52. A merchant sold 20 yards of broadcloth for $39.90, thereby losing .525 of what he had paid for it. At what price per yard had the merchant bought it?

53. A man bought 8294 pounds of coffee at 15 cents per pound, and made a partial payment thereon which was just .65 of what he still owed. What was the amount of his payment?

54. A grocer bought sugar and coffee amounting to $114.80, the cost of the sugar being .435 of the cost of the coffee. What did he pay for each?

55. A man's salary is $650 per annum, of which he pays $200 for board, $125 for clothes, and $97.50 for sundry other expenses. What decimal part of his salary does he save?

56. After making a payment of .475 of his debt, a man finds that he still owes $210. How much did he originally owe?

57. If $1025.10 is .268 of the value of a farm, what is the value of .426 of the same farm?

58. A man sold off 204 acres from his farm and has 221 acres remaining. What decimal part of his farm did he sell?

59. Divide 12.3 times 8.95 tons by 733.9 tons.

60. What is the value of ($8.062 + $750 + $35.08) — ($.0005 + $192.5$3.018) 92.65?

61. If a man has one hundred and eighty-five and seventeen tenthousandths acres; then buys sixty-eight and seventy-five thousandths acres; then sells ninety-five and forty-seven ten-thousandths acres; then buys forty-two and one hundred and thirty-two hundredthousandths acres; then buys one hundred and twelve and thirty-nine thousandths acres; then sells forty-eight and five hundredths acres; how much land has he remaining?

62. A grocer buys four bags of coffee which average 132.08 pounds per bag. If three of the bags weigh respectively 128.05, 131.75, and 134.15 pounds, what is the weight of the fourth bag?

63. A contractor employed 35 men at $1.50 per day, 48 men at $1.40 per day, 75 men at $1.30 per day, and 242 men at such a price per day as to make the average pay of all the men equal $1.29925 per day. What were the daily wages of the 242 men?

64. If .174 of a job of work can be done in 6.09 days, in what time can the whole of it be done?

65. A and B at first had farms of equal size, but after A added 75.003 acres to his farm and B sold 15.043 acres from his, it was found that together they had 360.12 acres. How many acres had each at first?

66. The distance between two towns is 382.0135 miles. If A and B start simultaneously one from each town and walk towards the other, A traveling at the rate of 3.75 miles per hour and 8.50 hours per day, and B at the rate of 4.15 miles per hour and 6 hours per day, how far apart will they be at the end of the sixth day?

67. A clerk was originally employed at a salary of $300 per year; but at the end of his first year's service had his salary increased .25 of what it was before, and at the end of his second year's service had his salary further increased .248 of what it was before. At what salary was he employed for the third year?

68. The difference between .71 and .532 of my money is $62.30. How much money have I?

69. The sum of .25 and .345 of the number of bushels of wheat in A's granary is 499.80 bushels. If he reserves 75 bushels for home consumption and sells the remainder at $1.18 per bushel cash, how much money should he receive?

70. A and B are partners, A investing $6715 in the partnership and B $9085. What decimal part of the total capital did each invest?

71. If, in the preceding example, the profits of the firm for the first year were $2500, which the two partners agreed to divide according to their respective shares of the total capital, what sum did each receive?

72. If, in example 70, the net loss of the firm for the first year had been $1200, which the two partners had agreed to apportion according to their respective investments, what would have been the share of the firm's capital still remaining to each partner?

73. A dealer's sales of carpeting and matting for a year were $264320, and the sales of matting were .1875 of the total sales. The cost of the carpeting was.75 of its sales, and the total expenses of the business were .15625 of the cost of the carpeting. What were the sales of the matting? Of the carpeting? What was the cost of the carpeting? What were the total expenses?

COUNTING-HOUSE PRACTICE.

[TO THE TEACHER.] For useful contractions employed by business men in obtaining arithmetical results, see Appendix A.

To find the cost when the price is an aliquot part of $1.

INDUCTIVE EXERCISE.

1. What part of a dollar are 25 cents? At 25 cents or $1 per pound, how many pounds of coffee can be bought for $1? If 4 pounds of coffee cost $1, that is, one-fourth as many dollars as there are pounds, what is the cost of 8 pounds of the same coffee? Of 16 pounds? Of 24 pounds? Of 20 pounds? Of 36 pounds? Of 37 pounds? Of 39 pounds? Of 42 pounds? And, generally, of any number of pounds?

