6206,43!

20. If 4 yd. of cloth cost $9.75, what will 13 yd. cost? 21. If of a yard of cloth costs of a dollar, what will 2 yards cost?

3

32

22. If of a ship costs £273 2s. 6d., what will of her cost?

23. If a post, 8 feet high, casts a shadow 12 feet in length, what must be the height of a tree that casts a shadow 122 feet in length, at the same time of day?

24. If a man performs a journey in 22 days, when the days are 12 hours long, how many days will it take him to perform the same journey, when the days are 15 hours long?

25. If 7 cwt. 1 qr. of sugar cost $64.96, what will be the cost of 4 cwt. 2 qr. ?

26. A merchant, failing in trade, pays 65 cents for every dollar which he owes; he owes A $2750, and B $1975: how much does he pay each ?

27. If a person drinks 20 bottles of wine per month, when it costs 2s. per bottle, how much must he drink without increasing the expense, when it costs 2s. 6d. per bottle?

28. If 6 sheep cost $15, and a lamb costs one-third as much as a sheep, what will 27 lambs cost?

29. If 4 gallons of molasses cost $25, how much is it per quart?

30. A man receives of his income, and finds it equal to $3724.16: how much is his whole income?

31. A cistern, containing 200 gallons, is filled by a pipe which discharges 3 gallons in 5 minutes; but the cistern has a leak, which empties at the rate of 1 gallon in 5 minutes: if the water begins to run in when the cistern is empty, how long will it run before filling the cistern?

32. If 9 men, in 18 days, will cut 150 acres of grass, how many men will cut the same in 27 days?

33. If a garrison of 536 men have provisions for 326 days, how long will those provisions last, if the garrison be increased to 1304 men?

34. If 4 barrels of flour cost $343, how much can be bought for $175 ?

35. If 2 gallons of molasses cost 65 cents, what will 31 hogsheads cost?

36. What is the cost of 6 bushels of coal, at the rate of £1 14s. 6d. a chaldron ?

37. What quantity of corn can I buy for 90 guineas, at the rate of 5 shillings a bushel ?

38. A merchant, failing in trade, owes $3500, and his effects are sold for $2100: how much does B receive, to whom he owes $420?

39. If 3 yards of broadcloth cost as much as 4 yards of cassimere, how much cassimere can be bought for 18 yards of broadcloth?

40. What length must be cut off from a board that is 9 inches wide, to make a square foot, that is, as much as is contained in 12 inches in length and 12 in breadth?

41. If 7 hats cost as much as 25 pair of gloves, worth 84 cents a pair, how many hats can be purchased for $216? 42. How many barrels of apples can be bought for $114.33, if 7 barrels cost $21.63?

43. If 27 pounds of butter will buy 15 pounds of sugar, how much butter will buy 36 pounds of sugar?

44. If 42 tons of coal cost $206.21, what will be the cost of 21 tons?

45. If a certain sum of money will buy 40 bushels of oats, at 45 cents a bushel, how many bushels of barley will the same money buy, at 72 cents a bushel?

46. If 40 gallons run into a cistern, holding 700 gallons, in an hour, and 15 run out, in what time will it be filled?

47. A piece of land of a certain length, and 12 rods in width, contains 1 acres: how much would there be in a piece of the same length, 263 rods wide?

48. If 13 men can be boarded 1 week for $39.585, what will it cost to board 3 men and 6 women the same time, the women being boarded at half price?

49. What will 75 bushels of wheat cost, if 4 bushels 3 pecks cost $10.687?

DOUBLE RULE OF THREE.

246. The DOUBLE RULE OF THREE is an application of the principles of Compound Proportion.

1. If a family of 6 persons expend $300 in 8 months, how much will serve a family of 15 persons for 20 months?

the elements of the remaining term in the 2d place: then find the value of x, as in Art. 243.

2. If 32 men build a wall 36 feet long, 8 feet high, and 4 feet thick, in 4 days, working 12 hours a day, how long a wall, that is 6 feet high and 3 feet thick, can 48 men build in 36 days, working 9 hours a day?

ANALYSIS.-In this example, each term of the proportion contains 3 elements, and the required element is the length of the second wall. Denote this element by a, and write it, and the other elements of the term, 6 and 3, in the 4th place, as in the statement below. Then, write the term whose elements have the same units, in the 3d place; the term mentioned in the question in connection with the third term, in the first place; and the remaining term in the second place: this will give,

246. What is the Double Rule of Three? Give the Rule.

When quantity and cost are considered, it will give,

quantity quantity :: cost cost.

Finding the required element (Art. 244), we have,

48 × 36 × 9 × 36 × 8 × 4

648 ft. in length.

Hence, we have the following

Rule.

Write the term which contains the required element in the fourth place; the term having like units, in the third place; the term mentioned in connection with the third term, in the first place; and the remaining term in the second place. Then find the value of the required element, as in Art. 244.

Examples.

1. If I pay $24 for the transportation of 96 barrels of flour 200 miles, what must I pay for the transportation of 480 barrels 75 miles?

2. If 12 ounces of wool be sufficient to make 1 yards of cloth 6 quarters wide, what number of pounds will be required to make 450 yards of flannel 4 quarters wide?

3. What will be the wages of 9 men for 11 days, if the wages of 6 men for 14 days be $84?

4. How long would 406 bushels of oats last 7 horses, if 154 bushels serve 14 horses 44 days?

5. If a man travels 217 miles in 7 days, traveling 6 hours a day, how far would he travel in 9 days, if he traveled 11 hours a day?

6. How long will it take 5 men to earn $11250, if 25 men can earn $6250 in 2 years?

7. If 15 weavers, by working 10 hours a day for 10 days, can make 250 yards of cloth, how many must work 9 hours a day for 15 days, to make 607 yards?

8. A regiment of 100 men drank 20 dollars' worth of wine, at 30 cents a bottle: how many men, having the same allowance, will require 12 dollars' worth, at 25 cents a bottle?

9. If a footman travels 341 miles in 7 days, traveling 12 hours each day, in how many days, traveling 10 hours a day, will he travel 155 miles ?

10. If 25 persons consume 300 bushels of corn in 1 year, how much will 139 persons consume in 8 months, at the same rate?

11. How much hay will 32 horses eat in 120 days, if 96 horses eat 3 tons in 7 weeks?

12. If $2.45 will pay for painting a surface 21 feet long and 13 feet wide, what length of surface that is 10% feet wide, can be painted for $31.72 ?

13. How many pounds of thread will it require to make 60 yards of 3 quarters wide, if 7 pounds make 14 yards 6 quarters wide?

14. If 500 copies of a book, containing 210 pages, require 12 reams of paper, how much paper will be required to print 1200 copies of a book of 280 pages ?

15. If the transportation of 9 T. 15 cwt. 20 lb. for 260 miles, costs $76.50, what will be the cost of transporting 25 T. 16 cwt. 3 qr. for 189 miles, at the same rate?

16. If a cistern, 17 feet long, 10 feet wide, and 13 feet deep, holds 546 barrels of water, how many barrels will a cistern 12 feet long, 10 feet wide, and 7 feet deep, contain?

17. A contractor agreed to build 24 miles of railroad in 8 months, and for this purpose, employed 150 men; at the end of 5 months, but 10 miles of the road were built: how many more men must be employed, to finish the road in the time agreed upon?

18. If 336 men, in 5 days of 10 hours each, can dig a trench of 5 degrees of hardness, 70 yards long, 3 wide, and 2 deep what length of trench of 6 degrees of hardness, 5 yards wide and 3 yards deep, may be dug by 240 men, in 9 days of 12 hours each ?