 kilogram
100 kilograms = 1 quintal
10 quintals
= 1 metric ton
Common Units of Capacity
100 liters
=1 hectoUter
Common Units of Area
100 sq. meters = 1 are
100 ares
= 1 hectare
Approximate Equivalents
1 centimeter
1 meter
1 kilometer
1 Uter
1 gram
1 kilogram
1 quintal
1 metric ton
1 square meter
.39 in.
39.37 in.
1.1 yd.
. 621 mi.
about ^ mi.
1.06 liquid qt.
. 908 dry qt.
. 035 oz.
=
2.2 lb.
= 220 lb.
=
1.1 T.
=
1.2 sq. yd.
1 cubic meter =
1.31 cu. yd .
1 hectare
=
2.47 acres
1 in.
= 2.54 centimeters
1 yd.
-=
.9144 meters
1 mi.
=1.609 kilometers
1 gal. =3.8 liters
282

hdex
PAGE
Accounts
checking
12-13
cash
242
family
87
farm
26-27
postal savings
163
Add, subtract, multiply, or
divide?
53,59
Addition
column
10-11
decimals
11
fractions
16—17
horizontal
31
mixed numbers
17
practice. .10 -11 , 16-17 , 250 -51
Angles, measuring
222
Area
circle
229
cylinder
231
formula
120, 154, 228-29
parallelogram
228
trapezoid
228
Arithmetic
practice in
10
use of
9
Assets
87
Attendance records
'.
28-29
Automobile problems. .80, 84-85
Bank
balances
12-13, 242
discount
98-101 , 116-17
Base
finding
47
in percentage
44
Board foot
142
Bonds
buying
169
corporation
159, 171
government
164-65
U. S. savings
164-65
Borrowing money
96-100
Brokerage
170-72
Budgets
family
64, 66-67, 177
government
184-85
Calories and food elements . 70 -74
Cancellation
57-58 , 125
PAGE
Capacity, metric measures
of
235
Capital stock
156-58, 168
Carrying charge
76
Cash accounts
242
Checking
accounts
12-13
division
14
multiplication
14
Circle
area
229
circumference
229
radius
229
Circumference
229
Commercial short-term pa-
per.
.
..
118
Commission
114
formula
207
Compound interest
148-53
Cone, volume of
232
Corporation taxes
199
Corporations
156-59, 273
Corresponding sides.
.
.
.
.219, 223
Cost
automobile
84-85
dollar
76-77
formula
122, 154
government . . . 184 -86, 190-91,
196-98
help
86
house
82,131-36
problems
76-77 , 82 -86
rate per cent
110
Credit, buying on
76-80
Cylinder
area of
231
volume of
230
Decimal point, placing .....
15
Decimals
adding and subtracting.
.
11
changing to per cents ....
43
division
15, 25
from fractions
24
multiplication
15, 25
practice
32, 240, 242
square roots of
213
Deposits, bank.
..1 2-13, 148-53 ,
163
283

