rel; how many dollars did they cost? How much wood, at $6 a cord, would it take to pay for them? 4. 4 times 3 are how many times 6? 5. Mary bought 4 oranges, at 3 cents apiece; how many cents did they cost? She paid for them with pears, at 2 cents apiece; how many pears did it take? 6. 4 times 3 are how many times 2? 7. Bought 5 cords of pine wood, at $4 a cord, and paid for it with hay, at $10 a ton; how did it take? 8. 5 times 4 are how many times 10? many tons 9. Bought 5 barrels of flour, at $8 a barrel, and paid for it with cloth, at $4 a yard; how many yards did it take? 10. 5 times 8 are how many times 4? 11. How much wool, at 4 shillings a pound, will pay for 8 bushels of corn, at 6 shillings a bushel? 12. 8 times 6 are how many times 4? 13. 7 times 6 are how many times 3? 14. 6 times 6 are how many times 4? 15. How many dozen of eggs, at 12 cents a dozen, will pay for 7 pounds of veal, at 6 cents a pound? 16. 7 times 6 are how many times 12? 17. 8 times 3 are how many times? 4? 5? 6? 18. 5 times 7 are how many times 4? 6? 8? 9? 19. 8 times 5 are how many times 10? 7? 6? 9? 20. Bought 3 hundred weight and 3 eighths of a hundred weight of sugar, at 8 dollars a hundred weight, and paid for it with apples, at 3 dollars a barrel; how many barrels did it take? How much broadcloth, at 4 dollars a yard, would it take to pay for it? 21. 3 times 8 and 3 eighths of 8 are how many times 3? 4? 6? 5? 8? 9? 22. Sold 4 bushels and 3 eighths of a bushel of · wheat, at 8 shillings a bushel, and took my pay in butter, at 2 shillings a pound; how many pounds did I receive? 23. 4 times 8 and 3 eighths of 8 are how many times 2? 6? 4? 7? 24. How much flour, at $8 a barrel, will pay for 5 boxes and 5 ninths of a box of butter, at $9 a box? 25. 5 times 9 and 5 ninths of 9 are how many times 8? 10? 6? 7? 26. 7 times 10 and 9 tenths of 10 are how many times 8? 11? 6? 12? 27. 5 times 7 and 4 sevenths of 7 are how many times 12? 8? 6? 5? 9? 28. 9 times 8 and 3 eighths of 8 are how many times 5? 10? 12? 7? 11? 3? 29. How many dollars will pay for 8 bushels and 4 sevenths of a bushel of wheat, at 7 shillings a bushel? 30. 8 times 7 and 4 sevenths of 7 are how many times 6? 12? 8? 10? 9? 31. How many bushels of corn, at one dollar a bushel, will pay for 9 bushels and 3 fifths of a bushel of potatoes, at 5 shillings a bushel ? 32. 9 times 5 and 3 fifths of 5 are how many times 6? 8? 10? 12? 11? LESSON III. 1. IF 2 pears cost 6 cents, what will 4 pears cost? Solution. If 2 pears cost 6 cents, 1 pear will cost one half of 6 cents, which is 3 cents; and 4 pears will cost 4 times 3 cents, which are 12 cents; therefore, etc. Or, since 2 pears cost 6 cents, 2 times 2 pears, that is, 4 pears, will cost 2 times 6 cents, which are 12 cents; therefore, etc. NOTE. The first mode of answering the above example is the more obvious analysis; but the ready pupil will very often save labor, as in the second solution, by a quick perception of and a careful attention to, the relations of numbers. 2. 4 times one half of 6 are how many? 3. 6 times one half of 4 are how many? 4. If 3 apples cost 6 cents, what will 12 apples cost? 5. 12 times one third of 6 are how many? 6. 6 times one third of 12 are how many? 7. A man hired a laborer, and agreed to give him $5 for every 2 days' work; how much did he give him for 6 days' work? 8. 5 times one half of 6 are how many? 9. A man lays up 3 shillings a day; in how many days will he lay up $8? 10. 8 times one third of 6 are how many ? 11. If 4 boxes of raisins cost $7, what will 12 boxes cost? 12. 7 times one fourth of 12 are how many? 13. If 3 boxes of raisins cost $7, how many boxes may be bought for $35? 14. 