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. 240 ft.; 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 1 yr. being $18, what is the interest of $850 for the same time?

40. The interest of $800 for 6 m. 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? Ans. 6 yd.

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 12 a. 3 r. 16 rd. 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 2 bbl. of flour are worth as much as 3 cords of wood, 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?

many

50. If 13 men perform a piece of work in 45 days, how men must be added to perform the same in 3 of the time? 51. If the interest on $700 is $42 in one year, what will be · the interest on the same sum for 31⁄2 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? Ans. 49 men.

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

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

an acre,

57. If the earth revolves 366 times in 365 days, in what time does it revolve once? Ans. 23 h. 564m.

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? Ans. 9 days. 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? Ans. 113 h.

63. Paid $3.50 for 7 lb. of tea; what should I pay for 19 lb. ? 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 14 oz. of bread each per day for 120 days; how long will the same bread last them if each man is allowed but 12 oz. per day?

Ans. 140 d. of her worth?

lb. ?

68. If of a ship cost $25000, what is 1 69. At $27 per cwt., what is the cost of 37 70. The earth moves 19 miles per second in her orbit; how far does she go in 3 m. 27 sec.

COMPOUND PROPORTION.

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

3:12 16: 25

18: 9, 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.

2:6 8:24, and 30:5:: 24: 4, Ans.

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

In solving this question by simple proportion, we, in the first place, disregard the amount of labor, and inquire how long it will take 2 men to do as much as 6 men in 8 hours. Having found 24 hours to be the answer to this question, we next disregard the number of men, and inquire how long it will take to thresh 5 bushels of wheat if 30 bushels are threshed in 24 hours, and thus obtain 4 hours, the true answer to the question.

In this operation, the given number of hours, 8, is first multiplied by 6 and the product divided by 2, then this quotient is multiplied by 5 and the product divided by 30; but it will answer the same purpose to multiply the 8 by the product of the two multipliers, 6 and 5, then divide the number so obtained by the product of the two divisors, 2 and 30; thus,

It will be seen that, of the first two couplets, 33:5} (2:6) one

55

ratio is less than a unit and the other greater; but there is no impropriety in this, for one condition of the question requires the answer to be greater than the 3d term, and the other condition requires it to be less. Hence,

334. To solve questions in Compound Proportion.

RULE. Write that given number which is of the same kind as the required answer for the 3d term; take any two of the remaining terms THAT ARE ALIKE, and, considering the question as DEPENDING ON THESE ALONE, arrange them as in simplè proportion; arrange each pair of LIKE TERMS by the same principles; and then multiply the continued product of the 2d terms by the 3d term, and divide this result by the continued product of the 1st terms; the quotient will be the term sought.

334. Rule for compound proportion?

NOTE. The work may often be much abridged by canceling factors in the 2d and 3d terms, with like factors in the 1st terms (144, Note).

Ex. 2. If 6 men in 15 days earn $135, how many dollars will 9 men earn in 18 days?

6 men : 9 men

-15 days: 18 days)

:: $135: 4th term.

=

9X18X135=21870 continued product of 2d and 3d terms. 6×1590 continued product of 1st terms.

=

3. If 4 men, in 24 days of 9 hours each, build a wall 40 ft. long, 9 ft. high, and 4 ft. thick, in how many days of 6 hours each can 8 men build a wall 60 ft. long, 12 ft. high, and 5 ft. thick?

Ans. 45.

4. If a family of 6 persons spend $600 in 8 months, how many dollars will be required for a family of 10 persons in 14 months? Ans. $1750.

5. If a family of 6 persons spend $600 in 8 months, how many months will $1750 sustain a family of 10 persons?

6. If a family of 6 persons spend $600 in 8 months, how large a family may be sustained 14 months for $1750?

7. If the transportation of 12 boxes of sugar, each weighing 4 cwt., 40 miles, cost $8, what must be paid for carrying 40 boxes, weighing 34 cwt. each, 75 miles? Ans. $43.75. days, how many

8. If 4 men dig a trench 84 feet long in 2 men can dig a trench 336 feet long in 4 days? 9. If 4 men dig a trench 84 ft. long and 5 ft. wide how many men can dig a trench 420 ft. long and 3 ft. days?

Ans. 10.

in 3 days, wide in 4 Ans. 9.