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37. Frank is 6 years 8 months old, and his mother is 4 times as old. How old is his mother?

38. If a livery-stable keeper feeds 10 bu. 3 pk. of corn in 6 days, how much does he feed per day?

39. If a can of fruit weighs 2 lb. 8 oz., what is the weight of 6 such cans? 7 cans? 8 cans? 10 cans?

40. If 16 bu. 3 pk. of apples are needed to fill 6 barrels, how many are needed to fill each barrel?

41. How much linseed-oil will a painter use in 8 days, if he uses 2 gal. 2 qt. 1 pt. each day? In 10 days?

42. If a steamboat runs 57 mi. 30 rd. in 5 hours, how far does it run in 1 hr.? If 73 mi. 70 rd. in 6 hr.?

43. At $.50 a pound, what is the cost of 3 packages of tea, each 2 lb. 8 oz.? 5 packages, each 3 lb. 12 oz.?

44. If 4 bu. 1 pk. 4 qt. of corn cost $3.50, what is the price per bushel? If it cost $3.85? If $4.20 ?

45. If one barrel holds 2 bu. 3 pk. of apples, how many barrels are needed to hold 22 bu.? To hold 243 bu.?

46. If a field of grass will average 1 T. 15 cwt. to the acre, how much can be cut from 14 acres?

47. If from a barrel of vinegar 4 gal. 3 qt. be drawn, and the remainder put in 8 cans, what will each contain?

48. If a man can walk 7 miles in 2 hours, how far can he walk in 5 days, walking 10 hours a day?

What is the result of 49. 6 times £5 10 s. 6 d.? 50. 7 times 4 qt. 1 pt. 3 gi.? 51. 8 times 8 bu. 3 pk. 2 qt.? 52. 9 times 10 T. 10 cwt. 20 lb.?

53. of 10 yd. 2 ft. 6 in.? 54. 1 of 12 lb. 2 oz. 8 pwt.? 55. of 20 gal. O qt. 1 pint?

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56.4 of 25 bu. 2 pk. 3 qt.?

57. If a row contains 6 squares, each 1 in. long and 1 in. wide, how many square inches are in 5 such rows?

58. How many sq. in. in a pane of glass 8 in. long, 6 in. wide? 59. How many square feet of carpet are needed to cover a hall 10 ft. 6 in. long, 4 ft. wide? How many sq. yd.? 60. At 3 cents a square foot, or foot board measure, what is the cost of a board 15 ft. long, 6 in. wide?

61. The surface of a table 6 feet long contains 30 square feet. What is the width of the table?

62. What is the length of a field 20 rd. wide, and containing 600 sq. rd.? Area is 480 sq. rd., width 15 rd.? 63. How long is a floor, covered by 24 yards of yard-wide carpet, the width being 12 feet?

Find the area of 64. Length 5 yd. by 4 yd. 6 in. 65. Length 74 ft. by 3 ft. 6 in. 66. Length 40 rd. by 5 rd. 3 yd.

Find the required dimension, 67. Area 42 sq.ft.,width 5 ft.3 in. 68. Area 63 sq.yd., width 63 ft. 69. Area 24 A., breadth 10 ch.

70. What is the solidity of a block of marble 8 feet long, 3 feet wide, and 2 feet thick?

71. What is the solidity of a piece of marble 10 ft. long, 4 ft. wide, 3 ft. thick? 11 ft. 3 in. by 6 ft. by 4 ft.?

72. Find the cubical contents of a cistern 12 ft. 3 in. long, 6 ft. deep, 4 ft. wide. 15 ft. 6 in. long, 8 ft. wide, 6 ft. deep. 73. The solidity of a pile of wood is 128 cu. ft., the length is 8 ft., and the width is 4 ft. How high is it?

74. A pile of stones contains 64 cu. ft., the length being 8 ft., and the height 2 ft. How wide is it?

75. How long is a bin whose capacity is 135 cu. ft., the depth being 4 ft. 6 in., and width 3 ft.?

Find the solidity of a solid whose dimensions are 76.8 ft. 6 in. by 6 ft. by 4 ft. 77. 10 yd. 2 ft. by 8 ft. by 3 ft. 78. 12 ft. 9 in. by 9 ft. by 2 ft.

Find the required dimension of a solid whose content is 79. 216 cu. ft.,8 ft. long, 6 ft.wide. 80. 339 cu. ft., 6 ft.wide, 6 ft. deep 81. 540 cu. ft., 9 ft.long, 8 ft. deep

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1. What is of $100? ? ? .25? .50? .75?

