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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 I anl ] 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 1 seventh of a barrel cost ?

6. 2 is 3 times what number ?

7. If 4 thirds of a bunch of shingles ci st 5 dole lars, what does I 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 yould 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 ny 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 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 i 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 i 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 i 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 mari 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? 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 ņ 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 abar. rel 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!

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

. [Part 1. 67. 61 is 10 ninths of what number? 68. Bought 2 barrels and 1 fifth of a barrel of oil that is, 11 Sfths 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 i 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 5 eighths of it worth ?

5. A man bought 9 oranges for 6 cents and 2 seva 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 iť when the days are nine hours long ?

9. If when the days are 11 hours long, a man can 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, 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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