Let x represent the number of gallons; then

x

2

x -5 represents the number of gallons of cider;

3

and the Equation will be

+25 represents the number of gallons of wine; and

Let x represent the sum; then

X

3

14. After a person had expended $10 more than of his money, he had $15 more than of it remaining. What sum had he at first?

X

+10 represents the amount expended; and

-

X

3

Then, by the conditions of the problem, we shall have ·

10 represents the amount remaining.

X

10= +15;
2

15. Divide the number 91 into two such parts that if the greater be divided by their difference, the quotient may be 7.

X

2x-91

Let x represent the greater part; then -x represents the less; and

91

x-(91-x), or 2x-91, represents their difference; and the Equation will be

=7.

This Equation will give =49 the greater part; hence 91-49-42, is the less part.

16. A and B had equal sums of money; the first paid away $25, and the second $60, when it appeared that A had twice as much left as B. What sum had each?

Let x represent the sum each had; then

x-25 represents the sum A had after spending $25; and x-60 represents the sum B had after spending $60. Then, by the conditions of the problem, we shall have

x-25=2(x-60);

from which we shall find x=$95.

17. After paying away of my money, and then of what was left, I had $180. What sum had I at first?

Let x represent the sum; then

x

represents the first payment;

4

1 3x 3.x

5

of or represents the second payment; and
4' 20'

3x 3x

20' 5'

We shall then have the Equation

first

third.

X

4

or

is the remainder after both payments.

which will give x=$300.

18. A line 37 feet in length is to be divided into 3 parts, so that the may be 3 feet less than the second, and the second 5 more than the What are the parts?

Let x represent the length of the third part; then
x+5 represents the length of the 2d part; and
x+2 represents the length of the 1st part.
The Equation will then be

x+(x+5)+(x+2)=37;

=

from which a will be found 10 feet, the third part; hence 10+5=15 feet, the second part; and 10+2=12 feet, the first part.

19. A can perform a piece of work in 12 days, and B can perform the same in 15 days. In what time could both together do the work?

Let x represent the number of days.

Then, since A could do of the work, and B of it in 1 day,

X

represents the part A could do in x days; and

12

X

15

The Equation will then be

X

12

This Equation will give x=63 days.

represents the part B could do in x days.

6

20. If A can mow a certain field in 6 days, B in 8 days, and C in 5 days, in what time could the three together do it?

Let x represent the number of days.

Then, since A could mow of the field, B of it, and Cof 1 day,

drawn.

5

+

x represents the part A could mow in x days.

X

15

1, the entire work.

represents the part B could mow in x days; and

represents the part C could mow in x days.

We shall then have the Equation

which will give x=22 days.

3

2x

.

21. Out of a cask of wine which had leaked away a third part, 20 gallons were afterwards drawn, and the cask was then found to be but half full. How much did it hold?

1, the entire field,

Let a represent the number of gallons; then

represents the number lost by leakage;

represents the number then remaining; and

3

2x

-20 represents the number remaining after 20 gallons were

3

The Equation will then be

2x

3

from which we shall find x=120 gallons.

Let x represent B's share; then 2x represents A's share; and 3x represents C's share.

We shall then have the Equation

-20=

22. It is required to divide $300 between A, B, and C, so that A may have twice as much as B, and C as much as the other two together.

x+2x+3x=300;

which will give x=$50, B's share; hence 2× 50-$100 is A's share; and 3 x 50-$150 is C's share.

Let x represent his income; then

2x

3

2 X 2x
of or
3 3'

9'

2x

Ꮖ

2

23. A gentleman spends of his yearly income in board and lodging, of the remainder in clothes, and then has $20 left. What is the amount of his income?

x

represents the amount spent in board and lodging;

represents the amount spent in clothes; and

2x

9 represents the amount remaining.

3 We shall then have

from which x will be found equal to $180.

24. A person, at the time he was married, was three times as old as his wife, but 15 years afterwards, he was only twice as old. What were their ages on their wedding day?

Let x represent the wife's age; then
3x represents the husband's age;

+15 represents the wife's age 15 years afterwards; and
3x+15 represents the husband's age 15 years
Then, by the conditions of the problem, we shall have

afterwards.

3x+15=2(x+15);

from which x will be found = 15 years, the wife's age; hence 3 x 15=45 years, was the husband's age.

25. Two persons, A and B, lay out equal sums of money in trade ; the first gains $126, and the second loses $87, and A's money is now double of B's. What did each lay out?

Let x represent the sum each laid out; then

x+126 represents the sum A had after gaining $126; and x-87 represents the sum B had after losing $87. Then the Equation will be,

x+126=2(x-87);

which will give x=$300.

26. A courier who travels 60 miles a day had been despatched 5 days, when a second is sent to overtake him, who goes 75 miles a day. In what time will he overtake him?

Let x represent the number of days; then

x+5 represents the number of days the first traveled ; 60(x+5) represents the number of miles the first traveled; and 75x represents the number of miles the second traveled. Since both traveled the same number of miles, we shall have

27. An island is 60 miles in circumference, and two persons, A and B, start together to travel the same way around it; A goes 15 miles a day, and B 20. In what time would the two come together again?

Let x represent the number of days; then

15x represents the distance A traveled; and
20x represents the distance B traveled.

Since the distance B traveled exceeds the distance A traveled, by the circumference of the island, the Equation will be

20.x-15x=60;

from which x will be found equal to 12 days.

28. A man and his wife usually drank out a cask of beer in 12 days, but when the man was from home it lasted the woman 30 days. many days would the man alone be in drinking it?

How