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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 31 bushels of wheat at $ 2; per bushel ?

Ans. 168, bu. 31. If 15 cords of wood cost $ 57, what cost 1 cord ? what cost 197 cords ?

Ans. 32. If 197 cords of wood cost $ 76 676, how many cords may be obtained for $ 578?

Ans. 33. At 73 shillings per yard, what cost 47} yards ?

Ans. 17£. 5s. 6 d. 34. When 172£. 15s. O d. are paid for 471 yards of broadcloth, what is the value of 1 yard? Ans. 3£. 12s. 11325d.

35. If llb. of sugar cost of a dollar, what is the value of 43 lb. ?

Ans. $23.611. 36. If 173lb. of sugar cost $ 211, what cost 50lb, ?

Ans. $ 7.581915. 37. Bought 87 yards of broadcloth for $ 612; what was the value of 1470 yards ? -kom

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

Ans. 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 111 days, how long would it require 47 men to perform the same labor ?

43. When 47 men can grade a certain road in 4447 days, how long would it require 19 men to perform the same labor ?

44. If 4 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. 46. If ye 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 . It of a lub?

Ans. 48. If a man can mow a field of 71 acres in 81 days, when they are l hours long, how many days will it require to perform the same labor, when the days are 10 hours long?

Ans. 946 days. . 49. If 4 vards of cloth cost $19, what cost 25 yards ? .

Ans. $118.75. 50. When $ 87.25 is paid for 15 barrels of flour, what cost. 100 barreis?

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 1912 dozen ?

Ans. $193.38.14. 53. If 3cwt. of potash cost $ 47.25, what must be paid for 11,5 cwt.

Ans. $179.814. 54. If 47 casks of lime cost $ 50, what is the value of 5 casks?

Ans. $ 5.314. 55. Peter Quimby bought of Silas Noyes 19 tons of hay, for which he paid $ 300; what then was the cost of 134 tons ?

Ans. $ 209.777 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. 134 days. 58. If 23 men build 272 rods of wall, which is 53 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. 52, days. 60. If 15 tons 7cwt. 2qr. 181b. of cotton cost $ 2067.48, what cost llb. ? what lcwt.? what cost 1 ton ? what 78 tons ?

Ans. $10483.20. 61. If it cost $97 to carry 17cwt. 3qr. 73lb. of sugar 87 miles, how far may it be carried for $ 73.87 ?

Ans. 650159 miles. 62. Bought a bale of cloth for $ 963 ; I dispose of it for á of the cost, and by so doing I lose $ 2 on a yard ; required the number of yards in the bale ?

Ans. 18. syd. 63. Bought a horse and chaise for $ 250, and I paid for the harness 1 of what I paid for the horse. The chaise cost 11 the value of the horse. What was the price of each?

Ans. Horse, $ 1301?; chaise, $ 11911; harness, $ 837. 64. At 7 of a dollar a peck, how many bushels can be obtained for $175?

Ans. 3037 bushels. 65. If it require 23 bushels of wheat to sow I acre, how many acres will 174 bushels sow?

Ans. 74 acres.

66. If 174 bushels of wheat sow 74 acres, how many bushels will it require to sow I acre?

67. John Jones sold his horse for $ 176.18. He received in part pay 47 bushels of rye at $1,374 per bushel; and for the remainder he received wheat at $ 2% per bushel. Required the quantity of wheat.

Ans. 456.933 bushels. * 68. Sold apples at 4 of a dollar a bushel. What did I receive for 8} bushels ?

Ans. $ 1.174. 69. Sold 187 bushels of rye for $21.47. What was received for 1 bushel ? what for 79 bushels ? Ans. $ 9.1917.

70. Gave 17£. 8s. 11d. for 92 tons of coal. What cost 1 ton? what cost 194 tons ?

Ans. 36£. 16s. 5791d. 71. How many garments can be made of 7564 yards of cloth, if each garment requires 731 yards ?

Ans. 100 garments. 72. If 184 cords of wood cost $ 90.00, what cost 1 cord ? what cost 1718 cords?

Ans. $ 830.50 6. 73. If a man travel 147 $1 miles in 364 hours, how far will he travel in 1 hour? how far in 974 hours ? Ans. 392356 m.

74. If a man travel 500 miles in 972 hours, how far will he travel in 32 7 hours ?

Ans. 166 miles. 75. If a horse eat 193 bushels of oats in 873 days, how many will 7 horses eat in 60 days ? Ans. 934 bushels.

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MISCELLANEOUS QUESTIONS.

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1. How far will a man walk in 17.3 hours, provided he goes at the rate of 47 miles an hour ?

Ans. 82m. 4fur. 8rd. Ift. 4in. 2. How much land is there in a field which is 291 rods square ?

Ans. 5A. IR. 32p. 141ft. 10915 in. 3. How much wood in a pile which is 173 feet long, 71. feet high, and 4 feet wide ?

Ans. 4cd. 66107ft. 4. What is the value of 197 barrels of flour, at $ 63 a bar

Ans. $ 134.155. 5. What is the value of 3761 acres of land, at $ 75% per acre ?

Ans. $ 28387.064. 6. What cost 1719 quintals of fish, at $ 4.75 per quintal ?

Ans. $ 81.55 4. 7. What cost 167073 pounds of coffee, at 124 cents per pound ?

Ans. $ 212.995..

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8. What cost 2841 tons of Lackawana coal, at $11 a ton ?

Ans. $ 333.27 . 9. Bought 371} hogsheads of molasses, at $ 17.62] a hhd.; what was the whole cost ?

Ans. $655.20,. 10. What cost [of a cord of wood, at $ 5.75 a cord ?

Ans. $ 5.031. 11. What are the contents of a field which is 1394 rods long, and 384 rods wide ?

Ans. 33A. 3R. 15j p. 12. Bought 15 loads of wood, each containing 11% 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. $ 2.624. 14. If a hhd. of wine cost $ 98%, what is the price of one gallon ?

Ans. $ 1.56118. 15. If 5 bushels of wheat cost $ 87, what will a bushel be worth ?

Ans. $ 1.645 16. What will 11 hogsheads and 173 gallons of wine cost, at 19 cents a gallon ?

Ans. $ 140.323. 17. How many bottles, each containing la pints, are sufficient for bottling a hhd. of cider ?

Ans. 288. 18. I have a shed which is 1812 feet long, 10 feet wide, and 713 feet high ; how many cords of wood will it contain ?

Ans. Ilcd. 124:25ft. 19. What will 67 pounds of tea cost, at 65 cents per lb. ?

Ans. $ 4.5237. 20. How many cubic feet does a box contain, that is of feet long, 57 feet wide, and 3 feet high ? Ans. 146.ft.

21. How many feet of boards will it take to cover a side of a house which is 46 feet long and 174 feet high?

Ans. 812,7 ft. 22. Required the number of square feet on the surface of 7 boxes, each of which is 51 feet long, 2 feet high, and 312 feet wide ; required also the number of cubic feet they would occupy.

Ans. 52779ft. ; 28635 cubic feet. 23. A certain room is 12 feet long, 111 feet wide, and 7.1 feet high ; how much will it cost to plaster it, at 2 cents per square foot ?

Ans. $ 13.487. 24. A man has a garden that is 144 rods long, and 104 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 it box contain which is

147 feet long, 511 feet deep, and 4 feet wide, there being 2150 cubic inches in a bushel ?

Ans. 29434 3? bu. 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. $ 83.

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 51 feet in height and 31 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 2 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, $5.11; for papering, $ 4.37; for paper, $ 2.80

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, ir, o, 1957, &c.

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 to we write .5, for 15, .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

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