274. Oral Problems. 1. 16 is how many hundredths of 64? 2. What per cent of 25 is 5? 3. What part of is? Change both to the same denominator: 16 twentieths, 15 twentieths. 4. What part of 2 lb. 1 oz. is 1 lb.? Change both to the same denomination : 33 oz., 16 oz. 5. Divide 4 gallons by 3 pints. 6. How many pencils at 4 mills each can be bought for a dollar? 1 mill of a cent. = 7. Write as a decimal. 8. Divide 34 by 200. 9. How many pounds in one-quarter of a ton? How many pints in .25 of a bushel ? 10. Change 3714, 75¢, 814, 6214, 614, to fractions of a dollar? 11. How many pounds of cheese at $0.163 a pound can be bought for $5.00? 12. An agent collected rents amounting to $300. What was his commission at %? 13. Find the interest of $200 for 1 yr. 3 mo. at 4%. 14. A farmer raised 50 bushels of cranberries, and sold 60% of them. How many bushels did he sell? 15. What % of a number is of it? 16. What would 42 pounds of butter cost at 331 a pound? 17. When the tax rate is $12 per $1000, what will Mr. Smith's tax be if he owns $4500 worth of property? 18. A man pays $60 interest per year. How much interest does he pay in 3 yr. 7 mo. ? 2 19. At $45 per month, what is the rent of a house for 7 mo. ? yr. 20. Express in per cents: ; 1; 1; 1; 1. 275. Written Problems. 1. What is the interest on $760 for 5 months at 31% ? 2. A merchant insures property worth $20,000 for of its value. How much does he pay, the rate for insuring being 11% ? 3. What is the commission on $5678 worth of cloth at 21% ? 4. At 3%, what is the commission on the sale of 5000 pounds of sugar at 51 per pound? 5. What will be the interest on $720 for 3 mo. 24 da. at 41%? 6. A clerk's income is $800. He pays 25% of it for board, and 331% of the remainder for clothes. How much has he left? 7. 1% of my money is in my pocket, 38% is in the bank, and the rest is in real estate. I have in all $24,000. much is in the bank and in real estate? How 8. An auctioneer sold for Mrs. Paul, on 10% commission, 14 chairs at $1.75, 6 tables at $2.75, 40 yards carpet at 621 a yard, and a miscellaneous lot for $119.24. What sum did Mrs. Paul receive after paying commission? 9. How many feet in 62% of a mile? What part of a day is 18 hr. 30 min.? Reduce 9 cwt. 17 lb. to ounces. 10. If .625 of a cord of wood costs $3.75, what will .75 of a cord cost? 11. A business man's receipts for a week are $2575. His average rate of profit is 5% of his receipts. What is his profit for the week? 12. A certain city had 14,250 inhabitants in 1900. The population has increased 24 per cent. What is the present number of inhabitants? 13. A class has 56 pupils on register. When 142 per cent of the pupils are absent, how many are present? 14. A merchant's sales for 1903 were $45,276. What should be the sales for 1904 to make an increase of 163 per cent? 15. Thirty words were dictated as a spelling test. One pupil received a mark of 933 per cent. How many words did he misspell? 16. A certain regiment went into battle with 1000 men. Of these 5% were killed, 12% were wounded, 3% were taken prisoners, and 1% were missing. How many remained available for duty? 17. What is the duty at 35 cents per square yard on a piece of cloth measuring 56 yards, 27 inches wide? 18. A man bought a bill of goods amounting to $374.50, with a deduction of 2% for payment within 10 days. How much does he save by paying the bill within the 10 days? 19. A merchant places a bill of $840 in the hands of a collector, who collects 75% of the amount. How much does the merchant receive if the collector deducts 5% of the amount collected, as his commission? 20. How many pounds of bread can be made from 5 bushels of wheat weighing 60 pounds per bushel, if the wheat loses 30 per cent in the process of grinding into flour, and if the bread weighs 331 per cent more than the weight of the flour used? SURFACES. 276. Preliminary Exercises. 1. What is the length in inches of a row of four envelopes, each five inches long, placed end to end? What is the length in feet and inches. 2. What is the width in inches of four such rows, each envelope three inches wide, just touching each other? What is the width in feet? 3. How many envelopes are there? How many square inches are there in each envelope? How many square inches are covered by all of them? 4. How many envelopes 5 inches by 3 inches would cover the top of a table 4 ft. 2 in. long and 2 ft. 6 in. wide? 5. Draw a rectangle to represent a floor 24 feet long 18 feet wide. Draw rugs 6 feet long, 3 feet wide, and see how many will be needed to cover the floor. 6. What is the difference between three square inches and three inches square? 7. What is the distance around a room that is 40 feet by 30 feet? 8. A garden is 12 feet long and 9 feet wide. How many bunches of flowers will it furnish, if it takes 3 to furnish one bunch? square feet 9. A room is 36 feet long and 30 feet wide. How many square yards in the floor? 10. How many yards is it around a room 15 feet long and 12 feet wide ? 11. How many square inches in the surface of a sheet of paper 1 foot 8 inches long, 11 inches wide? 12. How many pieces of paper 2 inches square will exactly cover a slate 12 inches long, 8 inches wide? 277. Written Problems. 1. How many boards 12 feet long, 6 inches wide will be required for a floor 8 yards long, 6 yards wide ? The floor is 24 feet long, 18 feet wide; its area in square feet is 18 x 24. The area of the board in square feet is 12 ×, or 6. NOTE. Labor is frequently saved in examples involving multiplication and division by first indicating the operations and then using cancellation. 2. How many bricks 8 inches by 4 inches will be needed for a walk 24 yards long, 6 feet wide, making no allowance for waste? Area of top surface of one brick = (8 x 4) square inches. The length of the walk in inches = 24 × 3 × 12; width in inches = 6 x 12. Area of walk in square inches = 24 × 3 × 12 × 6 × 12. Divide this by 8 x 4, the number of square inches in the top surface of a brick. NOTE. - It will be remembered that the divisor and the dividend must be of the same denomination, square inches in this example. |