3 times one seventh of 35 are how many? 15. If 7 bushels of wheat are worth as much as 2 cords of wood, how many bushels of wheat will pay for 10 cords of wood? 16. 7 times one half of 10 are how many ? 17. If 10 cords of wood are worth as much as 35 bushels of wheat, how many bushels of wheat will pay for 2 cords of wood? 18. 35 is how many times one half of 10? 19. How many bushels of corn, at 4 shillings a bushel, will pay for 2 barrels of apples, at 3 dollars a barrel? 20. 2 times 3 times 6 are how many times 4? 21. At 5 shillings a gallon, how many gallons of molasses will pay for 2 yards of cloth, at 5 dollars a yard? 22. 2 times 5 times 6 are how many times 5? 10? 12? 8? 23. How many bushels of wheat, at 8 shillings a bushel, are worth as much as 4 barrels of potatoes, at 2 dollars a barrel? 24. 4 times 2 times 6 are how many times 8? 12? 9? 11? 25. A can build 12 rods of wall in 4 days, and B can build 5 rods as often as A builds 3 rods; how many rods can B build in 4 days? 26. 5 times one third of 12 are how many? 27. A can lay 10 rods of wall in 6 days, and B can lay 7 rods as often as A can lay 5 rods; how many rods can B lay in 9 days? 28. 7 times one fifth of 10 are 2 thirds of what number? 29. A can mow 10 acres of grass in 6 days, but B can mow only 4 acres while A is mowing 5; how many acres can B mow in 3 days? 30. 4 times one fifth of ten are 2 times what number? 31. A boy bought 20 peaches, at the rate of 2 for 3 cents; how many cents did he pay for them? Solution. Two peaches in 20 peaches 10 times; and 10 times 3 cents are 30 cents; therefore, etc. Or, 20 peaches, at 3 cents apiece, cost 60 cents; but since two peaches were bought for 3 cents, the 20 peaches cost one half of 60 cents, which is 30 cents. 32. 3 times 20 are how many times 2? 33. How many eggs, at the rate of 3 for 5 cents, can you buy for 30 cents? How many at the rate of 5 for 3 cents? 34. 3 times one fifth of 30 are how many? 38. A hare has 18 rods the start of a hound, but the hound runs 5 rods while the hare runs 3; how many rods must the hound run to overtake the hare? Solution. The hound gains 2 rods by running 5 rods; he must gain 9 times 2 rods, and therefore must run 9 times 5 rods, which are 45 rods. 39. 5 times one half of 18 are how many? 40. A hare has 24 rods the start of a hound, but the hound runs 10 rods while the hare runs 7; how many rods will the hare run before the hound overtakes him? LESSON IV. 1. A BOY having 12 peaches, kept 1 third of them himself, and divided the other 2 thirds equally among 4 of his companions; how many did he give them apiece? 2. Two thirds of 12 are how many times 4? 3. A boy having 21 apples, kept 2 sevenths of them himself, and divided the other 5 sevenths equally among 6 of his playmates; how many did he keep for himself? How many did he give to each of his 6 playmates? 4. Two sevenths of 21 are how many? 5. Five sevenths of 21 are how many times 6? 6. A man gave 4 fifths of 30 cents for 8 oranges; what was the price of 1 orange? 7. Four fifths of 30 are how many times 8? 8. A man who had $36, divided 3 fourths of his money equally among 6 poor persons; how many dollars did he give to each? 9. Three fourths of 36 are how many times 6? 10. A man bought a sheep for 15 shillings, and sold. it for 5 thirds of what he gave for it; for how many `dollars did he sell it? 11. Five thirds of 15 are how many times 6? 12. A boy bought a rabbit for 25 cents, and sold him for 6 fifths of his cost; for how many dimes did he sell him? How many cents did the boy gain? What part of a dime? 13. Six fifths of 25 are how many times 10? 14. A grocer having 40 pounds of raisins, sold 5 eighths of them in 10 equal parcels; how many pounds were there in each parcel? |