4. The rent of my house is $200 for 5 months; what is the rent for a year? 5. The interest on my money for 3 months is $75; what is the interest on the same amount for 18 months? 6. Paid $67.50 for 9 tons of coal; what is the cost of 1 ton? 7. 3 bushels 2 pecks of potatoes cost $3.50; what is the cost of 1 peck ? 8. 12 men can do a piece of work in 17 days; how long will it take 36 men to do the work? 9. $111.50 : $27.50 :: 33 : what? 10. 560 miles : 28 miles :: 20 hours : how many hours? 11. If of a dollar will purchase 1 bushel of peaches, what will 5 bushels cost? 12. If 23 yd. of cloth cost $5.50, what will 1 yd. cost? 13. If £1 is worth $4.8665, what is the value of £7 6s.? 14. If a horse can travel 42 miles in 10 hours and 30 minutes, how far can he travel in 16 hours? 15. If six men can do a piece of work in 12 days when the days are 12 hours long, how long would they require to do the same work when the days are only 8 hours in length ? 16. If 14 acres of land cost $600, what is the worth of 33 acres, at the same rate? 17. If a certain sum of money earns $25 in 34 months, how long will it require to earn $125? 18. 24 yards of carpet cost £16 10 s.; what will 48 yards cost? 19. At the rate of $25 a month, what is the rent of a house for 4 years? 20. If 124 cents will buy 1 lb. of tea, how much can be bought for $1.25? COMPOUND PROPORTION. A Compound Proportion expresses the equality of two ratios, one or both of which are compound. ORAL EXERCISES. 1. If 4 men can dig a well in 8 days, how many such wells can 12 men dig in 16 days? ANALYSIS.—As 12 men can dig more wells than 4 men, the ratio of the men is 12:4, or 12. As more wells can be dug in 16 days than in 8 days, the ratio of the days is 16 : 8, or 16. As the required answer is a number of wells, 1 well is the third term. Multiplying the compound ratio 1.2 x 16 by 1, and cancelling common factors, we obtain 6 as the number of wells required. 2. If 2 men pay $10 for 10 days' board, what should 4 men pay for 20 days' board ? 3. If a 4-cent loaf weighs 8 oz., when flour is $4 per barrel, what should an 8-cent loaf weigh, when flour is $8 per barrel ? 4. If $10 earn 6 cents in 1 month, how much should $20 earn in 6 months ? 5. If I can buy 4 apples for 5 cents, when apples are $4 a barrel, how many apples ought I to receive for 10 cents, when a barrel can be bought for $2? 6. If a man can travel 100 miles in 10 days, walking 10 hours a day, how far can he travel in 5 days, walking 5 hours a day? my. If 6 men can do a piece of work in 10 days, working 10 hours a day, how long will it require 10 men to do the same amount of work, if they work 3 hours a day? 8. 8:12 4.2 :: 18 : what? x = how many 18ths? WRITTEN EXERCISES. 1. If 1 man can saw 40 cords of wood in 10 days of 9 hours in length, how many cords can 4 men saw in 6 days of 10 hours in length? * * L * * x 40 = sql = 1063, cords. ANALYSIS.--As less work can be done in 6 days than in 10, the ratio of the days is 6 : 10, or b. As in 10 hours more work can be done than in 9, the ratio of the hours is 10 : 9, or 10. 4 men can do more work than 1, in the ratio of 4 : 1, or 4 40 cords is the remaining term, the answer being required in cords. Multiplying the product of the compound ratios by 40, and cancelling common factors, we obtain 106 as the number of cords. RULE. Express the ratio of each pair of terms that are of the same kind, as a proper fraction when the answer, considered with reference to that pair, requires to be less than the term which is of the same kind as the answer, and as an improper fraction when the answer requires to be greater, and mul"tiply the product of these fractions by the term which is of the same kind as the answer. 2. 10: 4 14:91 15:7). 3. If 24 men in 9 days of 9 hours each, can dig a ditch 300 feet long, 3 feet wide, and 1 foot deep, how long will it take 60 men to dig a ditch 150 feet long, 2 feet wide, and 3 feet deep? 4. 40 : 65 40: 801 75 : 20 30: 50 32 : 8) :: 300 : what? 60: 15% :: 125 : what? 9:27 25 : 100 14: 77 33: 60 / 5. If 2 barrels of four will last 10 persons 7 weeks, how many persons would be required to consume 40 barrels of flour in 1 week? 6. If $60 is the interest of $1000 for 12 months, at 6 per cent., what is the interest of $50 for 5 months, at 8 per cent. ? 19. If $25 gain 15 cents in 30 days, what will $75 gain in 90 days? 8. If 12 men can earn $240 in 20 days, working 9 hours a day, what should 36 men earn in 15 days, working 12 hours a day? 9. If 15 yards of silk will make 1 dress, the silk being 36 inches wide, how many yards will be required for 10 such dresses, if the width of the silk is 42 inches ? 10. If 10 apples can be bought for 15 cents, when apples are worth $4.50 a barrel, how many apples can be bought for 25 cents, when a barrel is worth $5? 11. If cloth & wide is worth $3.75 a yard, what should 16 yards of similar quality cost, the width being ? 12. If the tax on a house worth $2500 is $56.25, at a rate of 21%, what should the tax be on a house valued at $15000, if the rate of taxation is 41% ? 13. If it costs $6150 to carry 30750 tons 10 miles, how much should it cost to carry 500 tons 1000 miles, at the same rate? 14. If a family of 8 persons can use 31 gallons of milk in one week, in how many days, at the same rate, can a family of 16 persons use one half as much? 15. It requires 15 days to build a wall 60.5 ft. long, 18 in. thick, and 25.25 ft. high; how long will it require, at the same rate, to build a wall 120 ft. long, 12 in. thick, and 274 ft. high? PARTNERSHIP. A Partnership is an association of two or more persons for the purpose of transacting business. A Simple Partnership is one in which each partner has his share of the capital employed for the same length of time. A Compound Partnership is one in which the capital of the partners is employed for different lengths of time. The Capital, or Stock, is the amount of property invested in the business. The Partners are known as a Firm, or Company, and are frequently called a House. The profits or losses of the firm are divided among the partners according to each one's share in the business. SIMPLE PARTNERSHIP. ORAL EXERCISES. 1. A and B enter into partnership; A puts in $1000, and B $500; they gain $100; what is the gain of each? ANALYSIS.—The total capital was $1500 and the gain $100; A puts in $1000, and is therefore entitled to 1600, or of $100 =$664; B puts in $500, and is therefore entitled to 1660, or $ of $100=$335. 2. Two boys buy 100 marbles; the first pays 4 cents, and the second 6 cents; how many marbles should each receive? 3. A and B own a house which rents for $500 a year; A paid $4000 as his share of the cost of the house, and B paid $6000; how should the rent be divided between them? |