PAGE
Depreciation
graphs
176
problems . . 104-5, 132-33, 135,
176
Depreciation-interest sched-
ule
133
Diagonals of rectangles ....
216
Discount
bank
98-101 , 116 -17
practice
95, 244
problems . 90 -95 , 98 -101 , 116-17
retail
90
trade
91-92
Discount series
.91—92
Distance
finding
224
formula
120, 154
Dividends
corporation
157—58
insurance
139
Division
decimals
15, 25
formula
120, 154
fractions
20, 57
mixed numbers
20
practice
14, 253
Dollar cost
76-77
Drawings, scale
202—3
PAGE
Formulas
—
continued
surface of cyUnder
231
surface of sphere
233
test on
154
triangle
214
use of
120, 122 -23
volume
122, 154
volume of cylinder
230
volume of sphere
233
Fractional equivalents of per
cents
48
Fractional per cents
45
Fractions
addition
16-17
cancellation in
57
changing from per cents . .
48
comparison of with per
cents
43
division
20, 57
multiplication
19, 57
practice . 32, 241-42, 257-59, 261
reduction to decimals ....
24
reduction to lowest terms .
57
reduction to per cents .... 46, 48
sight work
16
Fundamentals
practice
68, 254
test. 34, 60, 88, 126, 180, 208
Equations
meaning of
36
members of
36
practice
227, 262
problems
40, 224, 262
proportion
220-21 , 223
solving
36-38 , 41
steps in
39
Excise taxes
199
Farm records
26-27
Financial statements
87
Food, problems on
70-75
Formulas
area
120, 154, 228-29
area of circle
229, 231
circumference
229
commission
207
cost
122, 154
distance
120, 154
division
120, 154
interest
122, 154
percentage
44, 122, 154
price
154
problems
121-23 , 154
profit and loss
109, 154
sight work
120-21
subtraction
120
Gasohne tax
192
Government, cost of. 184 -86, 190-
91, 196-98
Gram
235
Graphs
bar
177,276
circle
177, 276
line
175-76, 276
practice
276
use of
174
Hectare
238
Horizontal addition
31
House, cost of
82-83, 131-36
Hypotenuse
214
Income taxes
192, 199
Installment buying
76-80, 134
Insurance
fire
136-37
life
138-39
Interest
computing.
. 1 19, 124-25, 148-
53, 164
formula
122, 154
problems.
.
.78-80 , 96-97, 102-
6, 119, 124, 131-35, 148-53
rates of
102, 106
284

PAGE
Interest
—
continued
savings deposits
148-53
schedules
133-34
table
153
Investment
in bonds
164-65, 169
in house
131, 135
in stocks
169-72 , 175
saving for
162
Land, measures of
238
Least common denominator .
1
7
Length, metric measurement
of.
.
234-36
Liabilities
87
Liter
235
Loss
87,109
Lumber
measurement of
142
problems
143-44
PAGE
Multiplication
decimals
15, 25
fractions
19
mixed numbers
19
practice
14, 26, 253
Negotiable instruments ....
100
Net gain
87
Net loss
;.
.
.
87
Net price
90
Net proceeds
98, 171
Net worth
87
Notes, promissory.
.
.
.98-100. 116
Numbers
large, square roots of .. . .
213
rounded, practice
255
rounding off
22-24
Obsolescence
132
Overhead
108-10
Machines, computing
10-13
Maps, scales of
202
Margin
108, 110
Maturity of notes
99
Maturity value
164
Measurements
board feet
142-43
land, metric
238
length, metric
234-36
tables of
281-82
weight, capacity, metric.
.
235
Measuring
angles
^
222
distance
224-26
Members of equations
36
Meridian, prime
206
Meter
234-35, 238
Metric system
equivalents
236
problems
235-38
relations among units ....
238
sight work
236
tables
281-82
units of
234-35
Mixed numbers
addition
17
division
20
multiplication
19
practice
32, 257-59, 261
reduction to per cents ....
46
subtraction
18
Mixed practice
32, 252, 256
Mixed test
61
Money
borrowing
96-100
investing
162
Par value
156
Parallelogram, area
228
Partnerships
158
Per cent
finding
44-45
rate
46,110
Percentage
base and rate
44, 46 -47
formula
44,122,154
practice.
.
. 4 8, 146, 161, 242-44,
263, 265
problems ... 45 -47, 49 -52, 110
sight work
49-50 , 52
use of
42
Per cents
changing from fractions . . 46, 48
changing to decimals
43
changing to fractions ....
48
comparison with fractions .
43
fractional
45
Pi. ....
229
Policies, insurance
136—39
Population, data on . .
.
.22-23, 43
Postal savings
163
addition. .10 -11, 16-17, 250-51
decimals
32, 240, 242
discounts
95, 244
division
14, 253
equations
227, 262
fractions
32, 241-42, 252,
257-^^.9, 261
fundamentals
68, 254
graphs
276
mixed
32, 252, 256
mixed numbers. .3 2, 257 -59, 261
285

