3 72. 1. § of 36 is of how many times 2 of 42 ?* ANALYSIS. Of as many times of 42 as 2 times ✈ of 42 is contained times in 9 times of 4 times of 36; 1 of 36 is 12, and 4 times 12 is 48; 1 of 48 is 12, and 9 times 12 is 108; of 42 is 6, and 2 times 6 is 12, and 12 is contained in 108, 9 times. of 42. of 36 is of 9 times Therefore of of 20? 15. of of 36 is off of how many times of of 120? 16. A man pays $400 rent, and of this is just of of twice his annual income; what is his annual income? 17. A boy being asked his age said that 18 years was 2 years less than times of his age; how old was he? ğ 18. The distance from Baltimore to Washington is 39 miles; if 5 miles be subtracted from of this For "changes" see Appendix, 72, page 173. distance, the remainder will be times the distance from Philadelphia to Baltimore; what is the distance from Philadelphia to Washington? 19. Mr. B., who is 64 years of age, is 23 times as old as his eldest son, and his eldest son is 23 times as old as his youngest brother; what is the difference in the ages of the two brothers? 20. Oscar earned a certain number of pennies; Rufus earned as many minus 4, and David earned as many as Rufus, plus 7; Oscar earned 50 pennies; how many did Rufus and David earn? 21. A man put his money into 4 packages; in the first he put 2, in the second, in the third, and in the fourth $24; how much money had he? 22. A sold of his sheep on Monday; Tuesday he bought as many as he had sold; he then had 60 sheep; how many had he at first? 23. Mrs. D.'s shawl cost $30; of the cost of the shawl was of 6 times the cost of her dress; what was the cost of her dress? 24. B and C engaging in play, B had as much money as C; C gained $16, which was of 12 times 3 as much as he commenced with; how much did he commence with, and how much had B left? 25. A farmer, being asked how many sheep he had, replied that he had just sold 150, and that the number he had sold was 6 times of what he had left; how many had he left? 26. Mr. S. gave of 1 times his ready money for a buggy, of what was left for a harness, and had $12 remaining; what did he pay for the buggy? 27. A paid $4800 for his farm; of this is 41 times of 2 times what it cost to build the house; what was the cost of the house? 28. of of 80 is of of how many times of of 100? CHAPTER VII. RATIO AND PROPORTION. 73. 1. What part of 4 is 1 ? of 4 is 3?* Since 1 is of 4, 3 must be 3 times part ANALYSIS. of 4, or 2 of 4. Therefore 3 is of 4. ANALYSIS. 1 is the same as 13, and } = 18; the ratio of 10 to that of their numerators, 10 to 12: what part of 12 is 10? 12. Therefore is of t, and the of 20 is 17? 9? is? What is the ratio? 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 4, the What part of 4 is 3? It is 3 divided by 4, equal to , the ratio. 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 2 of 8 miles? 29. What part of 4 acres is of 34 acres? 30. A man, having $15, gave $31 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 4 miles while another walks 33 miles; what part of the distance that the first walks does the second walk? 34. 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 $7 for a barrel of flour, and 1 times as much for a ton of hay; what was the cost of the nay? 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 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? |