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Ans. 3 is 2 times the half of 3; but i half of 3 is 3 halves, or 1 and i 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,

* Sre Seci. 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 i 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 8is 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 y 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 i 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 followina

dollars ;

41. A man had 4 sixths of a week's board for 3

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 a 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 i 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 docs 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 uumber?
70. 71 is 8 elevenths of what number?

many

C. 1. A boy gave away 2 apples and i half, which was 1 fourth of all he had; how 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 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?

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4. A cask of wine cost 67 dollars; what is 5 eighths of it worth?

5. A man bought 9 oranges for 6 cents and 2 serenths 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 tu gain 14 dollars ?

7. If, when the days are 12 hours long, a man perform a journey in 3 days, how many bours 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 caja 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 dded to 2 fifths of 33 will make the number 17 ?

11. How many yards of cloth, that is 1 quarter et 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, 3 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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