350. Rule for Simple Proportion. Make that number which is of the same kind as the answer the third term. If from the nature of the question the answer is to be larger than the third term, make the larger of the remaining numbers the second and the smaller the first term ; but if the answer is to be smaller than the third term, make the second term smaller than the first. Divide the product of the means by the given extreme, and the quotient is the fourth term, or answer. 40. When $ 120 are paid for 15 barrels of flour, what will 79 barrels cost ? 41. If 7 gallons of molasses cost $ 5.88, what will 27 gallons cost? 42. If a man travel 319 miles in 11 days, how far will he travel in 47 days ? 43. If 27 men can do a piece of work in 12 đays, how long will it take 36 men to do it ? 44. Find the cost of 7 sheep when 98 cost $ 441. 45. What time should 24 men take to perform a piece of work which 18 men can perform in 15 days ? 46. A garrison of 2100 men has provisions for 9 months, but receives a reinforcement of 600 men. How long will the provisions last ? 47. If 47 bushels of oats cost $27, what will 19} bushels cost ? 48. 74 men had provisions for 35 days, but after five days 20 men were sent away. How long will the provisions last the remaining 54 men ? 49. If 6336 stones of 34 feet in length will make a certain quantity of wall, how many similar stones of 23 feet in length will make a like quantity ? 50. If 3 tons of coal cost $ 27.50, what will 45 tons cost ? 51. A certain piece of work was to have been performed by 288 men in 72 days, but, a number of them having been sent away, it was performed in 108 days. What was the number of men sent away ? 52. If 3} cords of wood cost $11.37}, what will 12} cords cost ? COMPOUND PROPORTION. 351. A Compound Proportion is an equality between a compound and a simple ratio. Thus, 3:4) = 45 : 96 is a compound proportion. It applies to the solution of questions which would require several simple proportions. · WRITTEN EXERCISES. 53. If 4 men can earn $ 64 in 8 days, how much can 12 men earn in 3 days ? Solution. — As the answer sought 8: 2}= $64 : $3 is in dollars, we make the $64 the Or, third term, and X, representing the 3 8 answer, the fourth term. If the an12 X 3 X 64 swer depended only on the number 2 = 72 of men, it would be larger than the 8 X4 third term, as 12 men will earn inore than 4 men; hence the first ratio is 4 to 12. But if the answer depended only on the number of days worked it would be smaller than the third term, as less can be earned in 3 days than in 8 days ; hence the second ratio is 9 to 3. Dividing the product of the means by the product of the given extremes, we have $ 72 as the answer. Or, if 4 men can earn $ 64 in 8 days, 12 men in the same time can earn 4 of $ 64, and in 3 days f of 4 of $ 64, or $72. 352. Rule for Compound Proportion. Make that number which is like the answer the third term. Form a ratio of each pair of the remaining numbers of the same kind according to the rule for simple proportion, as if the answer depended on them alone. Divide the product of the means by the product of the given extremes, and the quotient is the fourth term, or answer. 54. If 3 men can make 108 pairs of shoes in 2 days, how many pairs can 2 men make in a week ? 55. If $ 250 yields $175 interest in 7 years, how long will it take $ 500 to yield $ 360 at the same rate ? 56. If 24 men can reap 76 acres in 6 days, how many men will reap 114 acres in 9 days ? 57. How many acres can 10 men plow in 14 hours, if 5 men plow 6 acres in 102 hours ? 58. Two cogged wheels, one of which has 15 cogs and the other 28, work in each other. If the first turns 16 times in 71 seconds, how often will the other turn in 4 seconds ? 59. If 15 men are fed for 7 days when flour is $8 a barrel, what must be the price when 10 men are fed 8 days at the same cost ? 60. If a man travels 117 miles in 15 days, employing only 9 hours, how far would he go in 20 days, traveling 12 hours a day? 61. If 96 horses eat 192 tons of hay in one winter, how many tons will 150 horses eat in 6 winters ? 62. If a man, walking 12 hours each day, travels 250 miles in 9 days, in how many days, walking 10 hours each, at the same rate, would he travel 400 miles ? 63. If the expenses of a family of 8 persons amount to $ 84 in 16 weeks, how long will $ 200 support a family of 6 persons ? 64. If a pasture of 16 acres will feed 6 horses for 4 months, how many acres will feed 12 horses for 9 months ? 65. If 180 bricks, 8 inches long and 4 inches wide, are required for a walk 20 feet long and 6 feet wide, how many bricks will be required for a walk 100 feet long and 4 feet wide ? 66. If 34 men can saw 90 cords of wood in 6 days, when the days are 9 hours long, how many cords can 8 men saw in 36 days when they are 12 hours long? 67. If 12 men in 15 days can build a wall 30 feet long, 6 feet high, and 3 feet thick, working 12 hours a day, in what time will 30 men build a wall 300 feet long, 8 feet bigh, and 6 feet thick, working 8 hours a day? 68. If a loaf which sells for 20 cents when wheat is $4 a bushel, weighs 3 pounds, what is the price of wheat when a 12-cent loaf weighs 2} pounds ? . . 69. If a bin 8 ft. long, 4) ft. wide, and 2} ft. deep, holds 67} bu., how deep must another bin be made, that is 18 ft. long and 38 ft. wide, to hold 450 bu. ? 70. If the annual salary of a man who works 8 hours a day, 48 weeks in the year, is $ 1200, how much ought a conductor to receive per month who works 14 hours daily the year round? QUESTIONS. 338. What is ratio ? 338. How is it determined ? 340. What are the terms of a ratio ? 341. What is an inverse ratio ? 342. A simple ratio ? 343. A compound ratio ? 344. What are the principles of ratio ? 345. What is a proportion ? 346. What is each term of a proportion called ? What is a mean proportional ? 348. What are the principles of proportion ? 319. What is a simple proportion ? 350. Which number is made the third term ? How are the terms arranged ? How, then, is the required extreme found ? 351. What is a compound proportion ? 352. Which term is made the third term ? How is each pair of the remaining numbers arranged? How, then, is the required term found ? PARTNERSHIP. 353. 1. Two men share between them $35, the one receiving $3 as often as the other $ 4. How much does each receive ? 2. What number is of 35 ? of 35 ? 3. A and B are in business together. A put in $ 3000 and B $ 5000. They gain $ 800. What are their respective shares of it? 4. Divide $ 800 into two parts having the ratio of 3 to 5. 5. Divide 54 oranges between two boys in the ratio of 4 to 5. 354. Partnership is the association of two or more persons in business. 355. The Company, or Firm, is the association, and the Partners are the members. 356. The Capital, or Stock, is that which is invested in the business, and the Dividend is the profits shared by the partners. The profits or losses are usually shared according to the terms of the agreement, or contract, made when the partnership is formed. In the absence of a special agreement, dividends are in proportion to the capital invested and the time during which it is invested. WRITTEN EXERCISES. 6. A, B, and C engage in trade. A furnishes $ 200, B $ 250, and C $350. They gain $ 100.80. What is each partner's share of the gain ? |