a rule. Let the following examples be solved by analysis and by proportion.

2. If a man earn $24 in 2 months how much will he earn in 9 months?

2:9: 24: 4th term.

9

2)216

$108, Ans.

Since we are seeking for dollars, we make $24 the 3d term, and then, as a man will earn

more in 9 months than he will in 2 months, we make 9 the 2d term and 2 the 1st. To analyze

the above, we say, If a man earn $24 in 2 months, then in 1 month he will earn of $24, i. e. $12; and if he earn $12 in 1 month, then in 9 months he will earn 9 times $12, i. e. $108, Ans.

3. If 15 bush. of wheat make 3 bbl. of flour, how many bushels of wheat will be required to make 7 bbl. of flour? Ans. 35. 4. If 40 bush. of wheat make 8 bbl. of flour, how many barrels of flour will 75 bush. of wheat make? Ans. 15.

5. If a man can walk 75 miles in 3 days, how far can he walk in 8 days? Ans. 200 miles. 6. If a man travel 64 miles in 2 days, how long will it take him to travel 160 miles? Ans. 5 days.

7. If a locomotive run 39000 miles in 13 weeks, how far, at that rate, would it run in 52 weeks?

8. If 20 men perform a piece of work in 8 days, in how many

days will 4 men perform the same?

Ans. 40.

9. If 24 cords of wood cost $60, what will 18 cords cost. 10. If $30 pay for 5 cords of wood, how many dollars will pay for 12 cords?

Ans. 72.

11. If 4 cords of wood cost $20, how many cords may be bought for $45?

Ans. 9.

12. If 6 horses eat 42 bushels of oats in 5 weeks, how many bushels will 11 horses eat in the same time?

13. What cost 7 tons of coal when 4 tons cost $24?

14. In how many days can 6 men build a house, if 10 men can build it in 72 days?

15. If 72 lb. of cheese are worth as much as 30 lb. of butter, how many pounds of cheese will pay for 201b. of butter?

16. How many tons of coal can be bought for $84, when 3 tons cost $18? Ans. 14.

17. If 9 horses eat a ton of har in 20 days, how many horses will eat a ton in 30 days? Ans. 6. 18. How many tons of hay will 6 horses eat in 25 weeks, if 8 horses eat 20 tons in the same time?

19. If I pay 2s. 8d. per week for pasturing 2 cows, what shall I pay for pasturing 11 cows?

20. If I pay 2s. 8d. for pasturing 2 cows, how many cows can be pastured the same time for 14s. 8d.?

21. If 8 acres of land cost 75£ 6s. 4d., how many acres may be bought for 131£ 16s. 1d.?

22. If 14 acres of land cost 131£ 16s. 1d., what will 8 acres cost?

23. If of a ship cost $9875, what are of her worth?

24. If of a barrel of flour cost $3.20, what will 6 bbl. cost? 25. If a man walk 192 miles in 6 days of 8 hours each, in how many days of 12 hours each will he walk 192 miles?

26. Lent a friend $400 for 6 months; afterwards he lent me $300. How long may I keep it to balance the favor?

27. How many yards of cloth of a yard wide are equal to 20 yards 14 yard wide?

28. If when flour is worth $9 per bbl., a penny loaf weighs 4oz., what will it weigh when flour is worth $6 per bbl.?

29. If 10 horses eat 45 bushels of oats in 3 weeks, how many bushels will 12 horses eat in the same time?

30. Three men can do a piece of work in 12 days; how many men must be added to the number to do the same in 4 days?

31. A ship's crew of 12 men has food for 24 days, how many men must be discharged that it may last 12 days longer?

32. Paid $1.50 for 3 lb. of tea; what should I pay for 9 lb.? 33. If .25 of a ship cost $3000, what cost .375 of her? 34. At $24 per cwt., what is the cost of 62 lb.?

35. If a steeple 180 feet high casts a shadow 240 feet, what is the length of the shadow cast by a staff 3 feet high, at the same time?

NOTE 2. Since each of the three terms in the above example is in feet, the learner may be uncertain which number to place as the third term; but he has only to notice that he is required to find the length of a shadow, :. the third term should be the number expressing the length of shadow in the given example, viz. 240ft.; thus,

180 3: 240: 4th term = 4 ft., Ans. 36. If a staff 3 feet long casts a shadow 4 feet, what is the hight of a steeple which, at the same time, casts a shadow 240 feet? Ans. 180 ft.