PAGE
Practice
—
continued
multiplication
14, 26, 253
percentage .. 48, 146, 161, 242-
44, 263, 265
proportions
227, 275
rounded numbers
255
scale
203
subtraction
11, 250-51
Premiums, rates of
136-39
Price
formula
154
list
91
marking
90, 112
Principal and interest
97, 134
Problem practice.
.
.
.40, 55, 107,
113, 115, 125, 141, 145, 147, 160,
166-67 , 189 , 195, 201 , 207, 215,
217, 225, 239, 260, 264, 268, 271,
279
Problem solving, test in ...
.
63, 89,
127, 155
Problem tests .
.
35, 62 -63, 89 , 127-
29, 154-55, 181-83, 209 , 246-49
Problems.
.12 -13, 18 , 21-23, 25-
26, 28-30, 33, 35, 38-40, 42, 45-
47, 49-56, 58-59, 62-70, 72-87,
89-98 , 100-13, 115 -19 , 121 -25,
127-29 , 131-36, 138, 140 -41 ,
143-45 , 147-60, 162 -67 , 169 -73 ,
175-79 , 181-83, 185 -91 , 193 -
201, 203 , 205 -7, 209, 215 -17 ,
221, 224-27, 229, 231 -33 , 235-
39, 245-49, 255 , 260 , 262, 264,
266-74 , 276-80
automobile
80, 84-85
choosing the operation in . 53 , 59
commission
114
corporation
156-59 , 273
cost
76-77 , 82-86
depreciation
104-5 , 132 -33,
135, 176
diagonals
216
discount.
.
.90 -95, 98 -101, 116 -
17
equations in
40, 224, 262
formulas in
121-23 , 154
government costs . . 185 -86, 190-
91, 196-98
graphs in
276
home
82-83 , 86, 131-36
installment buying .
.
. 76-80, 134
insurance
136, 138
interest
78-80, 96-97, 102-
6, 119, 124, 131-35, 148-53
investment .. 162, 164, 169-72,
175
lumber
143-44
PAGE
Problems
—
continued
measuring distance
224-26
methods in solving
54, 58
metric system in
235-38
overhead
109-10
percentage . . 45 -47, 49-52, 110
prices
112
profit and loss
108, 110, 178
proportion
221
sight work.
.50, 52, 93, 112, 121,
140, 169, 173, 194
social topics .
. 1 2 -13, 25-26, 28-
30, 56, 64, 66-70, 72-75, 77,
79, 82-87, 90-92, 100, 104,
106, 116 -17 , 131 -36 , 138,
156-59, 162, 164 -65 , 177,
185-86, 191 , 197 -98 , 245
tax
187-88, 193,200
time
205-6
trade acceptances
118
volume
232-33 , 245
without numbers
Ill
test
62, 181
Proceeds
98, 114, 118, 171
Profit
108-10 , 178
formula
109, 154
Promissory notes
98-100 , 116
Property tax
186-87, 192
Proportion
in similar triangles
223
meaning of
218-19
practice
227, 275
problems
221
solving
220,275
uses for
220
Pyramid, volume of
232
Quotients, rounding off
24
Radius
229
Rate
discount
90
finding
46
in percentage
44
interest
78-79 , 102 , 106
overhead
109
per cent
110
premiums
136-39
tax
187-88 , 199
Ratio
meaning of
218
finding
.
219
Records
attendance
28-29
family
68-69 , 87
sales
30
Rectangle, diagonals
216
286

