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 12? 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 st run 9 times 5 rods, which are 45 rods. 39. 5 times one half of 18 are how many? 40 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? |