2. What part of a dollar are 163 cents? If at 163 cents or $1 per dozen, 6 dozen eggs cost $1, that is, one-sixth as many dollars as there are dozens, what is the cost of 18 dozen of the same eggs? Of 24 dozen? Of 42 dozen? Of 54 dozen? [a] The cost in dollars is such a part of the number of units as the price per unit is of $1.

13. What is the total cost of 85 barrels of potatoes bought at $2.25 per barrel, 36 barrels of onions at $1.75 per barrel, 50 barrels of apples at $3.50 per barrel, and 350 bushels of turnips at 25 cents per bushel?

14. A owes B $500, and in part payment delivered 50 bushels of corn at 75 cents per bushel, 240 bushels of oats at 663 cents per bushel, and 124 bushels of wheat at $1.25 per bushel. How much does A still owe B?

15. A owed B $375.50, and became further indebted to him for 8760 pounds of Rio coffee bought at 12 cents per pound, 1224 pounds of Laguayra coffee at 163 cents per pound, and 300 pounds of Mocha coffee at 33 cents per pound. How much did A then owe B?

16. What is the amount of the following bill: 32 pounds of sugar at 6 cents per pound, 8 pounds of coffee at 20 cents per pound, 1 cheese, weighing 48 pounds, at 25 cents per pound, and 27 gallons of molasses at 663 cents per gallon?

17. If I buy 240 barrels of potatoes at $2.18 per barrel, 128 barrels at $2.37 per barrel, 56 barrels at $1.62 per barrel, and 112 barrels at $1.87 per barrel, what is the total cost?

18. What is the total cost of 75 bushels of corn at 83 cents per bushel, 192 bushels of oats at 564 cents per bushel, 272 bushels of rye at 81 cents per bushel, and 136 bushels of wheat at $1.35 per bushel?

To find the quantity when the price is an aliquot part of $1.

INDUCTIVE EXERCISE.

1. What part of $1 are 50 cents? At 50 cents or $1 per pound, how many pounds of tea can be bought for $1? If at 50 cents per pound, 2 pounds of tea can be bought for $1, that is, twice as many pounds as there are dollars, how many pounds can be bought for $2? For $5? For $7? For $9? For $12? And, generally, for any number of dollars?

2. What part of $1 are 123 cents? At 12 cents or $1 per pound, how many pounds of sugar can be bought for $1? Hence, how many pounds can be bought for $3? For $6? For $4? For $9? For $7? For $5?

[b] The number of units is as many times the units of cost in dollars, as $1 is times the price per unit.

29. How many bushels of corn can be bought for $537 at 75 cents per bushel?

30. How many pounds of coffee at 163 cents per pound should be given in exchange for 320 pounds of sugar at 10 cents per pound, and 140 gallons of molasses at 75 cents per gallon?

31. I bought 50 yards of cloth at $2.50 per yard, 182 yards at $3.25 per yard, and 153 yards at $1.33 per yard, and in payment agreed to deliver 500 yards of muslin at 12 cents per yard, 800 yards of jeans at 25 cents per yard, and the remainder in cottonades at 20 cents per yard. How many yards of cottonades should I deliver?

32. How many more gallons of molasses at 50 cents per gallon than at 75 cents per gallon can be bought for $60?

33. At 37 cents per yard, how many more yards of alpaca can be bought for $57 than for $45?

34. I bought $60 worth of sugar at 64 cents per pound, $35.50 worth of butter at 25 cents per pound, $12.50 worth of cheese at 163 cents per pound, and $12.80 worth of tea at 40 cents per pound. How many pounds of each did I buy?

35. How many gallons of vinegar can be bought for $52.50 at 621 cents per gallon?

To find the cost when the price of 100 or 1000 units is given.

INDUCTIVE EXERCISE.

1. If the price of boards be $3 per 100 feet, how would you find the price of one foot? By what simple process can the division of $3 by 100 be indicated? Employing this method, at $3 per 100 feet, what is the cost of 15 feet of boards? Of 25 feet? Of 18 feet? Of 30 feet? Of 32 feet?

2. How many times 100 feet are 800 feet? Hence, if the price of 100 feet of boards is $4, what is the cost of 8 times 100 feet, or 800 feet? Of 8 times 100 feet, or 850 feet? Of 6 times 100 feet, or 625 feet?

3. If you wish to know the cost of 125 feet of boards at $2 per 100 feet, and you prefer to multiply 125 by $2, the price of 100 feet, how much too great will be the product? By what process can you rectify this result and obtain the true product? Employing this method, at $2 per 100 feet, what is the cost of 115 feet of boards? Of 350 feet? Of 230 feet? Of 120 feet?

[c] Any product is as many times the true product, as the multiplier is times the true multiplier.