CHAPTER VII. RATIO AND PROPORTION. 73. 1. What part of 4 is 1? of 4 is 3?* ANALYSIS. Since 1 is of 4, 3 must be 3 times ≥ part of 4, or of 4. Therefore 3 is of 4. 10. What part of ANALYSIS. 13, and =1; the ratio of 18 to is the same as that of their numerators, 10 to 12: what part of 12 is 10? 19. Therefore is of , and the ratio is . *The quotient arising from dividing_one number by another is called the ratio. Thus, what part of 4 is 1? It is 1 divided by 4, equal to , the ratio. What part of 4 is 3? It is 3 divided by 4, equal to 3, the ratio. 74. 1. What part of 25 dollars is 5 dollars? is 10 dollars? 2. What part of 16 pounds is 4 pounds? is 7 pounds? is 12 pounds? 3. What part of 1 bushel is 1 peck? is 2 pecks and 4 quarts? is 6 quarts? 4. What part of 1 pound is 12 shillings? 5. What part of 1 dollar is 20 cents? is 5 dimes? 6. What part of 1 cwt. are 15 pounds? 7. What part of 1 cwt. are 6 lbs. ? 9 lbs. ? 8. What part of 1 ton is 14 cwt.? 15 cwt.? 18 cwt.? 9. What part of 3 pounds is 10 oz. ? is 1 lb. 6 oz.? 10. What part of 1 foot is 3 in.? 10 in.? 11 in. ? 11. What part of 2 yds. is 1 foot? 1 foot 10 inches? 12. What part of 1 mile is 3 furlongs? 5 furlongs 20 rods? 13. What part of 1 mile is 140 rods? 160 rods? 14. What part of 1 gallon is 1 quart? 1 pint? 15. What part of 1 hhd. is 5 gallons? 21 gallons? 16. What part of 1 quart is 1 pint? 2 gills? 17. What part of 1 hour is 15 minutes? 40 minutes? 18. What part of 1 day is 3 hours? 8 hours? 16 hours? 19. What part of 3 weeks is 2 days? 5 days? 9 days? 20. What part of 1 year is 3 weeks? 7 weeks? 21. What part of 5 pounds 6 ounces is 3 pounds 10 ounces? 22. What part of 3 hhd. is 1 hhd. 22 gallons? 23. What part of 1 mile 3 fur. is 4 fur. 20 rods? 24. What part of 3 pecks is 6 quarts 1 pint? 25. Two pounds is what part of 1 cwt. ? of 2 cwt. ? 26. Eight inches is what part of a foot? of 2 feet? of 1 yard? of 4 yards? 27. Three quarts is what part of a gallon? of 5 gallons of 10 gallons? of 1 hhd.? 28. What part of 9 miles is 3 of 8 miles ? 29. What part of 4 acres is of 31 acres? 30. A man, having $15, gave $3 for a hat, and $4 for a pair of boots; what part of his money did he use, and what part had he left? 31. A farmer, having 160 bushels of wheat, sold of of it, floured of of it, and kept the remainder for seed; what part of the whole did he use for each purpose? 32. If I have sold of of 120 sheep, what part of the whole flock have I left? 33. One man can walk 43 miles while another walks 33 miles; what part of the distance that the first walks does the second walk? 34. A gentleman paid of $39 for a coat, and $9 for a pair of pantaloons; how many times as much did he pay for the coat as for the pantaloons? 35. Paid $7 for a barrel of flour, and 1 times as much for a ton of hay; what was the cost of the ray? 36. A man bought a horse for $225, and a car riage for of of this sum; what part of $125 did' the carriage cost? 37. If a vessel sail 40 miles in 5 hours, what part of 144 miles will she sail in 9 hours? how many miles? 38. A man gave to his 3 sons 360 acres of western land; to the first he gave of it, to the second of 3 times as much, and the remainder he gave to the third; what part.of the whole did each receive? how many acres? 39. A merchant gained on a hogshead of sugar of $463, which was of 2 times what it cost him; what did it cost him? what part of the cost was the gain? 75. 1. If 6 cords of wood cost $15, what will 4 cords cost? ANALYSIS. Four cords are , or of 6 cords. If 6 cords of wood cost $15, 4 cords will cost of $15; of $15 is $5, and 3 of $15 is 2 times $5, or $10. Therefore, &c. Or, the pupil may use the form of analysis used in section 22, on page 41. 2. If 9 pounds of sugar cost 75 cents, what will 12 pounds cost? 3. If 6 men can cut 45 cords of wood in 3 days, how many cords can 8 men cut in the same time? 4. If 31 yards of cloth cost $101, how much will 7 yards cost? 5. If 42 pounds of butter cost 66 cents, what will 23 pounds cost? 6. If a mechanic earn 13 shillings in 11 days, how much can he earn in a week? 7. If $74 will buy 3 cords of wood, how many cords can be bought for $101? 8. If barrel of flour cost $43, what will of a barrel cost? ANALYSIS. What part of is? = f, and f = f; the ratio of tot is the same as of 3 to 4, Then, since barrel of flour cost $43, of a barrel will cost of $4}; 1 of 2 = 3.6. 36 $6. Therefore, &c. 9. If a man can run 6 miles in 3 of an hour, how far can he run in 34 hours? 10. How many yards of carpeting of a yard wide are equal to 12 yards of a yard wide? 11. If a staff 3 feet long cast a shadow 5 feet in length, what would be the length of the shadow cast by a pole 13 feet long? 12. If the sawing of of a cord of wood cost 61 shillings, what would the sawing of 33 cords cost? 13. John earns 9 cents as often as James earns 15 cents; when John has earned 63 cents, how much has James earned? 14. Two persons start from different points and travel towards each other; the first one travels 7 miles while the other travels 5 miles, and when they meet the first one has traveled 70 miles; how far apart were they when they started? 15. If 4 men can build a wall 60 feet long in 6 days, in what time can 3 men build a wall 90 feet in length? ANALYSIS. In of 8 of 6 days, which are 12 days. Or thus if it will take 4 men 6 days to build a wall 60 feet long, it will take 1 man 4 times 6 days, or 24 days, and 3 men can do it in of 24, or 8 days; to build a wall 1 foot long will require of 8, or 3 days, and to build a wall 90 feet long will require 90 times as many days, or 90 times , equal to 12 days. Therefore, &c. 16. If 5 men can do a piece of work in 10 days, how many men will do a piece of work 4 times as large in 20 days? 17. If a man perform a journey in 8 days, by traveling 9 hours a day, how many days will he require to perform the same journey, if he travel 12 hours a day? 18. If 5 horses eat 11 tons of hay in 1 month., how many tons will 6 horses eat in 2 months? 19. How many days will it take 5 men to earn $113, if 3 men earn $3 in 1 of a day? 20. If 1 horse eat 1 bushels of oats in 3 days, in how many days will 4 horses eat 49 bushels ? 21. If a barrel of flour will supply a family of 4 persons 5 weeks, how much will supply a family of 3 persons 2 weeks? 22. If 3 furnaces consume 121 tons of coal in 7 days, how long will 17 tons last 5 furnaces? |