9. A gave $43.50 for pigs, at the rate of $7.25 for 3 pigs; how many did he buy?

Ans. 18 pigs.

10. B gave $54 for flour, at the rate of $6 for 4 bushels; how many bushels did he buy?

CASE II.

Ans. 39 bushels.

191. To pass from a fraction to an integer.

1. If & of an acre of land cost $108, what will one acre

1. If of a yard of cloth is worth 24 dimes, what are 8 yards of the cloth worth?

2. If of a barrel of sugar cost $12, what will 7 barrels cost?

3. I bought 5 yards of summer silk at the rate of $10 for 3 yards · what was the cost?!

}

4. Mary bought 9 apples, at the rate of of an apple for 4 of a cent; what did they cost?

4

5. Henry bought 25 peaches, at the rate of of a peach for of a cent; required the cost.

6. Three-fifths of what I paid for a cow was $24; what did I pay for a horse whose value was 5 times that of the cow?

WRITTEN EXERCISES,

2. If of the cost of A's farm is $2480, what did the farm cost? Ans. $3720.

3. If of a barrel of flour cost $2.50, what will 5 barrels 4

cost at the same rate?

Arts. $21.87.

4. If of a yard of cloth cost $2.10, what will enough for suit containing 9 yards cost?

Ans. $22.05.

5. If § of a cwt. of sugar cost $12.45, what will be the cost of 20 cwt, or 1 ton of sugar?

Ans. $298.80.

6. What will 21 tons of hay cost, if of a ton of hay cost $12.85 ? Ans. $308.40. 7. If $467 is of the price I pay for a horse, what would be the cost of 4 pairs of horses at the same rate?

Ans. $1200

8. If a lawyer's clerk could write 60 pages in 10 hours, how much would he write in a week, working 10 hours a day? Ans. 337 pages.

9. How much will it cost to transport 25 hundredweight of freight from Philadelphia to Pittsburgh at $4 for 2 hundredweight? Ans. $458.

10. How much will I pay for 15 acres of land, at the rate of 2 acres for $425.25? Ans. $2551.50. 11. A bought 40 bushels of grain, at the rate of 34 bushels for $3.20; what did it cost? Ans. $38.40. 12. B sold 77 gallons of milk, at the rate of $1.25 for 5 gallons; required the cost. Ans. $17.50. 13. C bought 39 cords of wood, at the rate of $12.45 for 31 cords; how much did it cost?

Ans. $149.40.

14. D bought 81 tons of coal, at the rate of 5 tons for $26.25; how much did it cost?

Ans. $393.75.

CASE III.

192. To pass from an integer to a fraction.

1. If 1 barrel of apples cost $8, what will of a barrel cost?

SOLUTION.-If 1 barrel of apples cost $8, of a barrel cost of $8, which is $2; and if of a barrel cost $2,4 of a barrel will cost 3 times $2, which are $6.

MENTAL EXERCISES.

1. What cost of a pound of beef, if 2 pounds cost 32 cents? 2. If a man can earn $51 in 3 days, how much will he earn in of a day?

3. If 2 harrels of flour cost $103, for what can I sell of a barrel at the rate of cost?

4. If Harry walks 63 miles in 2 hours, how far will he walk at this rate in 3 hours?

5. If 7 pounds of sugar cost 56 cents, for what can I sell 4 pounds, and neither gain nor lose?

6. A vessel sailed 60 miles in 12 hours; how far at this rate did it sail in 4 hours?

7. If a seamstress earns $1 in 2 days, how much will she earn in 10 days?

WRITTEN EXERCISES.

2. Henry paid $24.60 for a cow; how much would he have paid had he given as much? Ans. $19.68.

3. If 3 yards of cloth cost $7.50, what will of a yard of the same cloth cost? Ans. $2.183. 4. If 7 barrels of apples cost $193, what will § of a barrel cost at the same rate? Ans. $21. 5. How much will 107 tons of coal cost at the rate of $139 for 8 tons? Ans. $18 6. A bought 9 acres of land, at the rate of $1605 for 5 acres; required the cost. Ans. $3174. 7. How much must I pay for 1818 cords of wood, at the rate of $6 for 3 cords? Ans. $421. 8. If 9 tons of hay are worth $100, what must I give for 141 tons? Ans. $167. 9. If 12 bushels of beans cost $114, how much will 151 bushels cost? Ans. $148. 10. How much must I pay for 1818 tons of iron ore, at the rate of 17 tons for $33? 11. A gave $1968 for 21 acres of land; for what would he sell of an acre, at a gain of $4 an acre? 12. B gave $444 for 24 tons of hay; he sold C 18 of a ton, at $2 less a ton; what did he receive?

