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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 dollars, what will 1 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? 14. 3 is 5 times what number? 15. 8 is 5 times what number? 16. 9 is 4 times what number? 17. 11 is 6 times what number? 18. 13 is 7 times what number? 19. 14 is 8 times what number? 20. 17 is 5 times what number? 21. 18 is 8 times what number? 22. 17 is 9 times what number? 23. 15 is 10 times what number? 24. 20 is 9 times what number? 25. 22 is 10 times what number?

26. 24 is 7 times what number?

27. If 2 thirds of a barrel of beef cost 3 dollars,

* See Sect. X, Art. 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 for 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?
43. 9 is 5 eighths of what number?
44. 10 is 7 thirds of what number?
45. 11 is 6 fifths of what number?
46. 12 is 7 fifths of what number?
47. 15 is 2 sevenths of what number?
48. 17 is 3 tenths 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 barrel?

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 logwood for 48 dollars; what was that a ton?

64. 67 is 9 sevenths of what number?
65. 53 is 7 tenths of what number?
66. 58 is 9 eighths of what number?

67. 61 is 10 ninths of what number?

68. Bought 2 barrels and 1 fifth of a barrel of gin (that is, 11 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?

4. A cask of wine cost 67 dollars; what is a eighths of it worth?

5. A man bought 9 oranges for 6 cents and 2 sev¬ enths apiece, and sold them for 67 cents; what did he gain by the bargain?

6. A man bought 10 yards of broadcloth for 70 dollars; how must he sell it per yard in order to gain 14 dollars?

7. If, when the days are 12 hours long, a man perform a journey in 3 days, how many hours is he in performing it?

8. If a man perform a journey in 36 hours, how many days would he be in performing it, when the days are 9 hours long?

9. If, when the days are 11 hours long, a man ca} perform a journey in 5 days, in how many hours will he perform it? In how many days when the days are 9 hours long?

10. What number added to 2 fifths of 33 will make the number 17?

11. How many yards of cloth, that is 1 quarter of a yard wide, will line 10 yards that is 3 quarters wide?

12. 8 yards of cloth, that is 1 quarter wide, are equal to how many yards that is 4 quarters wide?

13. How many yards of cloth, that is 3 quarters wide, are equal to 7 yards that is 5 quarters wide ? 14. How many yards of cloth, that is 6 quarters wide, are equal to 37 that is 4 quarters wide?

15. If a piece of cloth 5 quarters wide be worth 37 dollars, what is a piece of the same length, quarters wide, worth?

16. If cloth 4 quarters wide is worth 8 dollars a yard, what is 1 yard of the same kind of cloth, that is 5 quarters wide, worth?

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