3 16 37. How many bushels of potatoes, at of a dollar a peck, must be given for 10 bushels of wheat, at $2 a bushel? 38. If a man can mow 1 acres in 1 day, how long will it take 6 men to mow 14 acres? LESSON XXXVI. 1. If a man walks 2 many hours will he walk 8 miles an hour, in how miles? ANALYSIS. At 2 miles an hour, he will walk 8 miles in as many hours as 2 miles are contained times in 81 miles. 2 = 2=15, 8: = 2,5 50; and 15 are contained in 50, 35, or 31⁄2, times. SECOND METHOD OF DIVIDING. 1 is contained in 25, 25 times; is contained in 23, 2 times 25, or 2o times; and are contained in 25, 1 of 5 times, which is 1o, or 31 times. 2. At of a dollar apiece, how many tickets can be purchased for of a dollar? 3. At of a dollar a pound, how many pounds of starch can be purchased for 2 of a dollar? 4. If a horse can trot of a mile in a minute, how long will it take him to trot § of a mile? 5. If 1 man can do a piece of work in 5 days, how many men can do it in 23 days? 6. How many men will be required to reap 21 acres, while 1 man is reaping 1 acres? 7. When $1 will buy 21 gallons of molasses, how many dollars must be paid for 5 gallons? 8. At of a dollar a day, in how many days will a man earn $61? 9. At of a will a man earn FIRST ANALYSIS. dollar a day, in what part of a day of a dollar? At $ a day, a man will earn $ 1, or $3, in the same part of a day, that $ & is of $ %, or that 3 is of 5, which is 3. Therefore he will earn $ in SECOND ANALYSIS. If a man earn $3 in will earn $↓ in of a day, and $3 in 3 times, day. of a day. 1 day, he or 3, of a 10. At of a dollar a day, in what part of a day will a man earn of a dollar? 11. If a man can do a piece of work in of a day, what part of the work can he do in of a day? 12. How many times is 13. How many times is contained in §? 6 of tea, at 3 of a dollar a of a dollar? contained in 17? 14. If a horse eats of a ton of hay in 1 week, how many weeks will he be in eating & of a ton? 15. How many times is contained in? 16. How many pounds pound, can be bought for 17. How many times is 18. How many times is 19. How many times is 3 20. How many times is 21. How many times is 22. How many times is 10 contained in 21 ? 9 23. How many times is 61 contained in 12§ ? 24. If a lamb cost $21, how many lambs can be bought for $82? 25. At g of a dollar a yard, how many yards of cloth can be bought for $41? 26. If 1 man can do a piece of work in 63 days, how many men must be employed to do it in 23 days? 27. How many bushels of apples, at & of a dollar a bushel, must be given for 7 bushels of potatoes, at of a dollar a bushel? 6 28. If a man can walk of a mile in of an hour, in how many hours can he walk 8 miles? 29. How many pounds of sugar, at of a dollar a pound, can be bought for of a bushel of cranberries, at $33 a bushel? 2 30. When 1 yard of cloth costs $11, how much cloth can be bought for $14? 31. A farmer, having sold a load of wood for $71, spent of the money for tea, at 3 of a dollar a pound, and the balance for coffee, at of a dollar a pound; how many pounds of each did he obtain? 32. 8 dozen of eggs, at a dozen, will pay for how many yards of cloth, at $ a yard? 33. How many times is of 21? In of? 34. corn $ contained in of When oats are of a dollar a bushel, and 5 16 of a dollar a bushel, how many bushels of oats must be given for 5 bushels of corn? LESSON XXXVII. RATIO is the relation, in respect to magnitude or value, which one quantity or number bears to another of the same kind. It is expressed by dividing one quantity by the other. Thus, the ratio of books to 3 books is 2, because 6 books are twice 3 books; the ratio of 3 to 6 is 2, because 3 is of 6; the ratio of 7 to 3 is, because 7 is of 3; and the ratio of 3 to is 24, because 3 is 2 of 7. Of 3 is 2? 1. What part of 3 is 1? NOTE. See Exs. 2, 20, Lesson XXVI. 2. What part of 5 is 1? 3. What part of 9 is 1? Of 5 is 3? Of 9 is 5? 4. What part of 7 is 3? Of 8 is 5? Of 14 is 17? 8. that 1 is What part of 9 11. What part of of 15, or 5. 10. What part of 1 pound is 9 shillings? 18. 12. What part of 13. What part of 14. What part of 15. What part of What part of 1 What part of 1 quarter is 14 pounds? NOTE. - Reduce both to half-pounds. 19. What part of 2 dimes i. 13 cents? 20. What part of 1 week 4 days is 5 days? 21. What part of 5 bushels is 3 pecks 6 quarts? 22. What part of 10 pounds is 4 pounds 12 ounces? 23. What part of 2 hogsheads is 1 hogshead 17 gallons? 24. What part of 3 yards 3 quarters is 3 quarters 3 nails? 25. What part of 3 leagues 2 miles is 1 mile 3 furlongs? 26. What part of 1 acre 2 roods is 3 roods 15 square rods? 27. What part of a mile is 3 furlongs 15 rods? 28. What part of 8 yards is 5 ells English 3 quarters? 29. What part of a pint is 12 of a gallon? ANALYSIS. Since 1 gallon 4 quarts, of a gallon 1 of 4 quarts, which is 2, or 3, of a quart; and since 1 quart2 pints, of a quart of 2 pints, or of a pint. 30, What part of an inch is of a yard? 31. What part of a pennyweight is = 15 65 48 of an ounce? of a mile? of a week? 2 of a gallon? 32. What part of a rod is 33. What part of a day is 34. What part of a gill is 35. What part of a shilling is ANALYSIS. Since 4 farthings=1 penny, 1 farthing= of a penny, and of a farthing of of a penny, or of a penny; and since 12 pence =1 shilling, 1 penny = of a shilling, and of a penny = or of a shilling. = of 11⁄2 of a shilling, of a day? 36. What part of a week is 37. What part of a yard is 38. What part of a ton is 39. What part of a bushel 40. What part of a pound is 41. What is the value of gallons? 42. What is the value of lings and pence? = = of a pennyweight? of a hogshead, in of a pound, in shil of 12 pence, or 6 7 shillings 6 pence. of a pound Troy? of a yard? of a hogshead? of a bushel? ANALYSIS. Since 1 pound 20 shillings, of a pound of 20 shillings, which are 7 shillings; and since 1 shilling 12 pence, of a shilling pence. Therefore of a pound 43. What is the value of 44. What is the value of 45. What is the value of 46. What is the value of 47. What is the value of 48. What is the value of |