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2. How much is 13 of $100? 100 of $50? .08 of 25? 3. What part of 100 is 1? Of $100 is $1? Of $100 are $7 ? 4. 5 ft. are what part of 50 ft.? How many hundredths? 5. How many hundredths of $100 are $6? $7? $81? 6. 5 ft. are how many hundredths of 100 ft.? Of 200 ft.? 7. How many hundredths of any number equal the number? 8. How many hundredths of any number equal of it? 9. What part of 100 hundredths are 50 hundredths? 10. What part of a number are 50 hundredths of it? .07 of it?

Definitions.

307. Per Cent. is an abbreviation of the Latin per centum, and means by the hundred.

Thus, 6 per cent. means 6 of every hundred; 121 per cent. is 123 hundredths, or 121⁄2 of every 100; 25 per cent. is .25, or 25 of 100; etc. 308. Percentage is the process of computing by the hundred.

309. The Sign of per cent. is %. It is read per cent. 310. Since per cent. is a 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. Thus,

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Exercises.

1. Express or write in the form of decimals:

3%; 10%; 25%; 75%; 100%; 125%; 61%; 81%; 121%; 66%; 100%; 118%; %; %; %; .5%; .25%; .71%; .061%.

2. Express or write in the form of decimals and of fractions: 5%; 15%; 50%; 100%; 25%; 21%; 561%; 87%; 100%; 112%; 1331%; %; %; %; 1%; .5%; .75%; .07%; .16%.

3. Read and express as rate with the sign %:

.05; .15; .25; 1; .12); .163; .561; 1.25; 1.121; .011; .061; 1.04}; 1.371; .001; .003; 1.003; 1.007; 2.50; .005; .0021; 2.

4. What per cent. of a number is of it?

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311. Model. Since the whole of any number is 100%, or 188 of itself, of the number is of 100%, or 25%.

What % of a number is of it? ? ? ? ? ? ? ? ? ? ? ? ? .05? .06? .12? .25? 2 times the number?

25

5. What part of a number is 5% of it?

312. Model.—Since 5% is 15,5% of a number is 15, or, of it. What part of a number is 6% of it? 12%? 25%? 37%? 50%? 60%? 100%? 250%? %? %? .5%? .25%? .16%? 200% ?

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GENERAL CASES OF PERCENTAGE.

313. In the operations and applications of percentage, at least three terms or elements are considered:

The Base, the Rate, and the Percentage.

314. The Base is the number of which the per cent., or number of hundredths, is taken.

Thus, in the expression 5% of $125, the base is $125.

315. The Rate is the number of hundredths taken.

Thus, in the expression 5% of 75 yards, the rate is 5 hundredths. 316. The Percentage is the result obtained by taking any per cent. of the base.

Thus, in the expression 5% of 40 yards is 2 yards, the base is 40 yards, the rate % is .05, and the percentage is 2 yards.

317. The Amount is the sum of the base plus the percentage.

318. The Difference is the remainder of the base less the percentage.

319. Principles.

I. The percentage of any number is such part of that number as the given rate is of 100%.

II. The rate is such part of 100% as the percentage is of the base. III. The base is as many times the percentage as 100% is times the given rate.

Exercises.

1. Express in decimal form

The amount of 1 at 3%; 12%; 25%; 85%; 100%; 150%; 61%; 121%; 33%; 1371%; 11%; 1%; %; %; 100%; 1.5%; 100.5%. 2. Express in both fractional and decimal form

The difference of 1 at 5%; 15%; 52%; 90%; 83%; 371⁄2%; 303%; 66%; 871%; %; 1%; %; 1%; %%; .5%; .25%; .75%.

3. Express in both forms

The amount and the difference of 1 at 6%; 13%; 36%; 80%; 100%; 11%; 31%; 5%; 7%; 183 %; 301% %; 87%; %; %;%;.5% .25%.

1. To Find the Percentage, and the Amount or the Difference.

1. What is 5% of 80 feet?

320. Analysis. Since 5% is 180, 5% of 80 feet is 15, or of 80 feet, which is 4 feet. Hence, etc.

2. What is 6% of 50? Of 200? Of $250? Of 300 A.? 3. Find 8% of 60; 12% of 80 acres; 163% of 120 men.

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