PAGE
Rectangular solid, volume . .
230
Reduction
fractions to decimals
24
fractions to per cents ....
46
mixed numbers to per
cents
46
Retail discounts
90
Risk and premiums
137
Rounding off numbers .
. 22 -24, 255
Sales records
30
Sales tax
192
Savings deposits,
interest
148-53 , 163
Scale practice
203
Scales, maps and drawings .
.
202
Selling price
90-91 , 112
formula
154
Severance taxes
192
Sight work
area
228
formulas
120-21
fractions
16
metric measures
236
multiplication
26
percentage
49-50, 52
problems.
.
.50, 52, 93, 112, 121,
140, 169, 173, 194
Similar triangles
222-23
Social topics
Bank Balances
12
Finding Bank Balances.
.
13
Standings of Basketball
Teams
25
Keeping Farm Records ...
26
Keeping School Records . .
28
School Attendance Rec-
ords
29
Sales Records
30
Buying by the Ton
56
Planning Budgets
64
Family Budgets
66
Family Budgets
67
Family Records
68
Ten Days in January ....
69
Calories and Food Ele-
ments
70
Calories Needed by Dif-
ferent Persons
72
Problems in Food Values
.
73
Comparing Costs of Cal-
ories
74
Buying Food in Smaller or
in Larger Containers ...
75
Dollar Cost of Credit
77
Installment Interest
79
Owning a House
82
PAGE
Social topics
—
continued
Home Problems
83
Cost of Owning and Op-
erating an Automobile.
84
Automobile Problems ....
85
Cost of Hiring Help
86
Family Financial State-
ments
87
Retail Discounts
90
Trade Discounts
91
Problems in Trade Dis-
count
92
Selling a Promissory Note 100
Interest on Manufactur-
ing Plants
104
Effects of Low Interest
Rates
106
Discounting Notes at the
Bank
.
116
Problems on Bank Dis-
counts
117
Interest on Investment in
a House
131
Depreciation of a House . . 132
Interest Schedule on a
House
133
Schedule of Payments on
House.
134
Costs of Renting and Buy-
ing a House
135
Fire Insurance
136
Life Insurance
138
Organizing a Small Cor-
poration
156
Dividends on Corporation
Stock
157
Comparison of Partner-
ship and Corporation.
.
158
Corporation Bonds
159
Saving Money to Invest
Safely
162
Postal Savings Accounts . .
163
United States Savings
Bonds
164-65
Family Budgets
177
Budgets for County and
City
185
Costs of Local Govern-
ments
186
Cost of State Government 191
Cost of the Federal Gov-
ernment
197
Comparing Costs of Gov-
ernments
198
The Great Pyramid
245
Solutions, indicating.
.
.
. 58-59, 93
Solving equations
36-38, 41
steps in
39
287

PAGE
Solving problems
54, 58
tests in
63, 89, 127, 155
Solving proportions
220, 275
Speculation
171, 175
Sphere, surface and volume
^
of
233
Squares and square roots.
.
.
210
table
211
Square root
approximate
212
of decimals and large num-
bers
213
Statements
87
Steps
in arithmetic
9
in solving equations
39
Stock exchange
168-72, 175
Stocks
buying
169-70, 172, 175
^
selUng
171-72
Subtraction
decimals, practice
11
formula
120
fractions
16, 18
mixed numbers
18
practice
11, 250-51
Surface
of cylinder
231
of sphere
233
Surplus
157
Table
compound interest
152—53
food values
71
formulas
282
measures
281-82
metric system
236, 282
equivalents
236, 282
length
236, 282
squares and square roots .
211
tax
188
Tax problems. 187 -88, 193, 200
Tax table
188
Taxes
184, 186-«8, 192-93.
199-200
PAGE
Testing your readiness fpr
next year's work
250-80
Tests. .34 -35, 60-63, 88-89, 126-
29, 154-55, 180-83, 208-9,
246-49
in fundamentals ... 34, 60, 88,
126, 180, 208
mixed
61
on formulas
154
problems.
.
.35, 62-63, 89, 127-
29, 154-55, 181-83, 209,
246-49
problems without num-
bers
62, 181
solving problems.
.
.63, 89, 127,
155
what you have learned.
.
.
246
Time
in finding interest
119
payments
76-80
standard
204-6
Topics for discussion.
.
.83, 85,
101, 140
Trad3 acceptances
118
Trade discounts
91-92
Trapezoids, area
228
Triangle
formula
214
measuring by
222, 224
right
214
similar
222
proportions in
223-24
Vertices of rectangle
216
Volume
formula
122, 154
pyramid and cone
232
rectangular solid and cyl-
inder
230
Weight, metric measures.
.
.
235
What you have learned, test
.
246
Whole numbers,
approxi-
mate
22
288

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