4. Take of a mile from of a degree.

Ans. 48m. 6fur. 17rd. 8ft. 7şin.

5. From of an acre take of a rod.

6. From 7. From

what remained?

Ans. 1R. 17p. 22yd. 2ft. 108in."

of a cord take of a cord.

of a hogshead of wine there leaked out of it; Ans. 6gal. 3qt. Opt. 177gi. 8. From Boston to Concord, N. H., the distance is 72 miles; of this distance having been travelled, how much remains? Ans. 30m. 6fur. 34rd. 4ft. 84in.

9. From of a year take of a week.

Ans. 101da. 5h. 54m. 174sec.

10. From of an acre take of a foot.

MISCELLANEOUS EXAMPLES IN FRACTIONS.

1. How far will a man walk in 173 hours, provided he goes at the rate of 43 miles an hour?

Ans. 82m. 4fur. 8rd. 1ft. 4in.

2. How much land is there in a field which is 297 rods square? Ans. 5A. 1R. 32p. 141ft. 10915žin. 3. How much wood in a pile which is 17 feet long, 7 feet high, and 4g feet wide? Ans. 4C. 6612zft. 4. What is the value of 197 barrels of flour, at $ 62 a barrel?

5. What is the value of 3761 acres of land, at $75 per acre? Ans. $28387.06. 6. What cost 17 quintals of fish, at $4.75 per quintal? Ans. $81.55 ff.

19 112

7. What cost 1670 pounds of coffee, at 12 cents per pound? Ans. $212.9919. 8. What cost 28 tons of Lackawana coal, at $112 a ton? Ans. $333.27. at $17.624 a hogs

9. Bought 37 hogsheads of molasses,

head; what was the whole cost?

Ans. $655.20 $5.75 a cord?

10. What cost of a cord of wood, at 11. What are the contents of a field which is 139 rods Ans. 33A. 3R. 15ļ?p.

long, and 38 rods wide?

12. Bought 15 loads of wood, each containing 113 feet, cord

measure.

I divide it equally between 9 persons; what does each receive? Ans. 194ft. 13. If the transportation of 183 tons of iron costs $48.152, what is it per ton? Ans. $2.62.

14. If a hogshead of wine costs $987, what is the price of one gallon?

15. If 5 bushels of wheat cost $83, what will a bushel be worth? Ans. $1.64. 16. What will 11 hogsheads and 17 gallons of wine cost, at 193 cents a gallon? Ans. $140.323. 1 pints, are suffiAns. 288. long, 10 feet cords of wood will it conAns. 11C. 124,829 ft.

17. How many bottles, each containing cient for bottling a hogshead of cider?

18. I have a shed which is 18 feet wide, and 711 feet high; how many tain?

19. What will 67 pounds of tea cost, pound?

20. How many cubic feet does a box long, 572 feet wide, and 3 feet high?

12

at 652 cents per Ans. $4.523. contain, that is 83 feet Ans. 146 ft.

take to cover a side of feet high?

21. How many feet of boards will it a house which is 46 feet long and 17 22. Required the number of square feet on the surface of 7 boxes, each of which is 5 feet long, 25 feet high, and 3 feet wide; required also the number of cubic feet they would occupy? Ans. 5279ft.; 286333 cubic feet. 12 feet long, 11 feet wide, and 7 it cost to plaster it, at 23 cents per Ans. $13.487.

23. A certain room is feet high; how much will square foot?

24. A man has a garden that is 144 rods long, and 10 rods wide; he wishes to have a ditch dug around it, that shall be 3 feet wide and 4 feet deep; what will be the expense, if he give 2 cents per cubic foot? Ans. $223.764.

25. How many bushels of grain will a box contain which is 14 feet long, 511 feet deep, and 44 feet wide, there being 2150 cubic inches in a bushel? Ans. 29432bu.

26. Which will contain the most, and by how much, a box that is 10 feet long, 8 feet wide, and 6 feet deep, or a cubical one, each of whose sides measures 8 feet?

Ans. The last contains 32 cubic feet the most.

27. Which will contain the most gallons, a cistern that is 7 feet long, 6 feet wide, and 5 feet deep, or one that is 9 feet long, 4 feet wide, and 54 feet deep?

Ans. The first cistern contains 924 gallons most.

28. My field has four sides. The first side is 31 rods 13% feet in length; the second, 41 rods 1% feet; the third, 38 rods 0 feet; and the fourth, 45 rods 12 feet. I wish to enclose this field with a rail-fence four rails high, using rails of equal length. Required the length of the longest rails that can be used, allowing that the rails lap by each other of a foot; also the number of rails it will take to fence it.

Ans. Length, 13 feet; number, 808. 29. Required the least number of yards of velvet, expressed by a whole number, that can be cut up without waste, into vest patterns of,, or yards each? Ans. 30 yards.

30. If a company whose capital stock is divided into 100 equal shares should conclude to divide the same stock into only 30 shares, how much larger would a share of the latter be than one of the former size?

