9. What will be the value of a hogshead of wine, containing 63 gallons, at 1 dollar 63 cents a gallon? Ans. $102.69.

10. Sold a sack of hops, weighing 396 pounds, at 11 cents 3 mills a pound; to what did it amount? Ans. $44.748.

11. Sold 19 cords of wood, at $5.75 a cord; to what did it amount?

12. Sold 169 tons of timber, at $4.68 a ton; what did I receive?

13. Sold a hogshead of sugar, weighing 465 pounds; to what did it amount, at 14 cents a pound? Ans. $65.10. 14. What will be the amount of 789 pounds of leather at 18 cents a pound? Ans. $142.02.

15. What will be the expense of 846 pounds of sheet-lead at 5 cents 7 mills a pound? Ans. $48.222. 16. When potash is sold for $132.55 a ton, what will be the price of 369 tons? Ans. $48910.95. 17. What will 365 pounds of beeswax cost at 18 cents 4 mills a pound? Ans. $67.16. 18. If 1 pound of tallow cost 7 cents 3 mills, what are 968 pounds worth? Ans. $70.664.

DIVISION OF UNITED STATES MONEY..

111. Ex. 1. If 78 barrels of fish cost $303.42, what will 1 barrel cost? Ans. $3.89.

RULE.

Divide as in division of simple numbers.

The quotient will be in the lowest denomination of the dividend, which must be pointed off as in reduction of United States money.

NOTE. - When the dividend consists of dollars only, and is either smaller than the divisor or not divisible by it without a remainder, reduce it to a lower denomination by annexing two or three ciphers, as the case may require, and the quotient will be cents or mills accordingly.

When it is required to find the number of times one sum of money is contained in another, both sums, if of different denominations, must be reduced to the same, before dividing.

Proof. The proof is the same as in division of simple

4. When 19 bushels of fine salt can be bought for $30.87, what costs one bushel?

5. At 12 cents a pound, how many pounds of sugar can be bought for $51?

6. If 78 barrels of fish cost $303.42, what will one barrel cost?

7. Bought 42 bushels of pears for $73.50; what cost one bushel? Ans. $1.75. 8. How many yards of broadcloth at $2.75 a yard can be bought for $904.75 ? Ans. 329 yards.

9. When rye is sold at the rate of 628 bushels for $ 471.00, what is that a bushel? Ans. $0.75. 10. If it should cost $1460 to support a family 365 days, what would be the expense a day?

Ans. $4.

11. How many gallons of oil at $1.62 a gallon can be bought for $234?

Ans. $3.75.

12. If 1624 pounds of pork cost $97.44, what cost one pound? Ans. $0.06. 13. If 47 thousand shingles cost $176.25, what is the cost per thousand? 14. Bought 148 tons of plaster of Paris for $ 337.44; what was it per ton? Ans. $2.28. 15. At $37.75 an acre, how many acres of land may be bought for $1774.25 ? Ans. 47 acres.

16. At 67 cents a pound, how many chests of tea, each weigh ing 59 pounds, can be bought for $672.01? Ans. 17 chests. 17. How many bushels of wheat at $1.25 a bushel can be bought for $863.75? Ans. 691 bushels.

18. Sold 169 tons of timber for $790.92; what cost one ton?

19. What cost one pound of leather, if 789 pounds cost $142.02 ?

20. If 369 tons of potash cost $48910.95, what will be the price of one ton? Ans. $132.55. 21. Bought 47 hogsheads of salt, each hogshead containing 7 bushels, for $368.48; what cost one bushel? Ans. $1.12.

GENERAL PRINCIPLES AND APPLICATIONS.

112. ANALYSIS is an examination of a question by resolving it into its parts, in order to consider them separately, and thus, by reasoning from the nature of the question, to render each step in the solution plain and intelligible.

113. An aliquot part of any number or quantity is such a part as will exactly divide that number or quantity. Thus, 3 is an aliquot part of 6; and 4, an aliquot part of 16.

114. The method of performing operations by means of aliquot parts is called PRACTICE, or ANALYSIS by ALIQUOT PARTS.

115. In business calculations frequent use is made of the following

ALIQUOT PARTS OF A DOllar.

