19. What is wheat per bushel, when 57 bushels cost £30 10. Ans. 10s. 81d.+39. 20. If 1 ounce of silver cost 72 cents, what will 3 pounds 5 ounces amount to?

21. When 1 pound of cinnamon will be the price of 135 pounds?

Ans. $29 52cts. costs 10 cents, what Ans. $13 50cts.

22. If 2 cwt. of cheese cost £7 12s. 6d., what must be paid for 15 tons 3 cwt.? Ans. £1155 3s. 9d.

23. Sold a quantity of brandy for £54 7s. 6d., at 4s. 10d. per gallon: how many gallons were there? Ans. 225gal. 24. What is the amount of board for one year, at 2 dollars and 50 cents per week? Ans. $130. 25. Sold a piece of land containing 34 acres 1 rood 17 perches, at 42 dollars 25 cents per acre: what am I to receive? Ans. $1451 55cts.+25. 26. If a pipe of wine, containing 131 gallons, cost £65 10s. what was it per gallon? Ans. 10s. 27. If 754 dollars pay for 1 tun of brandy, how much can I buy for 1754 dols.? Ans. 2T. 1hhd. 19gal. Oqt. 1pt. 28. If 7 yards of muslin cost 18s. 8d., what number of yds. can I buy for £36 16s. at the same rate? Ans. 276yd. 29. If 1 pound of sugar cost 91 cents, what will be the price of a hogshead weighing 5 cwt. 2 qrs. and 17 lbs.? Ans. $60 13cts. 5m.

30. When 114 cents is the price of a pound of tea, how much can I buy for 354 dols.? Ans. 310lb. 8oz. 6dr.+84. 31. If 100 skeins of silk cost £2 10s., how many skeins can be bought for £105 3s.? Ans. 4206 skeins.

32. If a piece of cloth, containing 39 yards, cost 350 dollars 22 cents, what is it per yard? Ans. $8 98cts. 4m.

33. If 1 pint of brandy cost 37 cents, what will be the price of 2 hogsheads, one containing 611 gallous, and the other 62 gallons 1 quart and 1 pint? Ans. $371 624cts. 34. A man sold two loads of corn, one containing 75 bushels and the other 87 bushels, at 52 cents per bushel: what will he receive? Ans. $84 24cts. 35. If a person spend daily 1 dollar 87 cents, and his annual income be 1022 dollars, what sum may he save at the year's end? Ans. $337 62 cts.

36. Bought a stove, weighing 4 cwt. 3 qrs. 24 lbs., at 2 dollars 10 cents per cwt., and 27 lbs. of pipe at 183 cents per pound, with two elbows at 50 cents each: what is the price of the stove, pipe, and elbows? Ans. $16 483cts.

37. A man covered 14 pair of window-shutters with tin, each shutter requiring 81 sheets, for which he was to have 11 cents per sheet: what will he receive when they are finished? Ans. $27 37cts.

38. A ship's crew, consisting of 45 men, are provided with 4500 lbs. of bread, of which each man eats 1 lb. per day: how many weeks will it last them? Ans. 14w. 2à. 39. If 12 acres 2 roods produce 443 bushels and 3 pecks of corn, what quantity will 37 acres 3 roods 5 perches produce? Ans. 1341bu. Op. 7qt. 1pt.

40. A merchant bought 27 cwt. 2 qrs. of sugar, for 204 dollars; paid for carriage 15 dollars 75 cents; storage 18 dollars 31 cents: what must he sell it for per hundred, to gain 57 dollars on the whole? Ans. $10 72cts. 9m.+60.

41. A bankrupt owes in all 18,234 dollars 40 cents, and delivers up his whole property, amounting to 9,142 dollars 20 cents: how much per cent. can he pay, and what does that creditor receive to whom he owed 472 dollars? Ans. 50 per cent.; $236.

INVERSE PROPORTION.

Note. In all cases wherein labour is required to be performed, the day must be reckoned at 12 hours.

