14. A man sold his house for $3005, this sum being $98.039 more than he gave for it: what did it cost him?

15. A man bought a pair of oxen for $100, and sold them again for $75.37: did he make or lose by the bargain, and how much?

16. A man starts on a journey with $100; he spend $87.57: how much has he left?

17. How much must you add to $40.173, to make $100? 18. A merchant stocked a store, at the beginning of a year, at an expense of $10500; during the year he bought goods to the amount of $94755, and sold to the amount of $14500.625; his expenses were $1267.314; and the goods in the store, at the close of the year, are worth $8965.459: what was his gain during the year?

19. A farmer had a horse worth $147.49. He traded him for a colt worth $35.048, and a cow worth $47%, and received the rest in cash: what cash did he receive?

20. My house is worth $8975.034; my barn, $695.879: what is the difference of their values, and what would be gained if both were sold for $10000?

21. What is the difference between nine hundred and sixtynine dollars eighty cents and 1 mill, and thirty-six dollars ninety-nine cents and 9 mills?

MULTIPLICATION.

171. 1. A farmer sells 8 sheep for $1.25 each: how much does he receive for the whole?

8

ANALYSIS. The price of one sheep is multiplied OPERATION. by the number of sheep. The multiplicand is the $ 1.25 price of one, in decimals; and the multiplier is an abstract number, denoting the number of things whose value is required. The product, however, will be the same, whichever number is used as the multiplier (Art. 51): Hence,

$10.00

Rule.

Multiply and point off, as in decimal fractions.

Examples.

1. What will 8 barrels of flour cost, at $6.375 per barrel? 2. What will 55 yards of cloth come to, at 371⁄2 cents per yard?

3. What will 300 bushels of wheat come to, at $1.25 per bushel?

4. What will 85.25 pounds of tea cost, at $1.37 per pound?

5. What is the cost of a cask of wine containing 29 gallons, at $2.75 per gallon?

6. What will be the cost of 47 barrels of apples, at $12 per barrel?

7. What is the cost of a box of oranges, containing 450, at 2 cents apiece?

8. What is the cost of 307 yards of linen, at 68 cents per yard?

9. If 1 pound of butter cost 12 cents, what will 4 firkins cost, each weighing 56 pounds?

10. At $1.33 a foot, what will it cost to dig a well 78 feet deep?

11. If it cost $2.3125 to keep a horse for 1 week, what would be the cost of keeping 3 horses for 18 weeks?

12. A flour merchant bought 125 barrels of flour at $5} each, and sold them at $5.9375: what was the amount of gain?

13. A speculator sold 16 houses at $2463.12 each, and received in exchange 25 lots of ground, each worth, on an average, $872, and the rest in cash: what cash did he receive?

14. A cloak required 63 yards of cloth. What would be the cost of the cloak, if the cloth cost $3 a yard, and as many yards of lining at $0.983 a yard, and the making cost $3.45?

172.

DIVISION.

1. Bought 9 pounds of tea for $5.85: what was the price per pound?

ANALYSIS.-One pound will cost as much as 9 pounds. of $5.85 is found by dividing by 9, according to the principles of Division of Decimals: Hence the

Rule.

OPERATION.

9) 5.85

.65

Arrange the numbers for division, and proceed as in division of decimals.

PROOF. The same as in division of decimals.

7. Paid $29.68 for 14 barrels of apples: what was the price per barrel ?

8. If 27 bushels of potatoes cost $10.125, what is the price of a bushel ?

9. If a man receive $29.25 for a month's work, how much is that a day, allowing 26 working days to the month?

10. A produce-dealer bought 3 barrels of eggs, each containing 150 dozen, for which he paid $63: how much did he pay a dozen?

11. A man bought a piece of cloth containing 72 yards, for which he paid $252: what did he pay per yard?

12. If $600 be equally divided among 26 persons, what

will be each one's share?

13. A lady bought 17 yards of silk for $15.75: what was the price per yard?

172. What is the rule for division of United States Money?

14. If $47.314 paid for the board of a family for 5 weeks, what was the price per week?

15. If I pay $4.50 a ton for coal, how much can I buy for $67.50?

16. At $7 a barrel, how much flour can be bought for $178.50?

17. How many pounds of tea can be bought for $6.75, at 75 cents a pound?

18. What number of barrels of apples can be bought for $47.50, at $2.37 a barrel?

19. At 44 cents a bushel, how many bushels of oats can be bought for $14.30?

20. At 34 cents a bushel, how many barrels of apples can I buy for $13.60, allowing 2 bushels to the barrel?

21. A farmer receives $840 for the wool of 1400 sheep: how much does each sheep produce him?

22. A merchant buys a piece of goods containing 105 yards, for which he pays $262.50; he wishes to sell it so as to make $52.50: how much must he ask per yard?

23. If 1 acre of land cost $28.75, how much can be bought for $3220 ?

24. Paid $40.50 for a pile of wood, at the rate of $3.371 a cord, how much was there in the pile?

Applications.

173. An ALIQUOT PART of a number is any exact divisor, whether fractional or integral. Thus, 3 months is an aliquot part of a year, being one-fourth of it; and 12 cents is an aliquot part of 1 dollar, being one-eighth of it.

CASE I.

174. To find the cost of several things, when the price of a single thing is an aliquot part of $1.

1. What will be the cost of 69 yards of cotton sheeting, at 33 cents a yard?

ANALYSIS. 33 cents = of a dollar: 69 yards,

at $1 a yard, would cost $69: at of a dollar a vard, it will cost of $69, which is $23: Hence,

OPERATION.

3) 69

$23

Rule. Take such a part of the number of things, as the price of a single thing is of $1.

Examples.

1. What will 100 cocoa-nuts cost, at 121 cts.= of a dollar apiece?

2. What will 250 water-melons cost, at 25 cents apiece? 3. What will 55 tops cost, at 64 cents each?

4. What will 650 yards of muslin cost, at 12 cents a yard?

5. What will 450 melons cost, at 5 cents apiece?

6. What will 6640 lemons cost, at 64 cents each?

7. What will 136 gallons of molasses cost, at 33 cents a gallon?

CASE II.

175. To find the cost, when the price of one, and the number of things are given.

1. What is the cost of 36 oranges, at 5 cents apiece?

ANALYSIS. Since 5 cents taken 36 times, is the same as 36 taken 5 times (Art. 51), the the product of 5 by 36, or of 36 by 5:

cost will be
Hence,

OPERATION.

36

5

$1.80

Rule.-Multiply the price of 1 by the number of things, or the number of things by the price of 1, and the product will be the cost.