31. D. Ripley's farm contains 31A. 3R. 6p., and J. Ford's farm contains 39A. 2R. 374p. What is the fraction, in its simplest form, that will express their comparative size? Ans. .

32. Bought 68 barrels of flour, at $71 per barrel; what was the amount of the whole? Ans. $5384.

33. What cost 83 acres of land, at $ 423 per acre?

Ans. $369.20. 34. How shall four 3's be arranged, that their value shall be nothing?

35. I have a room 20 feet long, 15 feet wide, and 81 feet high. This room contains 4 windows, each of which is 54 feet in height and 34 feet in width. There are two doors 7 feet high and 3 feet wide. The mop-boards are of a foot wide. A mason has agreed to plaster this room at 64 cents per square yard; a painter is to lay on the paper at 9 cents per square yard; the paper which I wish to have laid on is 23 feet wide, for which I pay 5 cents per yard. What is the amount of my bill for plastering, for papering, and for paper? Ans. For plastering, $5.1138; for papering, $4.37; for paper, $2.805g.

EXAMPLES TO BE PERFORMED BY ANALYSIS.

1. If of a bushel of corn cost 63 cents, what cost a bushel? what cost 15 bushels?

ILLUSTRATION.

Ans. $10.80.

-If 7 eighths of a bushel cost 63 cents. 1

=

9 cents; and 8 eighths

72 cents, and 15 bushels will cost

eighth will cost 1 seventh of 63 cents
will cost 8 times 9 cents
15 times 72 cents $10.80.

=

2. If 43lb. of pepper cost $2.15, what cost 1 pound? what cost 30lb.?

ILLUSTRATION.

Ans. $13.50.

In 43lb. there are 4lb. Then, if 43 ninths lb. cost $2.15, 1 ninth will cost 1 forty-third of $2.15 $0.05, and 9 ninths or 1lb. will cost 9 times $0.05 and 30lb. will cost 30 times $0.45

=

$13.50.

=

$0.45,

3. When $1728 are paid for 30 tons of iron, what cost 1 ton? what cost 77 tons?

Ans. $432.

4. When $432 are paid for 77 tons of iron, what quantity should be received for $1728?

5. For 77 tons of iron there were paid $432; what sum will it require to pay for 30 tons ?

5

6. For 30 tons of iron $1728 were paid; what quantity should be received for $ 432?

7. Gave 7 bushels of rye for a barrel of flour; how much rye will it then require to purchase 6 barrels of flour?

Ans. 492 bushels.

8. Divide $1728 among 17 boys and 15 girls, and give each boy as much as a girl; what sum will each receive?

Ans. Each girl, $ 6699; each boy $4242. 9. If of a ton of hay cost $14.49, what cost 43 tons? 10. If 4 tons of hay cost $82.50%, what part of a ton will 14.49 buy?

11. If $14.49 will buy of a ton of hay, how much hay can be obtained for $82.504?

12. When $82.502 are paid for 42 tons of hay, what will be the cost of of a ton?

13. When 14 tons of copperas are sold for $500, what is the value of 1 ton? what is the value of 911 tons?

14. When 9 tons of copperas are sold for $333.334, what is the value of 143 tons?

15. Gave $333.334 for 911 tons of copperas; what quantity of copperas should be received for $500?

16. For 143 tons of copperas $500 were paid; how much might be purchased for $333.331?

17. Purchased 973 gallons of molasses for $31.32; what cost 1 gallon? what cost 763 gallons?

18. Sold 763 gallons of molasses for $244.36; what should I receive for 977 gallons?

19. If $244.36 will buy 7633 gallons of molasses, what quantity can be obtained for $31.32 ?

20. Gave 1975lb. of flax for 40 barrels of flour; how many pounds were given for 1 barrel? how many pounds would it require to buy 144 barrels ? Ans. 7110lb.

35

21. If 17 bushels of rye cost $15.75, what cost 1 bushel? what cost 94 bushels? Ans. $8.5667. 22. If 9 barrels of flour cost $504, what cost 1 barrel? what cost 873 barrels ? Ans. $4925 23. If 13 boarders consume a barrel of pork in 78 days, how long would it last, if 7 more boarders were added to their number? Ans. 50 days. 24. If a man by laboring 10 hours a day can, in 9 days, perform a certain piece of work, how many days would it require to do the same work, were he to labor 15 hours a day?

25. If a man, by laboring 15 hours a day, in 6 days can perform a certain piece of work, how many days would it require to do the same work by laboring 10 hours a day?

26. If a man, by laboring 10 hours a day, can in 9 days perform a certain piece of work, how many hours must he labor each day to perform the same work in 6 days?

27. Sold 17 bushels of corn for $53; what was received for 1 bushel? what should I have charged for 971⁄2 bushels? Ans. $30398.

28. Bought 93 tons of hay at $197 per ton; for what must it be sold per cwt. to gain $7 on my bargain? Ans. $12730. 29. If I sell hay at $12 per cwt., what should I give for 93 tons, that I may make $7 on my bargain? Ans. $329. 30. How many bushels of corn at $0.75 per bushel will