46. If a man have an annual income of $1000, how much may he spend in a day to save $350 ? Ans. $1.78+

47. How many dollars, 4s. 6d. each, in £90? Ans. $400. 48. Bought 4 pieces of linen, 231, 231, 241, and 25 yds., at 421 cts. per yd.; how much money will pay the bill?

Ans. $40.90.6 +

49. When pork is $11.50 per barrel, how many barrels may be bought for $138 ? Ans. 12 barrels. 50. If 20 lbs. of flour make 6 loaves of bread, how many loaves can be made from 5 barrels of flour?

Ans. 294 loaves. 51. If, when wheat is 100 cts. per bushel, the shilling loaf of bread weighs 3 lbs. 2 oz., what ought it to weigh when wheat is 125 cents per bushel? Ans. 2 lbs. 8 oz.

52. If a man's wages be $375 a year, how much ought he to receive for 73 days?

Ans. $75. 53. How much stuff, of a yard wide, will line 12 yds. of cloth a yard wide? Ans. 16 yds. 2 qrs. 23 na. 54. Imported 12 pipes of wine; whole amount of the invoice $1560; paid freight, etc. $225: how must I sell this wine per gallon to gain $325 on the whole ? Ans. $1.39.5 +

55. Find the value in Federal money of 12 pieces of each of the gold coin mentioned in the table, taking the rates in the column. $1450.08.

56. Find the value in Federal money of 12 pieces of each of the silver coin mentioned in the table, taking the rates in the column. Ans. $119.35}.

57. How much for 264 acres of land at $12 per acre? at $9? at $93? at $7? at $73 ? at $85? at $87? at $10.62? at $10.84? at $12.65? at $14.73?

58. How much for 362 barrels of flour at $4 per barrel? at $41? at $41? at $43? at $41? at $4;? at $42? at $47?

59. A bankrupt compounds with his creditors at 75 cents on the dollar; how much for A., to whom he owes $1236? B., to whom he owes $1350.50? C., to whom he owes $2346.25? Ans. A. $927; B. $1012.87+; C. $1759.6960. A man owes $3264; his property is worth $2448: how much is he able to pay on a dollar? Ans. 75 cts.

61. Bought 4 bales of cloth, each bale 10 pieces, and each piece 16 yds.; what is the cost of the whole at $9 for 4 yds. ? Ans. $1485.

62. If 4 horses eat 48 qts. of oats in one day, how much will be sufficient for 20 horses for a week? Ans. 52 bush. 2 pks.

63. What length of board 8 in. wide will make 12 sq. feet? 64. If 2 cwt. 2 qrs. 14 lbs. of rice cost $10.25, what will 23 cwt. 2 qrs. 14 lbs. cost? Ans. $92.25. 65. If a man go 5 feet in 3 steps, how many steps will he take in going a mile? Ans. 3168 steps. 66. If 144 men require 280 lbs. of pork in a week, how many barrels will be sufficient for 720 men for the same length of time? Ans. 7 barrels.

67. If the clothing, etc. of a. regiment of soldiers, consisting of 750 men, cost $9000, what will it cost to furnish, after the same manner, 6 regiments of 1000 men each?

Ans. $72000.

68. If it require 7860 stones, 21 ft. in length, to build a certain wall, how many stones 2 ft. long, will it require to make a wall of the same dimensions? Ans. 9825 stones.

69. If it take 3 yds. of stuff, of a certain breadth, to line 23 yds. of another breadth, what quantity of the latter will be sufficient to line 24 yds. of the former? Ans. 19 yds.

70. At $10.50 for 4 weeks' board, how long may I board for £54 12s. New York cur.? Ans. 1 year.

71. If a field of 10 acres be sufficient to pasture 20 head of cattle through the summer, how many acres will be sufficient for 35 cattle for the same time? Ans. 17 A. 2 R.

72. If, by a pipe, 60 gallons run into a cistern of 1500 gallons in 20 minutes, and there be a leak that lets out 5 gallons in the same time; in what time will the cistern be filled?

Ans. 9 h. 5 min. 273 sec.

73. At $3.75 for 2 yds. of cloth, how much for 1225 yds.? 74. At $25.50 for 4.25 acres, how much for 38.25 acres? for 76.5 acres? for 153 acres?

Ans. $229.50; $459; $918. 75. At 12 cents for a conveyance for 6.5 miles, how much for 208 miles?

Ans. $4.

76. If for $5 I can have 2.5 tons conveyed 24.75 miles, how far may I have 22.5 tons conveyed for the same money? Ans. 222 mi. 6 fur.

