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. 3 9? 7. What part of 16 is 8. What part of 40 is 9? 9. What part of 30 is 27? 10. What part of ANALYSIS. is? What is the ratio? 12, and =1; the ratio of 10 to is the same as that of their numerators, 10 to 12: what part of 12 is 10? 19. atio is. 11. What part of 12. What part of Therefore is of §, and the 13. What part of *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 1, the ratio. What part of 4 is 3? It is 3 divided by 4, equal to 3, the ratio, of 31 is 2? ? of 71⁄2 is 34? 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 $31 for a hat, and $43 for a pair of boots; what part of his money did be 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 42 miles while another walks 33 miles; what part of the distance that the first walks does the second walk? 24. A gentleman paid of $391 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 $3 for a barrel of flour, and 14 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 carriage 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 2 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 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 $103, how much will 7 yards cost? 5. If 4 pounds of butter cost 66 cents, what will 23 pounds cost? 6. If a mechanic earn 13 shillings in 14 days, how much can he earn in a week? 7. If $71 will buy 31 cords of wood, how many cords can be bought for $101? 8. If barrel of flour cost $41, what will of a barrel cost? ANALYSIS. What part of is? = f, and f = f; the ratio of to is the same as of 3 to 4, barrel of flour cost $41, of a barrel will cost of $4; $. Then, since 1 of 2 = 36. 35 $6. Therefore, &c. 9. If a man can run 6 miles in & of an hour, how far can he run in 3 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 6 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 fai 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 88 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 requires of 8, or 3 days, and to build a wall 90 feet long will require 90 times as many days, or 90 time. , 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 iz 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 of a day? 20. If 1 horse eat 13 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? |