SOLUTIONS AND PRACTICE PROBLEMS 301. You are now ready to make some further applications of what you have learned about numbers to the solution of practical problems. (See Art. 144.) In making solutions you should endeavor to secure facility and accuracy. You also need to understand clearly each step of the operation. 302. In written solutions the work should be arranged in a neat and orderly manner, so as to suggest the reasons for the various steps. Diagrams are often helpful and suggestive. When practicable, shorten the work by cancellation. To avoid mistakes, always test your results. 303. 1. The area of a rectangle is 120 sq. in., and the width is 10 in. What is the length? GIVEN the width and area. We also know that the area is the product of the numbers measuring the length and width. TO FIND: the length. If the product and one factor are given, how is the other factor obtained? 120 sq. in. 10 sq. in. = 12, no. of strips, and hence the no. of inches in the length. Test by ascertaining if the area of a rectangle 10 in. by 12 in. is 120 sq. in. CALCULATION 10)120 2. A 5-acre lot is 20 rd. wide. How long is it? 12 3. A field containing 20 acres is 32 rd. wide. its length? What is 4. A farmer covered his barn with galvanized iron. What did it cost him at $7 per square (100 sq. ft.), if each side of the roof is 75 ft. by 25 ft.? 5. Each side of a roof is 50 ft. long and 20 ft. wide. What is the cost of roofing it at $8.75 a square? 6. If 1 gal. of paint covers 300 sq. ft. of surface with 2 coats, how many gallons are required to paint (with 2 coats) the outer walls of a building 35 ft. long, 28 ft. wide, and 20 ft. high? 7. If a man earns $1600 a year, and spends $790, in how many years can he save enough to buy a farm of 135 acres, at $24 an acre? 135 1600 8. A man earns $75 a month. He spends $10 a month for rent, $20 a month for board, and $140 a year for other expenses. In how many years will he save $2000 at this rate? 9. A dealer bought 200 barrels of apples at $3.50 a barrel. He sold 120 barrels at $4 a barrel, but owing to a decline in the market price he was compelled to sell the rest at $3.40 a barrel. How much did he gain on the transaction? 10. A dealer bought 120 arithmetics at 42¢ each, and sold them at 54 each. How much did he gain on the whole number? 11. A grocer bought 300 lb. of prunes for $27, and sold 160 lb. at 11 a pound, and the rest at 7¢ a pound. Did he gain or lose, and how much? 12. A grocer bought a barrel of sugar (320 lb.) at 41⁄2¢ a pound. It lost 5% of its weight by drying, and was then sold at 61 a pound. What did he gain? 13. A farmer bought 30 head of cattle at $50 a head, and sold them at a profit of 21%. What did he gain? 14. If it costs a farmer $4.25 per 100 bu. to have his wheat threshed, how many bushels will he have to give as toll for threshing a crop of 280 bushels, when the market price is 85 a bushel? $4.25 $.85 5, number of bushels for threshing 100 bu. = 5 bu. out of 100 bu. = 5%. .05 x 280 bu. = 14 bu., amount required. 15. A farmer who owed $250 gave in part payment 150 bu. of wheat at 90¢ a bushel, and paid the remainder with flour at $5 a barrel. How many barrels did he give? 16. The depth of a certain rainfall was 1.25 inches. What weight of water fell on a lot 40 feet by 120 feet, if a cubic foot of water weighs 1000 ounces? (a) 1.25 x 480 x 1440 = 864,000, number of cubic inches of water. (b) 1.25 x 40 x 120 × 144 × 1000 1728 Explain the advantage of first indicating the work, as in (b). Cancel and find the result. 17. A 2-acre pond is covered with ice 6 in. thick. If a cubic foot of ice weighs 920 oz., how many tons of ice are on the pond? 18. A and B rent a pasture for $24. A puts in 4 cows for 2 weeks, and B puts in 5 cows for 8 weeks. much should each pay? 4 cows for 2 wk. 8 cows for 5 wk. = 2 x 4 cows, or 8 cows, for 1 wk. = 5 x 8 cows, or 40 cows, for 1 wk. 8 cows for 1 wk. + 40 cows for 1 wk. = 48 cows for 1 wk. 48 cows for 1 wk. cost $24. 1 cow for 1 wk. costs of $24, or $.50. 8 cows for 1 wk. cost 8 x $.50, or $4, A's part. 40 cows for 1 wk. cost 40 × $.50, or $20, B's part. How 19. Three men pasture horses in the same field, the first pasturing 6 horses for 9 weeks, the second 9 horses for 8 weeks, and the third 12 horses for 7 weeks. They pay $105. How much of the rent should each pay? PRACTICAL ARITH.-14 20. A can build a fence in 4 days, and B can build it in 5 days. How long will it take both together? 21. A can do a piece of work in 2 days, B in 4 days, and C in 6 days. together? How long would it take them to do it 22. If 12 lb. of tea cost $6, how much must be paid for 18 lb. ? 23. If an automobile goes 54 miles in 3 hours, how far will it go in 8 hours at the same rate? 24. If 1 reaper can cut 15 acres a day, how long will it take 3 reapers to cut a field of 900 acres at the same rate? 25. If of a cord of wood costs $3, how much will 5 cords cost at the same rate? 26. If 8 barrels of flour cost $52.80, what will 3 barrels cost at the same rate? 27. A 3-acre field of potatoes yields 165 bu. At the same rate, how many bushels will a 20-acre field produce? If 5 people consume on an average 375 lb. of sugar in a year, how much does a family of 7 persons consume in the same time? 28. 29. If 12 bales of cotton weigh 5760 lb., what do 8 bales of the same average weigh? 30. A lady bought a dress pattern for $11.25. If she paid 90 a yard for the material, how many yards were in the pattern? |