77. At $1.10 per ounce for silver, how much for 5 pieces, each weighing 4 lbs. 10 oz. 16 dwts.? Ans. $323.40.

78. If 9 shillings make $2, how many dollars in £244 12s. 10 d.? Ans. $1087.30. 79. At 4s. 8d. Sterling per doz., how much, in Federal mey, for 7626 case-knives? Ans. $664.92.1 +

80. How much for 200 boards, 12 feet long and 1 foot wide, at $3.25 per 100 feet? Ans. $78. 81. How much for 350 boards, 12 feet long and 10 inches wide, at $2.87 per 100 feet? Ans. $100.621. 82. How much for 20 hewn logs, each 20 feet long, 2 feet wide, and 1 foot thick, at $7.50 per ton?

Ans. $180.

DOUBLE PROPORTION,

OR

THE DOUBLE RULE OF THREE.

DOUBLE PROPORTION, or The Double Rule of Three, teaches to resolve questions by one statement, which, by Single Proportion, or The Single Rule of Three, would require more than

one statement.

I. Rule for placing the terms.

1. Place that term in the third place which is like the answer; then place two terms of the same kind in the first and second places, as in Single Proportion.

2. Place the other two terms under the first and second terms, as in the first example.

II. Rule for working the question.

1.-Reduce compound terms to the lowest denomination, and similar terms to like denominations, before you make the statement.

2.-Multiply the terms in the first place for a divisor, and those in the second and third places for a dividend; the quotient thence arising will be the answer.

Sometimes it will be best for the scholar to find the answer to the question by two statements in Single Proportion; he will get a clearer understanding by that method.

PROOF.-Reverse the statement, make the answer and the two last terms the terms of supposition. (Compare Examples 1 and 2.)

What is Double Proportion? What is the rule for placing the terms1st? 2d? What is the rule for working the question-1st? 2d? By what other method may Double Proportion be worked? Proof?

EXAMPLES.

1. If 6 men can reap 48 acres of grain in 7 days, how many acres can 12 men reap in 15 days?

Ans. 192 acres.

2. If 12 men in 15 days can reap 192 acres of grain, how much can 6 men reap in 7 days?

Men 12: 6

Ans. 48 acres.

:: 192 Hf. days 30 15 Š

3. If $200 yield $36 interest in 3 years, how much will $500 yield in 5 years ?

Ans. $150.

4. If $200 yield $24 interest in 2 years, what sum will yield $150 in 5 years?

Ans. $500. 5. If I can have the use of $100 for two years for $12, how long ought I to have the use of $700 for $252 ?

Ans. 6 years.

6. If 2 men's wages for a year amount to $250, how much will be the wages of 6 men for 2 years?

By analysis 250 = $125 ... 125 × 6 × 21 Ans. $1875.

7. If 20 horses eat 40 bushels of oats in 8 days, how many bushels will be sufficient for 30 horses for 16 days?

Ans. 120 bush.

8. If 20 lbs. of bread be sufficient for 5 men for 4 days, howe much will 40 men require for 2 weeks?

Ans. 560 lbs.

Ans. $5200.

9. If 6 men can earn $240 in 4 weeks, how much can 10 men earn in a year? 10. If $30 be the wages of 12 men for 21 days, how much will pay 16 men for 7.5 days' work?

11. If 7 yds. of cloth,

for 15 yds. 11 yd. wide?

Ans. $120. of a yard wide, cost $15, how much Ans. $60.

12. If 6 taps will empty a cistern of 300 gallons in 30 min., how many taps of the same size will empty a cistern of 600 gallons in 45 min. ? Ans. 8 taps.

13. If 4 men can build 480 feet of wall in 6 days, how many men will it require to build 1440 feet of wall in 9 days?

Ans. 8 men.

A TABLE OF ALIQUOT, OR EVEN PARTS.

103

14. If 20 men în 5 days require 80 lbs. of beef, how much wil be sufficient for 10 men for the three winter months?

Ans. 720 lbs.

15. If a man travel 160 miles in 4 days, when the days are 12 hours long, how far will he travel in 6 days, when the days are 16 hours long? Ans. 320 miles. 16. If 3 barrels of flour will last 8 persons 5 months, for how many men will 24 barrels be sufficient for 11 months? Ans. 32 men.

17. If the expenses of a family of 6 persons for 3 months be $225, what will be the expenses of a family of 9 persons for a year at that rate? Ans. $1350. 18. If 22.5 yds. of stuff, 6 qrs. of a yard wide, will make 6 suits of clothes, how many yards of stuff, one yard wide, will it require to make 25 suits? Ans. 140 yds. 2 qrs. 2 na.

19. If 6 men can build 350 feet of wall in 18 days, in what time can 10 men build 1750 feet? Ans. 54 days.

20. If 20 boards, 12 feet long, will cover a space 16 feet long and 15 feet wide, how many boards, 10 feet long and of the same width, will it require to cover a space of 36 feet in length and 20 feet in width? Ans. 72 boards.