measure. I divide it equally between 9 persons ; what does each receive ? Ans. 193ft. 13. If the transportation of 183 tons of iron costs $ 48.152, what is it per ton ? Ans. $ 2.6245 14. If a hogshead of wine costs $985, what is the price of one gallon ? 15. If 5 bushels of wheat cost $ 87, what will a bushel be worth ? Ans. $1.649 16. What will 11 hogsheads and 17} gallons of wine cost, at 19 cents a gallon ? Ans. $ 140.32%. 17. How many bottles, each containing 14 pints, are sufficient for bottling a hogshead 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. 11C. 1243293ft. 19. What will 67 pounds of tea cost, at 65 cents per pound? Ans. $ 4.5232 20. How many cubic feet does a box contain, that is 82 feet long, 57 feet wide, and 3 feet high? Ans. 146 1Gft. 21. How many feet of boards will it take to cover a side of a house which is 46 feet long and 171 feet high? 22. Required the number of square feet on the surface of 7 boxes, each of which is 5} feet long, 2 feet high, and 375 feet wide; required also the number of cubic feet they would occupy ? Ans. 52743ft. ; 286333 cubic feet. 23. A certain room is 12 feet long, 11į feet wide, and 73 feet high ; how much will it cost to plaster it, at 21 cents per Ans. $ 13.485. 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 41 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 1412 feet long, 511 feet deep, and 41 feet wide, there being 2150cubic inches in a bushel ? Ans. 294313 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, each of whose sides measures 8 feet ? Ans. The last contains 32 cubic feet the most. square foot ? 27. Which will contain the most gallons, a cistern that is 74 feet long, 6 feet wide, and 5 feet deep, or one that is 93 feet long, 4 feet wide, and 5! feet deep? Ans. The first cistern contains 924 gallons most. 28. My field has four sides. The first side is 31 rods 136 feet in length; the second, 41 rods 110 feet; the third, 38 rods 0feet; and the fourth, 45 rods 12 10 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 jo 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 4 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 31 A. 3R. 6p., and J. Ford's farm contains 39A. 2R. 373p. What is the fraction, in its simplest form, that will express their comparative size? Ans. 32. Bought 68 barrels of flour, at $ 7 14 per barrel ; what was the amount of the whole ? Ans. $5381 33. What cost 8 acres of land, at $ 42% 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 84 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 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, $ 5.113%; for papering, $ 4.37 ; for paper, $ 2.80 EXAMPLES TO BE PERFORMED BY ANALYSIS. 1. If } of a bushel of corn cost 63 cents, what cost a bushel ? what cost 15 bushels ? Ans. $ 10.80. ILLUSTRATION. - If 7 eighths of a bushel cost 63 cents, 1 eighth will cost 1 seventh of 63 cents 9 cents; and 8 eighths will cost 8 times 9 cents 72 cents, and 15 bushels will cost 15 times 72 cents $ 10.80. 2. If 4žlb. of pepper cost $ 2.15, what cost 1 pound ? what cost 30lb. ? Ans. $ 13.50. ILLUSTRATION. - In 4žlb. there are 431b. Then, if 43 ninths lb. cost $ 2.15, 1 ninth will cost 1 forty-third of $ 2.15 $ 0.05, and 9 ninths or llb. will cost 9 times $ 0.05 - $ 0.45, and 301b. will cost 30 times $ 0.45 $ 13.50. 3. When $ 1728 are paid for 304 tons of iron, what cost 1 ton ? what cost 737 tons ? Ans. $ 432. 4. When $ 432 are paid for 737 tons of iron, what quantity should be received for $ 1728? 5. For 737 tons of iron there were paid $ 432; what sum will it require to pay for 304 tons ? 6. For 304 tons of iron $ 1728 were paid ; what quantity should be received for $ 432 ? 7. Gave 770 bushels of rye for a barrel of flour; how much rye will it then require to purchase 6g barrels of flour? Ans. 4935 bushels. 8. Divide $ 1728 among 17 boys and 15 girls, and give each boy It as much as a girl ; what sum will each receive ? Ans. Each girl, $ 6691 ; each boy $ 4247. 9. If f of a ton of hay cost $ 14.49, what cost 43 tons ? 10. If 4 tons of hay cost $ 82.504, 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 $ 82.503 ? 12. When $ 82.50$ are paid for 4 tons of hay, what will be the cost of į of a ton ? 13. When 143 tons of copperas are sold for $500, what is the value of 1 ton ? what is the value of 911 tons ? 14. When 911 tons of copperas are sold for $ 333.33], what is the value of 14} tons ? 15. Gave $ 333.33; for 911 tons of copperas ; what quantity of copperas should be received for $ 500 ? 16. For 14} tons of copperas $ 500 were paid ; how much might be purchased for $ 333.331? 17. Purchased 97} gallons of molasses for $ 31.32; what cost 1 gallon ? what cost 7634 gallons ? 18. Sold 763 gallons of molasses for $244.36; what should I receive for 97 gallons ? 19. If $244.36 will buy 763 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. 21. If 17 bushels of rye cost $ 15.75, what cost 1 bushel ? what cost 91 bushels ? Ans. $8.5665. 22. If 9 barrels of flour cost $ 504, what cost 1 barrel ? what cost 87barrels ? Ans. $ 492 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 17 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 11 bushels of corn for $54; what was received for 1 bushel ? what should I have charged for 97ş bushels ? Ans. $ 30315. 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. $1,735 29. If I sell hay at $ 14 per cwt., what should I give for 9} 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 $2} per bushel ? Ans. 168. bu. 31. If 15 cords of wood cost $ 571, what cost 1 cord? what cost 19% cords? 32. If 19] cords of wood cost $ 76970, how many cords may be obtained for $ 57 41 ? 33. At 73shillings per yard, what cost 47} yards? Ans. 17£. 5s. 6 d. 34. When 172£. 15s. O d. are paid for 47} yards of broadcloth, what is the value of 1 yard ? Ans. 3£. 12s. 113.gd. 35. If ilb. of sugar cost 13 of a dollar, what is the value of 4391b.? Ans. $23.6113 36. If 173lb. of sugar cost $ 211, what cost 501b. Ans. $ 7.581928. 37. Bought 874 yards of broadcloth for $ 612; what was the value of 1470 yards ? 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 ? 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 ? 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, ti of a ton ? 46. If It 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 To of a tub? 48. If a horse eat 193 bushels of oats in 874 days, how many will 7 horses eat in 60 days? Ans. 93} bushels. 49. Henry Smith can reap a field in 10 days, by laboring 8 hours a day. His son John can reap 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. 524 days. |