15. What number is that to which, if of itself be added, the result will be 56? 16. Henry sold of his hens and had 35 remaining; how had he at first? many 17. If of 14 yards of silk cost $12, how much will 33 yards cost? 18. If of 10 cords of wood cost $6, how much will of 3 cords cost? 19. If 21 barrels of apples cost $9, how much will 31 barrels cost? 20. When 40 acres of land cost $1800, how much will 51 acres cost? 4. COMPARISON OF FRACTIONS WITH FRACTIONS. 1. If of a bushel of wheat cost 64 cents, how much will of a bushel cost? ANALYSIS.-If of a bushel of wheat cost 64 cents, of a bushel will cost of 64 cents, or 32 cents; and 1 bushel will cost 3 times 32 cents, or 96 cents. Since 1 bushel of wheat costs 96 cents, of a bushel will cost of 96 cents, or 72 cents. 2. of my age is 30 years; what is of my age? 용 3. If of a pound of cheese cost 6 cents, how much will of a pound cost? 4. When of my monthly salary is $9, how much do I earn in of a month? 5. of the cost of my horse is $100; what do I get for him if I sell him at g of his cost? 6. When of a dozen of eggs cost 18 cents, how much will 1 dozen cost? 7. If 11⁄2 barrels of apples cost $6, what must I pay for 23 barrels ? 8. If of a box of soap cost 90 cents, what is the cost of 2 boxes? 9. If a horse travel 14 miles in 2 hours, how far will he travel in 5 hours? 10. If 3 pounds of meat cost 50 cents, how much will 41 pounds cost? 11. If g of a ton of coal is worth $33, how much are 21 tons worth? 12. How much will 54 pounds of sugar cost, if 21 pounds cost 20 cents? 13. When 2 barrels of flour are worth $131, how much are 1 barrels worth? 14. 12 years is of my age; what is twice my age? 15. If 33 pounds of butter are worth $1.35, what are 21 pounds worth? 16. If of a barrel of vinegar is worth $33, how much are 1 barrels worth? 17. How much will 13 yards of silk cost, if of a yard cost of a dollar? 18. If a ship sail 4 miles in of an hour, how far will it sail in 8 hours? 19. Henry can mow an acre of grass in 10 hours, and William in of that time; how long does it take William to mow the acre? 20. When 3 dozen of eggs are worth 70 cents, how much are 31 dozen worth? 21. If 2 yards of cloth cost $31, how many yards can I buy for $5? 22. If a boy can earn $63 in 4 days, how much can he earn in of of a day? 23. How many sheep at $54 apiece can I get for 5 tons of coal at $43 a ton? 10 24. How many pounds of butter at of a dollar a pound will pay for 16 pairs of chickens at 3 of a dollar a pair? 25. How many pounds of coffee at of a dollar a pound can I get for 3 pairs of ducks at § of a dollar a pair? 5. A FRACTIONAL PART WITH AN INTEGRAL REMAINDER. 1. A boy lost of his money and had $12 remaining; how much had he at first? ANALYSIS. Since he lost of his money, he had remaining 7-3, or, of his money, which is $12: if of his money is $12, of his money is of $12, or $3, and 7, or his money, is 7 times $3, or $21. 2. George spent of his money and had $20 remaining; how much had he at first? 3. A farmer sold of his wheat to one man and to another, and had 160 bushels remaining; how much had he at first? 4. Mr. A sold of his corn to one man and to another, and has 210 bushels remaining; how much had he at first? 5. If Henry spend of of his money and has $30 remaining, how much had he at first? 6. In an orchard of the trees are peach trees, pear trees, and apple trees; the remainder, 24, are plum trees; how many are there of each, and how many together? 7. Samuel spent of his money, then earned as much as he spent, and had $20; how much had he at first? 8. A lady sold of her hens, then bought as many as she had at first, and then had 84; how many had she at first? 9. George won 40 marbles, then lost of what he won, and had 25; how many had he at first? 10. 1⁄2 of a man's money, being increased by and of his money, equals $620; how much money has he? 11. Henry spent of his money, and then earned as much as he had at first, and then had $65; how much had he at first? 12. My expenses are of my annual income; what is my income, if I save $340? 13. A man's board is of his salary, and his other expenses what is his salary, if he save $200 ? 14. What number diminished by its and its equals 48? 15. A merchant who owed me failed, and I received only of my money; what was the debt, if I received $540? 16. I find that of of the trees in my orchard have died, but I still have 76; how many had I at first? 17. If James spends of his income for board and for other expenses, what is the income, if he saves $120? 18. If I pay of my salary for rent and of 3 of it for other expenses, what is the salary, if I have remaining $210? 19. After spending, 4, and of my money I find $26 is of the remainder; how much money had I? 20. Mr. Thomas sold of his potatoes to A, 3 of the remainder to B, and had 40 bushels remaining; how many bushels had he at first? 21. What number is that to which if you add 3 of itself the result is 140? 22. A young man, being asked his age, replied, If to my age you add and of my age, the sum is 39 years; how old was he? 23. Paid of my money for a book, for pens, and 26 cents for a slate, and then had of my money remaining; how much had I at first? 24. I spent of my money, then borrowed as much as I had remaining, when I had 20 cents less than at first; how much had I at first? 25. of 12 is how many eighths of 16? 26. of 30 is how many fifths of 25? 27. of 48 is how many sevenths of 49? of how many times of 25? 37. of 72 is of William's, and of William's is of George's; how much money has each, if George has $48? REVIEW PROBLEMS. 1. Henry had of a dollar and spent of a dollar; how much had he remaining? 2. If be added to a certain fraction, the sum will be ; what is the fraction? 3. If of a dozen of oranges cost 16 cents, how much will 3 dozen cost? 4. Bought of a ton of coal in June, of a ton in July, and 13 tons in August; how much did I buy in the three months? 5. Bought a coat for $12 and a hat for $43; how much change did I get from a 20-dollar bill? 6. Henry is 20 years old, and of his age is of his father's age; how old is his father? |