PRACTICAL QUESTIONS BY ANALYSIS.

116. The price of a unit of any quantity being given, to find the cost of that quantity.

Ex. 1. If 1 barrel of flour cost $7, what will 125 barrels cost?

ANALYSIS. Since 1 barrel costs $7, 125 barrels will cost 125 times as much: $7 × 125:

$875.

2. If 1 pound of beef cost 13 cents, what will 914 pounds cost? Ans. $118.82. 3. If 1 yard of calico cost 23 cents, what will 311 yards cost?

4. When 44 cents are paid for 1 pound of tea, how much must be paid for 15 chests of tea, each containing 47 pounds? 5. At 39 cents a pound, how much must be paid for 9 bales of wool, each containing 317 pounds? Ans. $1126.93. 6. If the cost of building 1 mile of railroad be $41315 what will be that of 113 miles? Ans. $4668595.

117. The price of a unit of any quantity being a given aliquot part of a dollar, to find the cost of that quantity.

7. At 12 cents a yard, what will 208 yards of calico cost? Ans. $26. ANALYSIS. Since, at $1 a yard, the cost would be as many dollars as there are yards, the cost at 12 cents, or of $1, will be one eighth as many dollars as there are yards, or as many dollars as 8 is contained times in 208; 208 ÷ 8 26. Therefore 208 yards cost $26. That is, we take such a part of the number denoting the quantity as the price is of 1 dollar.

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8. What will be the cost of 362 pounds of feathers at 331⁄2 cents a pound? Ans. $120.663. 9. At 50 cents a bushel, what will 7 loads of potatoes cost, each containing 30 bushels? Ans. $105.

10. At 64 cents a pound, how much must be paid for 1163 pounds of shingle nails?

11. What will be the cost of 96 yards of broadcloth at $4.33 a yard? Ans. $416. ANALYSIS. Since, at $1 a yard, the cost would be as many dollars as there are yards, the cost at $4.33}, or $ 43, will be 4 times as much: $43 × 96 $416.

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12. If the cost of 1 pair of boots be $3.163, what will be the cost of 20 cases, each case containing 60 pairs?

13. At $2.25 each, what will 150 hats cost?

Ans. $337.50.

14. What will 98 dozen knives cost at $5.12 a dozen?

Ans. $502.25.

15. If James Spooner spends uselessly every day for cigars 64 cents, how much does he thus spend in 360 days?

16. At $2.20 a bushel, what will 15 car-loads of wheat, each containing 212 bushels, cost? Ans. $6996.

118. The price of any article sold by the 100, or 1000, with the quantity, being given, to find the cost of that quantity. 17. What will 732 fishes cost at $5 a hundred?

Ans. $36.60.

ANALYSIS. Since 100 fishes cost $5, 1 fish will cost

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of

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$ 5, or $18; and if 1 fish cost $13, 732 fishes will cost 732 times as much: $5 × 732 $3660; $3660 ÷ 100 $36.60. That is, we multiply the quantity and price together, and cut off two figures at the right (Art. 79).

18. How much must be paid for 950 apple-trees at 20 dollars a hundred?

19. What will 7235 arithmetics cost at $ 45 a hundred? Ans. $3255.75.

20. What will it cost to excavate 19875 solid feet of earth, at the rate of 52 cents per hundred solid feet? Ans. $103.35. 21. What is the value of 1765 feet of timber at $3 a hundred? Ans. $52.95. 22. What is the value of 2355 cedar rails at $5.50 per hundred?

23. What will 3100 bricks cost at $6 a thousand?

Ans. $18.60. ANALYSIS. Since 1000 bricks cost $6, 1 brick will cost rooo of $6, or $1‰; and, if 1 brick cost $ To‰б, 3100 will cost 3100 times as much: $6 × 3100 $18600; $18600 ÷ That is, we multiply the quantity and price

1000 $18.60.

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together, and cut off three figures at the right (Art. 79).

24. At $142.50 a thousand, what will 6150 chestnut posts cost? Ans. $876.375. 25. How much must be paid for 15750 feet of boards at $30 a thousand?

26. At $2.25 per thousand, how much must be paid for 3550 laths? Ans. $7.983. 27. I have bought of L. T. Robbins 363 feet of plank at