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56. A man paid of his indebtedness the first year, of the remainder the second year, z of what then remained the third year, when he found that he still owed $1296. Find the amount he owed at first.
57. If a man can do a piece of work in 6 days by working 9 hours a day, how long will it take him to do it, working 8 hours a day?
58. Mr. Williams has of his money in government bonds, in the bank, and $520'in cash. How much is he worth?
59. A real estate agent bought 2 houses; his income from the one was $480, which was of the income from the other. How much was his income from both houses ?
60. Four brothers agreed to pay the mortgage on their father's farm. The first payment made was of the mortgage, the second 1 of the remainder, and the third } as much as the first and second. If the difference between the first and third payments was $ 300, how much was the mortgage ?
61. A merchant bought 250 barrels flour at $4.80 per barrel. He sold 10 barrels which were damaged for of the cost. On the sale of 150 barrels he gained 15 cents per barrel. If his total gain was $28.50, at what price did he sell the remaining number of barrels ?
62. A merchant buys 36 pairs men's shoes, at $21 per pair; 24 pairs women's shoes, at $ 1% per pair; and 30 pairs slippers, at $3 per pair. What is the amount of his bill?
63. If the men's shoes in example 62 are sold for $3 per pair, the women's shoes for $24 per pair, and the slippers for $11 per pair, how much does the merchant make ?
64. A cubic foot of water weighs 621 pounds. A barrel contains about 41 cubic feet. Find the weight of a barrel of water.
65. A student, in a half year at college, spent his money as follows: tuition, $50; books, $ 93 ; 18 weeks' boarding, at $2% per week; incidental expenses, $41. What were his expenses for the half year?
66. of a barrel of oil, containing 51 gallons, was sold at 13 cents per gallon; the remainder of the barrel at 14 cents a gallon. If the oil cost 117 cents per gallon, what was the gain ?
67. A merchant bought a stock of goods for $6000. He sold 1 of it at a gain of of the cost, į of it at a gain of 1 of the cost, and the remainder at a loss of } of the cost. How much did he gain or lose ?
68. A hall is 21 feet long and 101 feet wide. At 81 cents per foot, how much will it cost to put a molding around this hall ?
69. Find the perimeters of each of five rooms, the dimensions being as follows : 22} ft. x 16 ft., 142 ft. x 154 ft., 12 ft. x 17 ft., 184 ft. x 15} ft., 301 ft. x 24 ft.
70. From a certain number 187 + 27% was subtracted, leaving a remainder of 93. What was the number?
71. From New York to Chicago by the Baltimore and Ohio railroad the distance is 1052 miles. From Chicago to El Paso by the Santa Fé railroad it is 1630 miles, and from El Paso to Mexico City by the Mexican Central railroad it is 1224 miles. What is the distance from New York to Mexico City, and how long would such a journey take, traveling 313 miles per hour ?
72. A freight train runs from Kansas City to St. Louis, 288 miles, traveling 16 miles per hour. How long does it take it to make the trip? How long would it take a passenger train, running as fast, to make the same trip?
PROBLEMS FOR ANALYSIS
Pupils should be taught :
(1) To express themselves accurately and rapidly; (2) to do this work without the aid of pencil and paper ; (3) to give clear analytic statements in the solution of a problem.
1. The coal for the school buildings in a certain town cost $94.50. How many tons were purchased at $3 per ton ?
2. A shoe dealer buys shoes at $21 per dozen pairs and retails them at $2.50 a pair. How much does he gain on each pair ?
3. A laborer earns $18 in 12 days. At that rate how much can he earn in 80 days ?
4. What is of of 24 ?
5. A lady buys 10 yards of ribbon and uses 6 yards. What part of the ribbon has she left ?
6. If eggs are bought at the rate of 4 dozen for $1.08 and sold at 30 cents per dozen, what will be the gain on 3 dozen ?
7. A man buys a farm of 102 acres and divides it into lots of 6 to the acre. How many lots are there if i of the farm is laid out in streets ?
8. How many sheep, at $5 per head, may be purchased with the money from the sale of 10 head of cattle at $42 per head ?
9. A contractor buys 8000 bricks at $12.50 per thousand. Find the amount of his bill.
10. If I pay 6 cents for the use of $1 for one year, how much should I pay for the use of $150 for 2 years?
11. If I buy goods at $1.37 per yard and sell them at $1.50 per yard, how much do I gain on 12 yards ?
12. A boy earns 75 cents per day and pays of his wages for board. At that rate how much can he save in 26 days?
13. My father pays $ 252 per year rent. How much is that per month ?
14. A lady purchased 2 handkerchiefs at 35 cents each; 6 yards of ribbon at 12 cents per yard; 6 yards of cloth at $1.12 per yard. How much change should she receive from a ten-dollar bill ?
15. A man buys a farm for $2000 and pays of the cost, giving his note for the balance. For how much does he give his note ?
16. A farmer buys fertilizer at $28 per ton and retails it at $1.90 a hundred pounds. How much does he gain on 35 tons ?
17. At 16 cents per pound, how many pounds of steak does a woman get if the amount of the purchase is 83 cents ?
18. A huckster bought 61 pounds of butter at 16 cents per pound, and 64 dozen eggs at 18 cents pér dozen. How much did he pay for both ?
19. A huckster buys chickens at 81 cents per pound and sells them at 121 cents per pound. How many pounds must he purchase and sell in order to gain $25 ? SOLUTION. -- On each pound he gains 41 cents.
To gain $1 he must sell 24 pounds.
. pounds. 20. A street car conductor earns 231 cents per hour. How much does he earn in 10 hours ?
21. If the conductor averages 10 hours per day, how much will he earn in 30 days?
22. If a box of 40 dozen oranges is purchased for $5 and retailed at 40 cents a dozen, what is the entire gain ?
23. What fraction of a gallon is a pint ? a gill ? a quart ?
24. A man sold of his farm for $1800. At the same rate, how much would he receive for the whole farm ? SOLUTION. — of the amount received for the farm = $1800.
of the amount received for the farm = 1 of $1800, or
$ 900. š, or the amount received for the farm = 3 times $900,
25. In a certain school there are 40 pupils in the grammar grade, which are of the number in the intermediate grade. How many pupils are there in both grades?
26. A man sold a piano for $360, which was 4 of what it cost him. How much did it cost him ?
27. There are 112 cubic feet in of a cord of wood. How many cubic feet are there in 1 cord ?
28. A farmer sold of his farm for $1521. At that rate, what was the value of of the farm ?
29. There are 198 cubic inches in of a gallon. How many cubic inches are there in 2 gallons ?
30. If 4 of a ton of hay costs $16, how much will 21 tons
31. A lady paid 84 cents for of a yard of silk. At the same rate, how much would she pay for 1 yard ?
32. If şof an acre produces 160 bushels of potatoes, how many bushels will an acre produce ?
33. A man saves $220, which is of his yearly salary. What is his yearly salary?