42. If six men can do a piece of work in 18 days, how long will it require 12 men to do it? Ans. 9days. 43. Suppose 20 days be required for 12 men to build a house, in what time can 18 men do the same? Ans.13d. 4h. 44. If eight men can mow a piece of meadow in 24 days, how many men can do it in 4 days? Ans. 48men. 45. In what time will 48 men make a fence, which 12 men can do in 24 days? Ans. 6days.

46. If a traveller performs a journey in 5 days, when the days are 11 hours long, how long will he require to do it when they are 15 hours long? Ans. 3days 10h. 47. How many yards of carpeting, 2 feet 3 inches broad,

will it require to cover a floor that is 48 feet long and 30 feet 6 inches broad? Ans. 216yd. 2ft. 8in. 48. How many men will it require to repair a piece of work in 50 days, when 14 men can do it in 100 days? Ans. 28men.

Promiscuous Examples.

49. If 1 cwt. of sugar cost 11 dollars 37 cents, what will 18 cwt. 3 qrs. 19 lbs. cost? Ans. $215 21cts.+10. 50. Bought 156 yards of cloth for 730 dollars, a part of which being damaged, I am willing to lose 22 dollars on the whole at what rate then must I sell it per yard? Ans. 4 53cts. 8m.+72.

51. Bought 19 cwt. 2 qrs. 17 lbs. of tobacco at 9 dollars 31 cents, per cwt., and sold it for 10 dollars 65 cents per cwt.: what was the prime cost; what was it sold for; what was the gain? Cost $183 00cts. 7m. Sold for $209 29cts. 1m.+

Ans.

Gain

52. If 47 yards of muslin cost 14 what was it per yard?

26 28cts. 4m. dollars 75 cents, Ans. 31cts. 3m.

53. A number, consisting of 354 men, are to be clothed; each suit to contain 32 yards of cloth that is 14 yards wide, and to be lined with holland which is three quarters of a yard wide; how many yards of holland will line them? Ans. 2212 yd.

54. A pole whose height is known to be 25 feet, at 12 o'clock at noon casts a shadow on level ground to the distance of 33 feet 10 inches. What is the breadth of a river which runs east and west close by the north side of the bottom of a tower known to be 250 feet high, if the shadow of the tower projects 18 feet 6 inches beyond the opposite bank of the river? Ans. 319ft. 10in.

55. The earth which we inhabit is three hundred and sixty degrees in circumference, and turns round on its axis once in twenty-four hours; a degree of longitude at the equator is 69 miles, but a degree of longitude in the lat itude of 40 degrees is only 46 miles: how many miles are the inhabitants at the equator carried in one minute by this motion, and how much farther in a minute are they

carried by it than the inhabitants who live in latitude 40 degrees?

Ans. The inhabitants of the equator are carried 17M. 3fur., and 5M. fur. farther than in lat. 40°.

DOUBLE RULE OF THREE.

THE Double Rule of Three is that in which five terms are given to find the sixth; three of the given terms being a supposition, and two a demand.

Rule.

1. Set that term which is of the same name with that in which the answer is required in the third place.

2. Consider each pair of similar terms separately, and the third one, as the terms of a statement in the single rule of three, and set them in the first or second places, as directed in the rule for stating the single rule of three. 3. Multiply the two terms in the first place together. 4. Multiply the two terms in the second place together. 5. Multiply the product of the two terms of the second place by the term standing in the third place, and divide that product by the product of the two terms standing in the first place, for the answer in the same denomination with that of the third place.

Note.-If the terms consist of different denominations, they must be reduced as in the single rule.

Proof.-By two statements in the single rule of three, or by inverting the statement.

Questions.

What is the Double Rule of Three?

When you are about to make a statement in the Double Rule of Three, which of the terms is first to be set down, and in what place?

What is then to be considered?

What is to be done with the two terms which stand in the first place?

What is to be done with the two terms which stand in the second place?

By what do you multiply the product of the two terms standing in the second place; and by what do you divide that product for the answer?

What is to be noted when the terms consist of different denominations?

How do you prove the Double Rule of Three?

Examples.

1. If 10 men in 18 days earn 56 dollars, how many dollars can 20 men earn in 35 days?