Hence,

x= 6, the number of oxen ; 3x=18, the number of cows;

and

4x=24, the number of sheep.

Prob. 24. A boy bought some oranges, some lem. ons, and some pears. The number of them all together was 132. There were four times as many lemons as oranges, and six times as many pears as oranges. How many were there of each?

Let x= the number of oranges.

Then 4x the number of lemons,

and 6x the number of pears.

x+4x+6x=132,

11x=132.

Hence,

or,

Hence,

x=12, the number of oranges; 4x=48, the number of lemons;

and

6x=72, the number of pears.

Prob. 25. Three persons are to share 364 dollars in the following manner. The second is to have five times as much as the first, and the third seven times as much as the first. What is the share of each? Let x the share of the first.

Then 5x the share of the second,

and 7x the share of the third.

Therefore,

or,

Hence,

x+5x+7x=364,

13x=364.

x= 28, the share of the first; 5x=140, the share of the second;

7x=196, the share of the third.

Prob. 26. A draper bought three pieces of cloth, which together measured 90 yards. The second piece was six times as long as the first, and the third was

eight times as long as the first. What was the length of each ?

Let x= the length of the first piece.

Then 6x= the length of the second piece. and 8x= the length of the third piece.

Hence, x= 6 yards, the length of the first piece;

and

6x=36 yards, the length of the second piece;

8x=48 yards, the length of the third piece. Prob. 27. A cask, which held 135 gallons, was filled with a mixture of brandy, wine, and water. It contained five times as much wine as water, and nine times as much brandy as water. What quantity was there of each?

Let x= the number of gallons of water. Then 5x the number of gallons of wine. and 9x the number of gallons of brandy. Therefore,

x+5x+9x=135,

Prob. 28. A gentleman, meeting three poor persons, divided 90 cents among them; to the second he gave twice, and to the third three times as much as to the first. What did he give to each?

Ans. He gave 15 cents to the first,

30 cents to the second,

45 cents to the third.

Prob. 29. Three men, A, B, and C, found a purse of money containing 175 dollars, but not agreeing

about the division of it, each took as much as he could get. A got a certain sum, B got twice as much as A, and C four times as much as A. did each get?

How many dollars

Ans.

A got

25 dollars,

Prob. 30. Three men, A, B, and C, trade in company. A puts in a certain sum, B puts in three times as much as A, and C puts in five times as much as A. They gain 765 dollars. What is each man's share of the gain?

Ans. A's share is 85 dollars;

B's share is 255 dollars;

C's share is 425 dollars.

the son's share was

Prob. 31. A gentleman left 24,000 dollars to be divided between his widow, his son, and his daughter. He directed that his son should receive three times as much as his daughter, and his widow six times as much as his daughter. Required the share of each Ans. The daughter's share was 2,400 dollars; 7,200 dollars; the widow's share was 14,400 dollars. Prob. 32. A farmer bought some oxen, some cows, and some sheep. The number of them all together was 64. There were three times as many cows as oxen, and four times as many sheep as oxen. How many were there of each sort?

Ans. There were 8 oxen,

24 cows,

32 sheep.

Prob. 33. A boy bought some oranges, some lemons, and some pears. The number of them all togeth

er was 165. There were four times as many lemons as oranges, and six times as many pears as oranges. How many were there of each?

Ans. There were 15 oranges,

60 lemons,

90 pears.

Prob. 34. Three persons are to share 598 dollars in the following manner. The second is to have five times as much as the first, and the third seven times as much as the first. What is the share of each ?

Ans. The share of the first is 46 dollars;

the second is 230 dollars;

the third is 322 dollars.

Prob. 35. A draper bought three pieces of cloth, which together measured 105 yards. The second piece was six times as long as the first, and the third was eight times as long as the first. What was the length of each?

Ans. There were 7 yards of the first piece,

42 yards of the second piece,

56 yards of the third piece.

Prob. 36. A cask which held 120 gallons was filled. with a mixture of brandy, wine, and water. It contained five times as much wine as water, and nine times as much brandy as water. What quantity was there of each?

Ans. There were 8 gallons of water,
40 gallons of wine,

The following problems are

72 gallons of brandy.

similar to the preceding,

except that a new term has been introduced. It is

recommended to the pupil that he should endeavor to

solve these problems unaided, before reading the solutions here given; and after he has succeeded, let him compare his solution with that of the book.

Prob. 37. The number of days that four workmen were employed were severally as the numbers 1, 2, 3, 4; and the number of days' work performed by them all was 170. How many days was each workman employed?

Let x represent the number of days the first was employed.

Then 2x will represent the days the second was employed,

3x the third,

and 4x the fourth.

Then, by the conditions of the problem,

x+2x+3x+4x=170;

that is, 10x=170,

or,

x=17 days the first was employed; 2x=34, the second;

3x=51, the third;

4x=68, the fourth.

The sum of all the numbers is 170.

Prob. 38. The estate of a bankrupt, valued at 14,400 dollars, is to be divided among four creditors according to their respective claims. The debts due to B are double those due to A; those due to C are four times those due to A; and those due to D are five times those due to A. What sum must each receive?

Let then

x= the sum A receives; 2x the sum B receives; 4x the sum C receives; 5x= the sum D receives.