29. If I sell hay at $1 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 it require to purchase 47 bushels of wheat at $23 per bushel ? Ans. 168.bu.

31. If 15 cords of wood cost $57, what cost 1 cord? what

cost 197 cords ?

32. If 193 cords of wood cost $76,67, how be obtained for $5791? 33. At 7

shillings per yard, what cost 47

yards?

Ans.

17£. 5s. 6d. 34. When 172£. 15s. 02d. are paid for 47 yards of broadcloth, what is the value of 1 yard? Ans. 3£. 12s. 11328d. 35. If 1lb. of sugar cost of a dollar, what is the value of 43 lb. ? Ans. $23.6173 36. If 173lb. of sugar cost $211, what cost 50lb. ? Ans. $7.581818.

yards?

37. Bought 87 yards of broadcloth for $612; what was the value of 14 Ans. $102.90. 38. If of an acre of land cost $ 43.75, what cost 10 acres? 39. When $500 are paid for 10 acres of land, how much might be obtained for $43.75?

Ans.

Ans.

40. If 9 hogsheads of sugar cost $71.87, what cost of a hogshead ?

41. Paid $4.56% for 4 of a hogshead of sugar; what ought to be given for 9 hogsheads?

Ans.

42. If 19 men can grade a certain road in 11 days, how long would it require 47 men to perform the same labor?

43. When 47 men can grade a certain road in 4411 days, how long would it require 19 men to perform the same labor? 44. If of a ton of hay cost $9.20, what cost 17 tons? 45. When $430.10 are paid for 17 tons of hay, what cost of a ton?

Ans.

Ans.

46. If of a tub of butter cost $7.15, what cost 7 tubs ? 47. When $114.40 are paid for 7 tubs of butter, what cost of a tub? 48. If a man can mow a field of 7 acres in 8 days, when they are 11 hours long, how many days will it require to perform the same labor, when the days are 10 hours long?

Ans. 9

49. If 4 yards of cloth cost $19, what cost 25 yards ?

days.

Ans. $118.75.

50. When $87.25 is paid for 15 barrels of flour, what cost

100 barrel ?

Ans. $581.663.

51. Gave $81.75 for 20 cords of wood; required the price of 70 cords at the same rate. Ans. $286.121. 52. John Smith gave Thomas Ayer $19.75 for 2 dozen of hats; what then should Smith give for 1972 dozen ? Ans. $193.3812.

53. If 3cwt. of potash cost $47.25, what must be paid for 11 cwt. Ans. $179.814. 54. If 47 casks of lime cost $50, what is the value of 5 casks? Ans. $5.3119. 55. Peter Quimby bought of Silas Noyes 19 tons of hay, for which he paid $ 300; what then was the cost of 13 tons ? Ans. $209.77133 56. If a staff 4 feet long cast a shadow 6 feet, what is the height of that steeple whose shadow is 180 feet?

Ans. 120 feet. 57. If 8 men eat a barrel of flour in 20 days, how long would it last 12 men? Ans. 13 days.

58. If 23 men build 273 rods of wall, which is 5% feet high, in 5 days, by laboring 10 hours each day, required the number of days it will take 46 men to perform the same labor by working 8 hours each day? Ans. 3 days.

59. Henry Smith can reap a field in 10 days, by laboring 8 hours a day. His wife, Sarah, the same field in 9 days, by laboring 12 hours a day. How long would it take both to reap the field, provided they labored 8 hours a day?

Ans. 53 days. 60. If 15 tons 7cwt. 2qr. 18lb. of cotton cost $2067.48, what cost 1lb.? what lcwt.? what cost 1 ton? what 78 tons? Ans. $10483.20. 61. If it cost $93 to carry 17cwt. 3qr. 73lb. of sugar 87 miles, how far may it be carried for $73.87?

Ans. 6501588 miles. 62. Bought a bale of cloth for $963; I dispose of it for § of the cost, and by so doing I lose $2 on a yard; required the number of yards in the bale? Ans. 18 yd.

63. Bought a horse and chaise for $250, and I paid for the harness of what I paid for the horse. The chaise cost the value of the horse. What was the price of each?

Ans. Horse, $13019; chaise, $11913; harness, $ 83713 64. At of a dollar a peck, how many bushels can be ob tained for $17§ ? Ans. 30 bushels.

65. If it require 23 bushels of wheat to sow I acre, how many acres will 174 bushels sow? Ans. 7 acres.

66. If 174 bushels of wheat sow 7 acres, how many bushels will it require to sow I acre?

Ans. 2 bushels.

67. John Jones sold his horse for $176.18. part pay 47 bushels of rye at $1.37 remainder he received wheat at $2 quantity of wheat.