Ans. $37.

Ans. $924.

Ans. $15.20.

NOTE.-The solution of several of the above problems is simplified by expressing the operations and cancelling.

CASE IV.

193. To pass from a fraction to a fraction.

1. If of an acre of land cost $150, what will of an acre cost?

SOLUTION.-If of an acre cost $150, of an acre cost of $150, which is $75; and of an acre will cost 3 times $75, which are $225. If 1 acre cost $225, of an acre cost of $225, which is $45, and of an acre will cost 4 times $45, which are $180. SOLUTION 2D.-If of an acre cost $150, of an acre cost of $150, and of an acre will cost $150; and of an acre will cost XX$150, which by cancellation we find is $180.

OPERATION.

xx $150-$180, Ans.

NOTE.-The 2d method, by cancellation, is preferred, especially with more difficult problema.

3. Mary gave of her money for a silk dress and for a cloak, and had $10 remaining; how much had she at first?

4. Frank, after spending of his money, found that $16 was } of what he had remaining; how much money had he at first?

5. If of an army were killed,

taken prisoners, and 800 mer

escaped, of how many men did the army consist?

6. What number is that which being increased by its, and that sum diminished by of the number, the remainder is 50?

7. When E was married he was 27 years old, and of his age was 4 years more than of bis wife's age; required the age of his wife. 8. A boy, after spending of his money for candies and for peaches, found that 20 cents was of what remained; how much. money had he?

9. A thief stole of Harry's money, and before he was caughɩ spent of it; the remainder, which was $20 less than he stole, was given back; how much money had Harry at first?

WRITTEN EXERCISES.

2. A invested & of his money in bank stock, and had $6045 remaining; how much money had he?

Ans. $24,180.

3. A drover sold of his cows, and then had 210 remain

ing; how many had he before the sale?

4. B sold of his gas stock to C and remaining 1463 shares; how many shares each, and how many had he at first?

Ans. 270.

to D, and had

did he sell to

Ans. 3135.

5. A gave of his fortune for a farm, and paid of the remainder for building a house, and then had $4671 remain. ing; how much had he at first? Ans. $46,710.

SUPPLEMENTARY PROBLEMS.

To be omitted unless otherwise directed.

6. A father gave of his fortune to his daughter, to his wife, and the remainder, which was $6720, to his son; what did the wife and the daughter receive? Ans. W., $5376; D., $4032. orchard bear apples, bear

7. One-third of the trees in an peaches, and the remainder, which is 100, bear plums; required the number of trees in the orchard.

Ans. 240.

feet, when

8. A boy lost of his kite string, and then added 53 he found that it was just of its original length; what was its original length?

Ans. 129 feet.

MENTAL EXERCISES.

MISCELLANEOUS EXAMPLES.

1. If a barrel of apples cost $54, how many "quarters" does it

cost?

2. If 4 boys can earn $63 in a week, how much does each boy earn? 3. If I buy at the mint 125 " 'quarters" for change, how many dollars must I pay?

4. What cost 8 barrels of apples, at the rate of $3 per barre. ?

5. of $40 is 2 times what A gave for a bureau; what was the cost of the bureau ?

6. of of a dolla is of the cost of a watch; how much did the watch cost?

7. A man owning of the stock of a bank sold of his share; how much did he sell?

8. Jane bought a slate for of a dollar, and an arithmetic for of a dollar; what was the cost of both?

9. If of a number, increased by of the number, equals 50, what is the number?

10. Maria owes a store bill of $3; if she hands the clerk $1, how much change would she receive?

11. If of a pole is in the air, in the water, and the rest in the mud, how much is in the mud?

12. How much will 43 yards of muslin cost, at the rate of 12 cents a yard?

13. How much will 10 pounds of sugar cost, at of a dime a pound?

14. If a yard of flannel costs $, how many yards can you buy for $12?

15. Mrs. Brown exchanged 10 pounds of butter, at 15 cents a pound, for calico worth 64 cents a yard; how many yards did she receive?

16. How much will 14 pounds of cloves cost, if 34 pounds can be bought for 50 cents?

17. If 24 yards of muslin cost 30 cents, how much will 10 yards cost, at the same rate?

18. How far will a man drive in 54 hours, at the rate of 21 miles in 3 hours?

19. If of a ton of hay is worth $43, what cost 7 tons of hay at the same rate?

20. John found 60 cents, which is of of what he then had; how much had he at first?

21. Henry gave his sister 20 cents, which is of what he had at first, and of what his sister now has; how much had each at first?