46. If 2bbl. of flour are worth as much as 3 cords or 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?

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 13 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 but 2 rods wide.

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

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 19lb.? 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 373lb.?

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: 25

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.

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

332. What is Compound Proportion? 333. May an example in compound proportion 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,

2:6

It will be seen that, of the first two couplets, {}, one”

30:5

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 simple 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?

9 X 18 X 13521870 = continued product of 2d and 3d terms. 6 X 15= 90 continued product of 1st terms. 2187090243, Ans.

=

THE SAME CANCELED.

9

: 18

=243, Ans.

9 × 27=

243, Ans.

5

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

Ans. 45.

8 men : 4 men
6 hours : 9 hours
40 ft. long: 60 ft. long
9 ft. high: 12 ft. high

:: 24 days:

4 ft. thick: 5 ft. thick

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 4cwt., 40 miles, cost $8, what must be paid boxes, weighing 33cwt. each, 75 miles?

for carrying 40 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 84ft. long and 5ft. how many men can dig a trench 420ft. long and days?

Ans. 10. wide in 3 days, 3ft. wide in 4

Ans. 9.

10. If 2 men dig a trench 50ft. long, 5ft. wide, and 3ft. deep in 3 days, how many men can dig a trench 300ft. long, 24ft. wide, and 4ft. deep in 7 days?

Ans. 4.

11. If 6 men dig a trench of 4 degrees of hardness, 35ft. long, 6ft. wide, and 5ft. deep in 5 days, how many men can dig a trench of 6 degrees of hardness 105ft. long, 4ft. wide, and 3ft. deep in 2 days? Ans. 27.

12. If 5 men, in 4 days of 10 hours each, dig a trench of 10 degrees of hardness, 50ft. long, 3ft. wide, and 61ft. deep, how many men can dig a trench of 5 degrees of hardness, 75ft. long, 41ft. wide, and 44ft. deep, in 9 days of 8 hours each?

13. If $100 gain $6 in 1 year, what will $300 gain in 8m.? 14. If $300 gain $12 in 8.months, what will $100 gain in 1 year?

15. If $100 gain $6 in 1 year, in what time will $300 gain $12?

16. If $100 gain $6 in 1 year, what principal will gain $12 in 8 months?

17. If a 2-penny loaf weighs 9oz. when wheat is 6s. 6d. per bushel, how much bread may be bought for 3s 2d. when wheat is worth 4s. 9d. per bushel? Ans. 14lb. 10oz.

18. A wall, which was to be built 32 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 9 days? Ans. 24.

19. If 6 bbl. of flour serve a family of 8 persons 12m., how many bbl. will serve a family of 12 persons 16 months?

20. If 16 horses eat 24 bushels of oats in 6 days, how many bushels will 23 horses eat in 20 days?

21. A garrison of 1600 men have bread enough to allow 24 ounces per day to each man for 25 days; but, the garrison being re-enforced by 400 men, how many ounces per day may each man have in order that they may hold out against the enemy 30 days?

22. If 3 compositors, in 2 days of 9 hours each, set type for 27 pages, each page consisting of 36 lines of 45 letters each, how may compositors will set 36 pages of 40 lines of 54 letters each, in 6 days of 8 hours each?