68. Sold apples at of a dollar ceive for 8 bushels?

He received in per bushel; and for the per bushel. Required the Ans. 45 6933 bushels. a bushel. What did I reAns. $1.174.

13600

17

Ans. $9.190.

69. Sold 183 bushels of rye for $21.47. What was received for 1 bushel? what for 74 bushels? 70. Gave 17£. 8s. 11d. for 9 tons of coal. What cost

1 ton? what cost 19 tons ?
71. How many garments can be
cloth, if each garment requires 7

72. If 184 cords of wood cost what cost 1713 cords?

Ans. 36£. 16s. 511d. made of 756 yards of

yards?

Ans. 100 garments. $90.00, what cost 1 cord ? Ans. $830.5038.

73. If a man travel 147 miles in 36 hours, how far will he travel in 1 hour? how far in 974 hours? 74. If a man travel 500 miles in 972 hours,

travel in 32 hours ?

Ans. 392356m.

how far will he Ans. 166 miles.

bushels of oats in 87 days, how Ans. 93 bushels.

75. If a horse eat 19 many will 7 horses eat in 60 days?

MISCELLANEOUS QUESTIONS.

1. How far will a man walk in 17 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. 10918ğin. 3. How much wood in a pile which is 17 feet long, 7 feet high, and 4 feet wide? Ans. 4cd. 66107ft. 4. What is the value of 193 barrels of flour, at $63 a barrel ? Ans. $134.15.

5. What is the value of 37611 acres of land, at $75 per acre? Ans. $28387.06.

19

6. What cost 1712 quintals of fish, at $4.75 per quintal? Ans. $81.55.

6

7. What cost 16707 pounds of coffee, at 12 cents per Ans. $212.992.

pound?

8. What cost 28 tons of Lackawana coal, at $112 a ton? Ans. $333.27.

9. Bought 37

hogsheads of molasses, at $ 17.62 a hhd.; what was the whole cost? Ans. $655.2025. 10. What cost of a cord of wood, at $5.75 a cord?

Ans. $5.03.

11. What are the contents of a field which is 1394 rods long, and 38 rods wide? Ans. 33A. 3R. 151⁄2p.

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 cost $ 48.15, what is it per ton? Ans. $2.62.

14. If a hhd. of wine cost $987, what gallon ?

15. If 5 bushels of wheat cost $83, worth?

16. What will 11 hogsheads and 17 at 19 cents a gallon?

is the price of one Ans. $1.56118. what will a bushel be Ans. $1.644. gallons of wine cost, Ans. $140.32g. 1 pints, are suffiAns. 288.

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

18. I have a shed which is 18 feet long, 10 feet wide, and 711 feet high; how many cords of wood will it contain? Ans. 11cd. 124829 ft.

19. What will 67 pounds of tea cost, at 65 cents per lb. ? Ans. $4.5232 contain, that is 82 Ans. 146 ft. to cover a side

20. How many cubic feet does a box feet long, 57 feet wide, and 3 feet high? 21. How many feet of boards will it take of a house which is 46 feet long and 17 feet high?

Ans. 812ft.

22. Required the number of square feet on the surface of 7 boxes, each of which is 5 feet long, 2 feet high, and 32 feet wide; required also the number of cubic feet they would Ans. 5279ft.; 2863 cubic feet. 23. A certain room is 12 feet long, 11 feet wide, and 7 feet high; how much will it cost to plaster it, at 2 cents per square foot? Ans. $13.48.

Occupy.

24. A man has a garden that is 14 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 gives 2 cents per cubic foot? Ans. $223.761. 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. 2942432bu.

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, whose each side measures 8 feet?

Ans. The last contains 32 cubic feet the most. 27. Divide $1112§ equally among 129 men. Ans. $88. 28. Bought 68 barrels of flour, at $711 per barrel; what was the amount of the whole? Ans. $5384. 29. What cost 8 acres of land, at $ 423 per acre?

Ans. $369.20.

30. How shall four 3's be arranged, that their value shall be nothing?

31. I have a room 20 feet long, 15 feet wide, and 8 feet high. This room contains 4 windows, each of which is 5 feet in height and 3 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, $ 2.805.

SECTION XXII.

DECIMAL FRACTIONS.

A DECIMAL FRACTION is a fraction whose denominator is a unit with as many ciphers annexed as there are places in the numerator. Thus, 10, 100, 100, &c.

15 157

The denominator being in all cases formed in this obvious manner, there is no necessity of expressing it, and therefore it is not written; but a point is placed before the first figure of the numerator, to indicate that the figure or figures on the right of the point denote a decimal, and not a whole number. Thus, for we write .5, for, .15, &c. This point is called the separatrix.

Ciphers annexed to the right hand of decimals do not increase their value; for .4, and .40, and .400 are decimals having