Practical Arithmetic, by Induction and Analysis

10. What cost 338 barrels of cider, at 1 dollar, 6 cents a barrel? Ans. $358.28 11. Sold 38 cords of wood, at 5 dollars, 75 cts. a cord: to what did it amount?

Ans. $218.50 12. At 7 cts. a pound, what cost 465 pounds of sugar? Ans. $32.55

NOTE. Instead of multiplying gives the same product, Art. 30. product, remember that 7 cents is the true multiplicand.

7 cents by 465, multiply 465 by 7, which But, in fixing the denomination of the

13. What cost 89 yards of sheeting, at 34 cts. a yard? Ans. $30.26 14. What will 24 yards of cloth cost, at 5 dollars, 67 cents a yard? Ans. $136.08 15. I have 169 sheep, valued at $2.69 each: what is the value of the whole? Ans. $454.61 16. If I sell 691 bushels of wheat at 1 dollar, 25 cts. a bushel, what will it amount to? Ans. $863.75

17. I sold 73 hogsheads of molasses, of 63 gallons each, at 55 cts. a gallon: what is the sum? Ans. $2529.45 18. What cost 4 barrels of sugar, of 281 pounds each, at 6 cents, 5 mills a pound? Ans. $73.06

19. Bought 35 bolts of tape, of 10 yards each, at 1 cent a yard: what did it cost? Ans. $3.50 20. If I earn 13 cts. an hour, and work 11 hours a day, how much will I earn in 312 days? Ans. $446.16 21. I sold 18 bags of wheat, of 3 bushels each, at $1.25 a bushel: what is the amount? Ans. $67.50 22. What cost 150 acres of land, at 10 dollars, 1 mill per acre?

Ans. $1500.15

23. What cost 17 bags of coffee, of 51 pounds each, at 14 cents, 7 mills per pound?

Ans. $127.44 9

ART. 75. DIVISION OF U. S. MONEY.

The object in Division of United States money is,

1st. To find how many times one sum of money is contained in another of the same order or denomination. Or, 2d. To divide a sum of money into a given number of equal parts, Art. 41.

1. How much cloth at 7 cts. a yard, will $1.75 buy? ANAL-AS 1 yard costs 7 cts., there will be as many yards as 7 cts. are contained times in 175 cts. 175÷7=25.

Here, the divisor and dividend are the same denomination, cents; and the quotient, how many yards, is an abstract number.

2. Divide 65 dollars equally among 8 persons.

SOLUTION.-In this case it is required to divide $65 into 8 equal parts, that is, to find one-eighth of it. One-eighth of $65 is $8, with a remainder $1=100 cts. One-eighth of 100 cts. is 12 cts., with a remainder of 4 cts. which equals

Mills.

8)65000 8125

$8.12 5

OPERATION.

$ cts. m. 8)65.00 0

8.12 5

40 mills. One-eighth of 40 mills is 5 mills; hence, one-eighth of $65 is $8.12 5

The operation may be performed by reducing the dollars to mills, then dividing by 8, and after this, reducing the quotient to dollars.

3. A farmer received $29.61 cents, for 23 bushels of wheat: how much was that per

SOLUTION.-To divide $29.61 into 23 equal parts, annex a cipher, which reduces it to 29610 mills; then divide by 23 as in Simple Numbers.

The quotient, 1287, is mills, (Art. 41) which reduce to $1.287, (Art. 70).

But, 1287 is not the exact quotient, as there is a remainder of

9 mills. It is, however, less than

a mill of being exact, which is

bushel?

sufficiently accurate for business purposes.

The signis annexed to denote a remainder.

Rule for Division.-1. To find how many times one sum of money is contained in another, reduce both sums to the same denomination, and divide as in Simple Numbers.

2. To divide a sum of money into any number of equal parts, reduce the sum to mills; divide as in Simple Numbers; the quotient will be mills, which reduce to dollars.

