57. What number increased by 5 times itself becomes 30? by 4 times itself, 20?

58. What number increased by of itself becomes 20? by of itself, 30?

59. What number diminished by of itself becomes 30? by of itself, 20?

60. A horse cost $60 and was sold at a gain of }. What was the selling price?

61. A horse cost $60 and was sold at a loss of 1. What was the selling price?

62. By selling a horse for $ 40, I lose. How much did he cost? 63. By selling a horse for $36, I gain. How much did he cost?

64. By selling a horse for $40, I gain 4. By how much must I increase my price to gain ?

65. If my gain was, or $40, what was the selling price? the cost?

66. If my loss was, or $20, what was the cost? the selling price?

67. If I buy at $3 and sell at $4, what part do I gain?

68. If I sell of an article for what the whole cost, what part of the whole do I gain?

69. An article was sold at a gain of; if it had cost $120 more, the same selling price would have entailed a loss of Find the cost.

70. A man sold an article for 40%, and thereby gained as much as if he had sold it for 60. What was the cost?

71. An agent sold flour for $200 at a commission of. What was the commission? the proceeds?

72. An agent bought flour for $200 at a commission of 6. What was the commission? the entire cost to his employer?

73. An agent sold flour at a commission of, and received as commission, $25. What were the proceeds?

PERCENTAGE

TERMS AND RELATIONS

In many cases, it has become customary to use the term per cent, written %, in place of hundredths.

The number on which the per cent is computed is the base; the product is the percentage; the base + the percentage, the amount; the base centage, the difference.

% means hundredths.

the per

188, difference

See p. 114.

6% means .06

A per cent expression may be changed to a fraction or an

9. State rapidly the per cent equivalents: 3, 3, 3, 4, 1, 1, 1, 1,

5 5

T2, 8, 8, 1, 3, 3, 3, 4, 16, 1. See p. 114.

10. State rapidly the fractional equivalents: 621%, 871%, 37%, 331%, 16%, 25%, 40%, 75%, 60%, 20%, 80%, 81%, 83%, 121%, 50%. See p. 114.

NOTE. A per cent expression must be reduced to a decimal or to a common fraction, before it can be used as a multiplier.

13. A farmer having 360 sheep, lost 5%. How many had he left?

360 no. sheep

.05

18.00

no. lost

342= = no. left

He lost .05 of 360 sheep, or 18 sheep; he had left the difference, or 342 sheep.

18% of 3825? 66% of 3483?

14. What is 16% of 5250? 15. A man wills 17% of his property to his son, and 18% to his daughter. If his property is worth $8200, how much will each receive?

16. A has $625; B has 86% as much as A; C, 78% as much as B. How much has C?

17. A lady buys 55 yards of muslin at 8¢ a yard, and 27 yards of cloth at 65 a yard. If she pays 66% of the bill, how much does she still owe?

18. A man's salary is $75 a month; if he spends 65% of his salary each month, how much will he have at the end of 6 months?

19. A gentleman gave $11.20 to his children; his sons received 65% of the money, and his four daughters the remainder. How much did each daughter receive?

20. A man has a library of 1600 volumes; 14% are biography; 62%, history, and 831% of the remainder, fiction. How many volumes of fiction are there in his library?

22. Of what number is 81,

163%?

1623% No. =81

1

6

No. =81÷ = 486

The sign of multiplication may be omitted.

Since either factor is equal to the product divided by the other factor, No. = 81, or 486.

NOTE. A per cent expression must be reduced to a decimal or to a common fraction, before it can be used as a divisor.

23. A farmer lost 18 sheep, or 5% of his flock. How many had he at first?

33. A general lost 16% of his army; 315 killed, 110 prisoners, and 70 deserters. How many men had he at first?

34. A man paid $750 for a house, which was 24% of what he paid for 160 A. of land. What was the cost of the land per acre?

35. Mr. Turner earns $85 a month; his salary for the year is 68% of his brother's salary for 8 months. How much does his

brother receive a month?

38. A farmer having 360 sheep, lost 18. What did he lose?

45. A man worth $250,000 lost $27,500. What % remained? 46. Mr. Brown works 6 days each week for 44 weeks of the year. What per cent of the time is he idle, counting 300 working days to the year?

47. The population of a certain town is 57,500; of these, 3450 are Irish; 22,540, Spanish; and the remainder, English. What per cent of the population is English?

48. A man having $1275, spent $210 for a carriage, $112 for a horse, and $86 for a harness. What per cent of his money remained?

49. A rectangular field 75 feet long, is as wide. The breadth is what per cent of the length?

50. The product of two numbers is 11,250; the first is 125. What per cent of the first is the second?

AMER. ARITH. - 13