13. If 154 pounds of sugar cost $18.48, what will 1 pound cost?

14. A merchant bought 14 boxes of tea for $560; it being damaged he was obliged to lose $106.75 on the cost of it; how much did he receive a box? Ans. $32.37.

ADDITIONAL APPLICATIONS.

CASE I.

167. To find the cost of any number or quantity, when the price of a unit is an aliquot part of one dollar.

168. An Aliquot Part of a number is such a part as will exactly divide that number; thus, 3, 5, and 7 are aliquot parts of 15.

An aliquot part may be a whole or a mixed number, while a factor must be a whole number.

ALIQUOT PARTS OF ONE DOLLAR.

1. What will be the cost of 3784 yards of flannel, at 25

cents a yard ?

OPERATION.

4) 3784 Ans. $946

as there are yards; or,

ANALYSIS. If the price were $1 a yard, the cost would be as many dollars as there are yards. But since the price is of a dollar a yard, the whole cost will be as many dollars of $3784 = $3784 ÷ 4 = $946.

RULE. Take such a fractional part of the given number as the price is part of one dollar.

EXAMPLES FOR PRACTICE.

2. What cost 963 bushels of oats, at 333 cents per bushel?

Ans. $321.

Case I is what? What is an aliquot part of a dollar? Give explanation. Rule.

3. What cost 478 yards of delaine, at 50 cents per yard ? 4. What cost 4266 yards of sheeting, at 84 cents a yard? Ans. $355.50.

5. What cost 1250 bushels of apples, at 12 cents per bushel? Ans. $156.25. 6. What cost 3126 spools of thread, at 61 cents per spool ? Ans. $195.375.

7. At 163 cents per dozen, what cost 1935 dozen of eggs? Ans. $322.50.

8. What cost 56480 yards of calico, at 124 cents per yard? 9. At 20 cents each what will be the cost of 1275 salt barrels ? Ans. $255.

CASE II.

169. The price of one and the quantity being given, to find the cost.

1. How much will 9 barrels of flour cost, at $6.25 per barrel?

OPERATION.

$6.25

9

ANALYSIS. Since one barrel cost $6.25, 9 barrels will cost 9 times $6.25, and $6.25 x 9= $56.25.

Ans. $56.25

RULE. Multiply the price of one by the quantity.

EXAMPLES FOR PRACTICE.

2. If a pound of beef cost 9 cents, what will 864 pounds cost? Ans. $77.76.

3. What cost 87 acres of government land, at $1.25 per acre?

4. What cost 400 barrels of salt, at $1.45 per barrel?

Ans. $580.

5. What cost 16 chests of tea, each chest containing 52 pounds, at 44 cents per pound?

Case II is what? Give explanation. Rule.

CASE III.

170. The cost and the quantity being given, to find the price of one.

1. If 30 bushels of corn cost $20.70, what will 1 bushel

2. If 25 acres of land cost $175, what will 1 acre cost? 3. If 48 yards of broadcloth cost $200, what will 1 yard cost? Ans. $4.16%.

4. If 96 tons of hay cost $1200, what will 1 ton cost? 5. If 10 Unabridged Dictionaries cost $56.25, what will 1 cost? Ans. $5.621.

6. Bought 18 pounds of tea for $11.70; what was the price per pound? Ans. $.65. 7. If 53 pounds of butter cost $10.07, what will 1 pound cost?

8. A merchant bought 800 barrels of salt for $1016; what did it cost him per barrel?

9. If 343 sheep cost $874.65, what will 1 sheep cost?

Ans. $2.55. 10. If board for a family be $684.37 for 1 year, how much is it per day? Ans. $1.87.

CASE IV.

171. The price of one and the cost of a quantity being given, to find the quantity.

1. At $6 a barrel for flour, how many barrels can be bought for $840?

Case III is what? Give explanation. Rule. Case IV is what?

OPERATION.

6) 840

Ans. 140 barrels.

ANALYSIS. Since $6 will buy 1 barrel of flour, $840 will buy as many barrels as there are dollars, or as many barrels as $6 is contained times in $840; 840÷6 140 barrels.

RULE. Divide the cost of the quantity by the price of one.

EXAMPLES FOR PRACTICE.

2. How many dozen of eggs can be bought for $5.55, if one dozen cost $.15? Ans. 37 dozen. 3. At $12 a ton, how many tons of hay can be bought for $216 ? Ans. 18 tons. 4. How many bushels of wheat can be bought for $2178.75, if 1 bushel cost $1.25? Ans. 1743 bushels. 5. A dairyman expends $643.50 in buying cows at $191 apiece; how many cows does he buy? Ans. 33 cows. 6. At $.45 per gallon, how many gallons of molasses can be bought for $52.65 ?

7. A drover bought horses at $264 a pair; how many horses did he buy for $6336?

8. At $65 a ton, how many tons of railroad iron can be bought for $117715 ? Ans. 1811 tons.

CASE V.

172. To find the cost of articles sold by the 100, or 1000.

1. What cost 475 feet of timber, at $5.24 per 100 feet?

Give explanation Rule. Case V is what? Give first explanation.

RULE. I. Reduce the given quantity to hundreds and decimals of a hundred, or to thousands and decimals of a thousand. II. Multiply the price by the quantity, and point off in the result as in multiplication of decimals.

The letter C is used to indicate hundreds, and M to indicate thousands.

EXAMPLES FOR PRACTICE.

2. What will 42650 bricks cost, at $4.50

3. What is the freight on 2489 pounds from Boston to New York, at $.85 per 100 pounds?

Ans. $21.156.

4. What will 7842 feet of pine boards cost, at $17.25 per M? Ans. $135.274. 5. What cost 2348 pine-apples, at $12 per 1000? 6. A broom maker bought 1728 broom-handles, at $3 per 1000; what did they cost him?

7. What is the cost of 2400 feet of boards, at $7 per M; 865 feet of scantling, at $5.40 per M; and 1256 feet of lath, at $.80 per C? Ans. $31.519.

8. What will be the cost of 1476 pounds of beef, at $4.371 per hundred pounds?

CASE VI.

173. To find the cost of articles sold by the ton of 2000 pounds.

1. How much will 2376 pounds of hay cost, at $9.50 per ton ?

Give second explanation. Rule, first step. Second. Case VI is what?