PROOF-As in Division of Simple Numbers.

be purchased for $3?

4. How many yards of calico, at 8 cents a yard, can be bought for $2.80? Ans. 35 yards. 5. How many yards of ribbon, at 25 cents a yard, can Ans. 12 yards. 6. At $8.05 a barrel, how many barrels of flour will $161 purchase? Ans. 20 barrels. 7. At 7 cents 5 mills each, how many oranges can be bought for $1.20? Ans. 16 oranges.

8. At $1.12 5 per bushel, how many bushels of wheat can be purchased for $234? Ans. 208 bush. 9. If 4 acres of land cost $92.25, how much is that an acre? Ans. $23.06 2+ 10. Make an equal division of $57 and 50 cents among 8 persons. Ans. $7.18 7+ 11. A man received $25 and 76 cts. for 16 days' work: how much was that a day? Ans. $1.61 12. I bought 755 bushels of apples for $328, 42 cts., 5 mills: what did they cost a bushel? Ans. $0.43 5 13. My salary is $800 a year: how much is that a day, 313 working days in the year? Ans. $2.55 5+ equally among 133 Ans. $75.18 7+

14. Divide ten thousand dollars men what is each man's share?

15. A man purchased a farm of 154 acres, for two thousand seven hundred and five dollars and one cent: what did it cost per acre?

16. I sold 15 kegs of butter, of 25

$60 how much was that a pound?

Ans. $17.56 5

pounds each, for

Ans. 16 cts.

17. I bought 8 barrels of sugar, of 235 pounds each,

for $122.20: what did 1 pound cost?

REVIEW.-75. What is the object of division?

Ans. $0.06 5

How is the number

of times one sum of money is contained in another found, Rule 1? How is a sum of money divided into equal parts, Rule 2?

ART. 76.-PROMISCUOUS EXAMPLES.

1. I owe A $47.50; B $38.45; C $15.47; D $19.43: what sum do I owe?

2. A owes $35.25; B $23.75; C as B, and $1 more: what is the amount?

Ans. $120.85 much as A and Ans. $119.

3. A paid me $18.38; B $81.C2; C, twice as much as A and B: how much did I receive?

Ans. $300. 4. I went to market with $5; I spent for butter 75 cts., for eggs 35 cts., for vegetables 50 cts., for flour $1.50: how much money was left?

Ans. $1.90 5. A lady had $20; she bought a dress for $8.10, shoes for $1.65, eight yards of calico at 75 cts. a yard, and a shawl for $4: what sum was left? Ans. 25 cts.

6. I get $50 a month, and spend $30.50 of it: how much will I have left in 6 months?

Ans. $117. 7. A farmer sold his marketing for $21.75: he paid for sugar $3.85, for tea $1,25, for coffee $2.50, for spices $1.50: how much had he left? Ans. $12.65

8. I owe A $37.06, B $200.85, C $400, D $236.75, and E $124.34; my property is worth $889.25: how much do I owe more than I am worth? Ans. $109.75 9. Bought 143 pounds of coffee at 13 after paying $12.60, what was due?

cts. a pound: Ans. $5.99 10. A owed me $400: he paid me 435 bushels of corn, at 45 cts. a bushel: what sum is due? Ans. $204.25

11. If B spend 65 cts. a day, how much will he save in 365 days, his income being $400 ? Ans. $162.75

12. Bought 21 barrels of apples, of 3 bushels each, at 35 cts. a bushel: what did they cost? Ans. $22.05 13. What cost four pieces of calico, each containing 19 yards, at 23 cts. a yard? Ans. $17.48

14. If 25 men perform a piece of work, for $2000, and spend, while doing it, $163.75, what will be each man's share of the profits? Ans. $73.45

15. If 16 men receive $516 for 43 days' work, how much does each man earn a day? Ans. 75 cts.

16. C earned $90 in 40 days, working 10 hours a day: how much did he earn an hour? Ans. 22 cts. 5 m.