19. The interest of 160 dollars, at 7 per cent., was $1,12; what was the time? Ans. 36 days.

20. In what time will any sum double itself at 6 per cent.? At any per cent.?

Ans. At 6 per cent., in 16 years; at any per cent., divide 100 by the per cent.

21. If 2 yards of cloth, 13 wide, cost 3 dollars 37 cents, how much will 36 yards cost, 1

yards wide? Ans. $52,79.

22. If 4 men spend of of of 14 of £30, in 71 of of 29 of 4 of 9 days, how many dollars, at 6 shillings each, will 21 men spend in 2 of 1 of of of 45 days? Ans. $630.

4 12

23. I lend a friend 200 dollars for 6 months; how long ought he to lend me 1000 dollars, to requite the favor-allowing 30 days to a month? Ans. 36 days.

24. If 1000 men, besieged in a town, with provisions for 5 weeks, allowing each man 16 ounces per day, be reinforced with 500 men more-and supposing that they cannot be relieved until the end of eight weeks-how many ounces a day must each man have, that the provisions may last them that time? Ans. 6 ounces.

25. If a foot-man, in 12 days, traveling 6 hours a day, perform a journey of 240 miles, in how many days will he perform one of 720 miles, if he travel 8 hours a day? Ans. 27 days.

26. If 20 men, in 12 days, working 5 hours a day, can perform a piece of work, how many hours a day must 15 men work, in order to perform 31 times as much work in 30 days? Ans. 83 hours.

27. In what time will $627,50, loaned at 7 per cent., produce as much interest as $2510, at 31 per cent., will produce in 1 year and 8 months? Ans. 3 years.

28. If a block of marble 2 feet 6 inches long, 1 foot 9 inches broad, and 1 foot 3 inches thick, weigh 9 hundred weight 2 quarters, what would it weigh, if each of its dimensions were doubled? Ans. 3 tons, 16 cwt.

29. Eight workmen, laboring 7 hours a day for 15 days, were able to execute of a job on which they were engaged; in how many days can they complete the res

idue, by working 9 hours a day, if 4 workmen are added to their number? Ans. 155 days.

30. How many men will reap 417,6 acres in 12 days, if 5 men reap 52,2 acres in 6 days? Ans. 20 men.

31. If a cellar 22,5 feet long, 17,3 feet wide, and 10,25 feet deep, be dug in 2,5 days, by 6 men, working 12,3 hours a day, how many days, of 8,2 hours, should 9 men take to dig another, measuring 45 feet long, 34,6 wide, and 12,3 deep? Ans. 12 days.

32. If 54 men, in 24 days, working 12 hours each day, can build a fort, in how many days will 75 men do the same, when they work but 10 hours each day? Ans. 21 days.

33. If 24 men, in 189 days, working 14 hours each day, dig a trench 33 yards long, 31 deep, and 5 wide, how many hours per day must 217 men work, to dig a trench 231 yards long, 21 deep, and 3 wide, in 5 days? Ans. 16 hours.

34. If a cistern, 16 feet long, 7 broad, and 15 deep, cost 36 dollars 72 cents, how much, in proportion, would another cistern cost, that is 17 feet long, 10 broad, and 16 deep? Ans. $64,26.

35. If a cistern 17 feet long, 10 broad, and 13 deep, hold 546 barrels, how many barrels will that cistern hold, that is 16 feet long, 7 broad, and 15 deep?

Ans. 384 bbls.

(ART. 85.) With the exception of square and cube root, and a few obvious principles in mensuration, we have now explained every arithmetical operation. The four ground rules, with reduction, and proportion, include all the principles that can be used in Practice, Interest, Barter, Loss and Gain, Exchange, &c. &c.; hence when we come to these subjects, we have no new principles to explain. It only remains to give clear definitions under each head, and teach how to apply the knowledge we are supposed already to possess; and now all the judgment and tact of the pupil will be called into full

exercise.

PRACTICE.

(ART. 86.) Practice is literally what the term implies: short and expeditious methods, practiced by merchants and business men, to find the amount of bills, and the aggregate cost of articles bought or sold. The principle involved in all such calculations, is proportion; but the price of the unit is generally given, which renders a formal statement unnecessary; and the computations are usually made by taking the number of times, and the aliquot parts of the unit.

(ART. 87.) The principles of computation being supposed to be well fixed in the mind, any formal rule that would, in any degree, restrain the free exercise of judgment, in the almost endless variety of cases, would prove an injury rather than an aid; therefore we shall explain only by examples.

Example 1. What will 64 bushels of oats cost, at 25 cents per bushel ? Ans. as many dollars as bushels, 16 dollars.

2. What will 47 bushels of wheat come to, at 871⁄2 cents?

3. What will 78 gallons of wine cost, at 1 dollar 621

4. What will 1 bushel 3 pecks 6 quarts of beans cost, at 1 dollar 12 cents per bushel? This is 2 quarts less than 2 bushels: hence, 2 bushels cost.

of 1,121, less, or 7 cents, nearly,

$2,25

7

Ans. $2,18

5. What will 75 bushels cost, at 33 cents a bushel?

3)75

25 dollars, Ans.

6. What will 224 barrels of flour come to, at 3 dollars

7. What will 462 yards of cloth cost, at $1,121 per yard?

Ans. $519,75.

8. What will 185 yards of cloth cost, at $1,20 per yard?

Ans. $222.

cost, at $1,311 per Ans. $196,871⁄2.

9. What will 150 yards of cloth yard? 10. What is the cost of 144 pounds of rice, at 31⁄21⁄2 pence This had better be done by canceling; 31=1.

a pound?

11. What will 45 barrels of flour come to, at 6 dol

lars 25 cents a barrel?

Ans. $284,371.

12. What will 18 cords of wood cost, at 4 dollars 75 cents a cord? Ans. $87,874. 13. What will 3 tons of coal cost, at 4 dollars 25 cents per ton? Ans. $15,933. 14. What will 2 hundred weight 2 quarters 14 pounds of sugar come to, at $8,50 per hundred weight? Ans. $22,311. 15. What will 3 bushels 3 pecks 6 quarts of beans cost, at $1,60 per bushel? [Find what 4 bushels cost.] Ans. $6,30.

(ART. 88.) In some States, particularly in New England and New York, the prices of articles are still given in shillings and pence; yet they never render a bill in pounds, shillings and pence, but always change it to dollars and cents. In New England, as there are 6 shillings to a dollar, 6 yards or 6 pounds will cost as many dollars as there are shillings and parts of a shilling to one yard, pound, &c.

Example 1. At 5 shillings 6 pence per yard, what will 6 yards cost, in dollars and cents? Ans. $5,50.

N. B. The 5 shillings are called 5 dollars, and 6 pence are called 50 cents.

Example 2. At 7 shillings 3 pence, New Egland currency, per yard, what will 18 yards of cloth cost?

Example 3. What will 15 bushels of wheat cost, at 5 shillings 9 pence (N. E.) per bushel ?

In New York currency, 8 yards, &c., cost as many dollars and parts of a dollar, as one yard, pound, &c. costs shillings and parts of a shilling.

N