33. How many bushels will a bin contain that is 7 feet square, and 6 ft. 8 in. deep? Ans. 301.339+bu. 34. How much must be paid for lathing and plastering overhead a room 36 feet long and 20 feet wide, at 26 cents a square yard?

35. How many shingles will it take to cover the roof of a building 46 feet long, each of the two sides of the roof being 20 feet wide, allowing each shingle to be 4 inches wide, and to lie 5 inches to the weather? Ans. 13248.

36. John Young was born at a quarter before 4 o'clock, A. M., Sept. 4, 1836; what will be his age at half past 6 o'clock, P. M., April 20, 1864? Ans. 27 yr. 7 mo. 16 da. 14 h. 45 min. 37. How many cubic yards of earth were removed in digging a cellar 28 ft. 9' long, 22 ft. 8' wide, and 7 ft. 6' deep? Ans. 181 cu. yd.

38. What will 30 bu. 54 lb. of wheat cost, at $1.37 per bushel? Ans. $42.4875.

39. How many square yards of carpeting will it take to cover a floor 24 ft. 8' long and 18 ft. 6' wide? Ans. 5019. 40. What is the cost of 54 bu. 8 lb. of barley, at 84 cents per bushel? Ans. $45.50. 41. What is the depth of a lot that has 120 feet front, and contains 18720 square feet?

42. How many steps of 30 inches each must a person take in walking 21 miles?

43. How long will it require one of the heavenly bodies to move through a quadrant, if it move at the rate of 3′ 12′′ per minute? Ans. 1 da. 4 h. 7 min. 30 sec. 44. How many times will a wheel, 9 ft. 2 in. in circumference, turn round in going 65 miles?

45. If a man buy 10 bushels of chestnuts, at $5.00 per bushel, dry measure, and sell the same at 22 cents per quart, liquid measure, how much is his gain? Ans. $31.92.

46. What will it cost to build a wall 240 feet long, 6 feet high, and 3 feet thick, at $3.25 per 1000 bricks, each brick being 8 inches long, 4 inches wide, and 2 inches thick?

Ans. $379.08.

PERCENTAGE.

231. Per cent. is a term derived from the Latin words per centum, and signifies by the hundred, or hundredths, that is, a certain number of parts of each one hundred parts, of whatever denomination. Thus, by 5 per cent. is meant 5 cents of every 100 cents, $5 of every $100, 5 bushels of every 100 bushels, &c. Therefore, 5 per cent. equals 5 hundredths.05 = 180: = 20 8 per cent. equals 8 hundredths: =.08 = 180 = 25. 232. Percentage is such a part of a number as is indicated by the per cent.

233. The Base of percentage is the number on which the percentage is computed.

234. Since per cent. is any number of hundredths, it is usually expressed in the form of a decimal; but it may be expressed either as a decimal or a common fraction, as in the following

What is meant by per cent.? From what is the term derived? What is percentage? What is the base of percentage? How is per cent. expressed?

EXAMPLES FOR PRACTICE.

1. Express decimally 3 per cent.; 6 per cent.; 9 per cent.; 14 per cent.; 24 per cent.; 40 per cent.; 1124 per cent.; 150 per cent.

2. Express decimally 64 per cent. ; 8 per cent.; 33 per cent.; 7 per cent.; 10 per cent.; 95 per cent.; 1031 per cent.; 225 per cent. 3. Express decimally per cent.; per cent.; per cent.; per cent.; per cent.; 14 per cent. ; 24 per cent.; 43 per cent.; 5 per cent.; 7 per cent.; 12 per cent.; 25% per

cent.

4. Express in the form of common fractions, in their lowest terms, 6 per cent. ; 8 per cent.; 12 per cent.; 14 per cent.; 183 per cent.; 21 per cent.; 31 per cent.; 37 per cent.; 40 per cent.; 112 per cent.; 225 per cent.

CASE I.

235. To find the percentage of any number.

1. A man, having $125, lost 4 per cent. of it; how many dollars did he lose?

RULE. Multiply the given number or quantity by the rate per cent. expressed decimally, and point off as in decimals. Or Take such a part of the given number as the number expressing the rate is part of 100.

EXAMPLES FOR PRACTICE.

2. What is 6 per cent. of $320 ?
3. What is 8 per cent. of $327.25 ?

Ans. $19.20.

Ans. $26.18.

Case I is what? Give explanation. Rule.

Ans. $4.11.

4. What is 7 per cent. of $56.75?
5. What is 12 per cent. of 2450 pounds?

Ans. 306.25 pounds.

6. What is 63 per cent. of 19072 bushels?

Ans. 1287.36 bushels.

7. What is 334 per cent. of/846 gallons?

Ans. 282 gallons.

8. What is 9 per cent. of 275 miles? 9. What is 14 per cent. of 450 sheep? 10. What is 50 per cent. of 1240 men? 11. What is 105 per cent. of $5760? 12. What is 175 per cent. of $12967? 13. What is 25 per cent. of ?

Ans. 26.95 miles.

Ans. $6048.

25 per cent. equals 25, and X, Ans.

100

20. A farmer, having 760 sheep, kept 25 per cent. of them, and sold the remainder; how many did he sell?

573

21. A man has a capital of $24500; he invests 18 per cent. of it in bank stock, 30 per cent. of it in railroad stocks, and the remainder in bonds and mortgages; how much does he invest in bonds and mortgages? Ans. $12740.

22. A speculator bought 1576 barrels of apples, and upon opening them he found 12 per cent. of them spoiled; how many barrels did he lose?

23. Two men engaged in trade, each with $2760. One of them gained 33 per cent. of his capital, and the other gained 75 per cent.; how much more did the one gain than the other? Ans. $1150.

24. A man, owning of an iron foundery, sold 35 per cent. of his share; what part of the whole did he sell, and what part did he still own? Ans. He still owned

25. A owed B $575.40; he paid at one time 40 per cent of the debt; afterward he paid 25 per cent. of the remainder ; and at another time 123 per cent. of what he owed after the second payment; how much of the debt did he still owe? Ans. $226.563.

CASE II.

236. To find what per cent. one number is of another.

1. A man, having $125, lost $5; what per cent. of his money did he lose?

RULE. Divide the percentage by the base, and the quotient will be the rate per cent. expressed decimally. Or,

Take such a part of 100 as the percentage is part of the base.

EXAMPLES FOR PRACTICE.

2. What per cent. of $450 is $90?
3. What per cent. of $1400 is $175?

4. What per cent. of $750 is $165?
5. What per cent. of $240 is $13.20?

6. What per cent. of $2 is 15 cents?

Ans. 20.

Ans. 12.

Ans. 51.

7. What per cent. of 6 bushels 1 peck is 4 bushels pecks

6 quarts?

Ans. 75 per cent. 8. What per cent. of 15 pounds is 5 pounds 10 ounces avoirdupois weight? Ans. 37 per cent. 9. What per cent. of 250 head of cattle is 40 head?

Case II is what? Give explanation. Rule.