37. If a staff 3 feet long casts a shadow 4 feet, how long is the shadow of a steeple which is 180 feet high, at the same time? 38. If a steeple 180 feet high casts a shadow 240 feet, what is the hight of a staff which, at the same time, casts a shadow 4 feet?

39. The interest of $300 for 1yr. being $18, what is the interest of $850 for the same time?

40. The interest of $800 for 6m. being $24, what principal will gain $45 in the same time?

41. If a man's salary amounts to $2700 in 3 years, what will it amount to in 11 years?

42. If a man's salary amounts to $9900 in 11 years, in how many years will it amount to $2700?

43. If 12 yards of silk that is of a yard wide will make a dress, how many yards of muslin that is 13 yards wide will be required to line it?

44. If of an acre of land is worth $36.40, what is the value of 15 acres, at the same price?

45. If 6 men can mow 12a. 3r. 16rd. of grass in 2 days, by working 6 hours per day, how many days will it take them to do the same if they work only 4 hours per day?

46. If 2bbl. of flour are worth as much as 3 cords or woud, how many barrels of flour will pay for 45 cords of wood?

47. A bankrupt, owing $25000, has property worth $15000; how much will he pay on a debt of $500?

48. A man, owning of a ship, sells of his share for $20000; what is the value of the ship?

49. A and B hired a pasture for $45.90, in which A pastured 11 oxen and B 19; what shall each pay

y?

50. If 13 men perform a piece of work in 45 days, how many men must be added to perform the same in of the time?

51. If the interest on $700 is $42 in one year, what will be the interest on the same sum for 3 years?

52. How many yards of paper 2 feet in width will paper a room that is 133 feet long, 12 feet wide, and 9 feet high?

53. If I pay $168 for 63 gallons of wine, how much water shall I add that I may sell it at $2 per gallon without loss?

54. A certain house was built by 30 workmen in 98 days, but, being burned, it is required to rebuild it in 60 days; how many men must be employed?

55. A garrison of 1500 men has provisions for 12 months, how long will the same provisions last if the garrison is reenforced by 300 men?

56. If a piece of land 20 rods long and 8 rods wide contains an acre, how long must it be to contain the same when it is bur 2 rods wide.

57. If the earth revolves 366 times in 365 days, in what time does it revolve once? Ans. 23h. 56,4m.

58. A wall which was to be built 24 feet high was raised 8 feet by 6 men in 12 days; how many men must be employed to build the remainder of the wall in 12 days more?

59. A wall was completed by 12 men in 12 days; how many men would complete the same in 4 days?

60. If a man perform a journey in 6 days when the days are 12 hours long, in how many days of 8 hours each will he perform the same?

61. A cistern has a pipe that will fill it in 6 hours; how many pipes of the same size will fill it in 45 minutes?

62. A cistern has 3 pipes; the first will fill it in 3 hours, the second in 4 hours, and the third in 5 hours; in what time will they together fill the cistern?

63. Paid $3.50 for 7lb. of tea; what should I pay for 191b.? 64. A can cut a field of grain in 8 days; A and B can cut it in 6 days. In what time can B do the same?

65. If 2 horses can draw a load of 16 tons upon a railway, how many horses will be required to draw 72 tons?

66. A farm was sold at $25.50 per acre, amounting to $1925.25; how many acres did the farm contain?

67. A garrison of 1000 men have 14oz. of bread each per day for 120 days; how long will the same bread last them if each man is allowed but 12oz. per day?

68. If of a ship cost $25000, what is of her worth? 69. At $27 per cwt., what is the cost of 371lb.?

70. The earth moves 19 miles per second in her orbit; how far does she go in 3m. 27sec.

COMPOUND PROPORTION.

332. COMPOUND PROPORTION is an equality of two ratios, one of which is compound and the other simple; thus,

3:12 16: 2

:: 189, is a compound proportion;

and 48: 24: 18: 9, is the same reduced to a simple form. NOTE. The compound ratio may consist of any number of couplets. 333. Every compound proportion may be reduced to a simple form, and, moreover, every example in compound proportion may be solved by means of two or more simple proportions.

Ex. 1. If 6 men in 8 hours thresh 30 bushels of wheat, in how many hours will 2 men thresh 5 bushels?

BY SIMPLE PROPORTION.

26 8:24, and 305: 24: 4, Ans.

332. What is Compound Proportion? 333. May an example in compound proportion be solved by simple proportion? Analyze Ex. 1.