4. 2 and 3 fourths is 1 third of what number? 5. If 1 half of a barrel of beer cost 2 dollars and 1 fourth of a dollar, how much will a barrel cost? 6. 2 and 3 fourths is one half of what number? 7. If 1 fourth of a box of lemons cost 3 dollars and 2 thirds of a dollar, what will a box cost? 8. 2 and 2 thirds is 1 fourth of what number? 9. 3 and 1 half is 1 fourth of what number? 10. If 1 third of a barrel of pork cost 4 dollars and I third of a dollar, what will 1 barrel cost? 11. 4 and 2 thirds is 1 third of what number? 12. If 1 sixth of a barrel of fish cost 2 dollars and 1 fifth of a dollar, what will a barrel cost? 13. 3 and 2 fifths is 1 sixth of what number? 4. If 1 fifth of a barrel of salmon cost 3 dollars and 2 sevenths of a dollar, what is that a barrel? 15. 4 and 3 sevenths is 1 fifth of what number? 16. If a man can travel 4 miles and 3 sevenths of a mile in 1 ninth of a day,lhow far will he travel in a whole day? 17. 5 and 3 sevenths is 1 ninth of what number? 18. 2 and 4 fifths is 1 seventh of what number? 19. 6 and 3 eighths is 1 eighth of what number? 20. 7 and 5 sixths is 1 third of what number ? 21. 8 and 3 sevenths is 1 fourth of what number? 22. 5 and 3 tenths is 1 seventh of what number? 23. 8 and 5 ninths is 1 fifth of what number? 24. 9 and 4 fifths is 1 eighth of what number? 25. 6 and 4 tenths is 1 tenth of what number? 26. 7 and 4 ninths is 1 fifth of what number? 27. 8 and 7 tenths is 1 seventh of what number 1 B. 1. If 2 thirds of a barrel of beef cost 3 dol lars, what does 1 third of a barrel cost? 2. 3 is 2 times what number ?* See section VI, article B. Ans. 3 is 2 times the half of 3; but 1 half of 3 is 3 halves, or 1 and 1 half,* therefore 3 is 2 times 1 and 1 half. 3. If 3 fifths of a yard of cloth cost 4 dollars, what will 1 fifth of a yard cost? 4. 5 is 3 times what number? 5. If 3 sevenths of a barrel of pork cost 2 dol. lars, what will I seventh of a barrel cost? 6. 2 is 3 times what number? 7. If 4 thirds of a bunch of shingles cost 5 dollars, what does 1 third of a bunch cost? 8. 7 is 4 times what number? 9. 2 is 4 times what number? 10. A man bought 4 ninths of a barrel of flour for three dollars; what would be the price of 1 ninth of a barrel at the same rate? 11. 5 is 4 times what number? 12. A man bought 5 eighths of a hundred weight of sugar for 6 dollars; what would 1 eighth of a hundred weight cost at the same rate? 13. 7 is 5 times what number? 26. 24 is 7 times what number? 27 If 2 thirds of a barrel of beef cost 3 dollars * See section X, article A. what will 1 third of a barrel cost? What will the whole barrel cost? 28. *If 5 is 2 thirds of some number, what is 1 third of the same number? 2 and 1 half is 1 third of what number? Then 5 is two thirds of what number? 29. If 3 fourths of a barrel of flour cost 5 dollars, what will 1 fourth of a barrel cost? What will the whole barrel cost? 30. If 8 is 3 fourths of some number, what is 1 fourth of the same number? 2 and 2 thirds is 1 fourth of what number? Then 8 is 3 fourths of what number? 31. A man bought 2 sevenths of a barrel of oil for 5 dollars; how much will 1 seventh cost at the same rate? how much would a barrel cost? 32. If 9 is 2 sevenths of some number, what is 1 seventh of the same number? 4 and 1 half is 1 seventh of what number? Then 9 is 2 sevenths of what number? 33. Bought 5 eighths of a chaldron of coal for 7 dollars; what is the price of 1 eighth, at the same rate? What is the price of the whole chaldron ? 34. If 12 is 5 eighths of some number, what is 1 eighth of the same number? 2 and 2 fifths is 1 eighth of what number? Then 12 is 5 eighths of what number? 35. If a man can do 7 ninths of a piece of work in 4 days, how long would it take him to do 1 ninth of it? how long would it take him to do the whole? 36. If 3 is 7 ninths of some number, what is 1 ninth of the same number? 3 sevenths is 1 ninth of what number? Then 3 is 7 ninths of what number? 37. If 3 fifths of a chaldron of coal cost 8 dollars, what is the whole chaldron worth? 38. 7 is 3 fifths of what number? 39. A man bought 6 sevenths of a cask of raisins or 5 dollars; what was the whole cask worth? 40. 8 is 6 sevenths of what number? * See Sect. VI.,Art. B.,Examples 8 and following. 41. A man had 4 sixths of a week's board for 3 dollars; how much is that for a whole week? 42. 3 is 5 sixths of what number? 49. A man bought 5 eighths of a cask of wine for 19 dollars, what would the whole cask cost? 50. 19 is 3 eighths of what number? 51. 21 is 4 fifths of what number? 52. Bought 5 ninths of a ton of logwood for 23 dollars; what would a ton cost at that rate? 53. 23 is 7 ninths of what number? 54. 21 is 3 tenths of what number? 55. 29 is 4 sevenths of what number? 56. 31 is 5 eighths of what number? 57. 33 is 6 sevenths of what number? 58. 38 is 4 ninths of what number? 59. A man bought 1 barrel and 1 seventh of a barrel of wine for 41 dollars; what was that a bar rel ? NOTE. 1 barrel and 1 seventh of a barrel is the same as 8 sevenths of a barrel. If 8 sevenths of a barrel cost 41 dollars, what does a barrel cost ? 60. 35 is 8 sevenths of what number? 61. A man bought 1 ton and 4 fifths of a ton (that is, 9 fifths of a ton) of fustic for 43 dollars, what was that a ton? 62. 52 is 9 fifths of what number? 63. Bought 1 ton and 2 sevenths of a ton of log wood for 48 dollars, what was that a ton? 67. 61 is 10-ninths of what number? 68. Bought 2 barrels and 1 fifth of a barrel of oil (that is, li fifths of a barrel) for 65 dollars; what was that a barrel ? 69. 65 is 9 fifths of what number? 70. 71 is 8 elevenths of what number? C. 1. A boy gave away 2 apples and 1 half, which was 1 fourth of all he had; how many had he? 2. A man gave away 3 dollars, which was 2 fifths of all the money he had; how much had he? 3. A man sold a cow for fifteen dollars, which was 4 fifths of what she cost him; how much did he lose by the bargain? 4 A man sold a piece of cloth for 37 dollars, which was 9 eighths of what it cost him; how much did he gain by the bargain? 5. There is a pole 3 fifths under water, and 7 feet out of the water; how long is the pole? 6. A man sold a piece of cloth for 47 dollars, by which bargain he lost 2 ninths of what the cloth cost him; how much did it cost him, and how much did he lose? Miscellaneous Examples. 1. If a staff 5 feet long cast a shadow 4 feet at 12 o'clock, what is the length of a pole that casts a shadow 67 feet at the same time? 2. If 53 gallons of water, in 1 hour, run into a cistern containing 97 gallons, and 44 gallons run out in an hour, in what time will it be filled? 3. A man bought a cask of wine containing 75 gallons; 2 sevenths of it leaked out, and he sold the remainder for 1 dollar a gallon; how much did he sell it for? |