800 feet being of the same kind as the answer, we make it the third term. But the number of feet required depends upon two conditions: 1st, the number of gas-burners, and, 2d, the number of hours during which they are burning. We shall deal with each condition separately, As 12 burners will consume more gas than 10 burners, we make 12 the second term and 10 the first term; and as they will burn more in 15 hours than in 3 hours, we make 15 the second term and 3 the first term. We find the fourth term, as in simple proportion, by dividing the product of the means, 12 X 15 X 800, by the product of the first extremes, 10 X 3. The process may sometimes be shortened by cancelling the terms as they stand in the proportion, remembering that the numbers which constitute the first terms are divisors, and those which constitute the second and third are multipliers. Thus, From the above we derive the following RULE FOR PERFORMING EXAMPLES BY COMPOUND PROPORTION. Make the number that is of the same kind as the answer the third term. Take each two numbers that are of the same kind, and consider whether, depending upon them alone, the answer will be greater or less than the third term. Arrange them as in simple proportion. Divide the continued product of the second and third terms by the continued product of the first terms. EXAMPLES. 1. If $90 is paid for the labor of 20 men 6 days, what should be paid for 5 men 8 days? Ans. $30. 2. If 85 tons of coal were required to run 6 engines 17 hours a day, what number would be required to run 25 engines 12 hours a day? Ans, 250 tons. 3. If 120 rods of wall were laid by 72 men in 33 days of 14 hours each, how many rods would be laid by 88 men, working 12 hours a day for 3 days? Ans. 134 rds. 4. If the wages of 75 men for 84 days were $68.75, for how many days could 90 men be employed for $41.25? Ans. 42 d. 5. If the freight on 450 lbs. of merchandise is 30 cents for 26 miles, how many miles can 3 tons be carried for $4? Ans. 26 m. 6. If, when flour is $7.50 per bbl., a 3-cent loaf weighs 2 oz., what should a 12-cent loaf weigh when flour is $16? Ans. 33 oz. 7. If a loaf, which sells for 10 cents when wheat is $2 a bushel, weighs 1 lbs., what is the price of wheat when a 6-cent loaf weighs 14 lbs.? Ans. $1.44. 8. If 500 lbs. of wool worth 42 cents a lb. is given for 75 yds. of cloth 1ğ yds. wide, how much wool worth 36 cents a lb. should be given for 27 yds. that is 14 yds. wide? Ans. 19311 lb. 9. If it costs $135.02 to carry 7 cwt. 2 qr. 15 lb. a distance of 64 miles, what will be the cost of carrying 11 cwt. 2 qr. a distance of 15 miles? Ans. $49.157+. 10. If 25 men, in 9 days of 10 hours each, build 200 rods of wall, how many rods would be built in 1 day of 12 hours by 12 men? Ans. 121 rds. 11. If 11 men, in 20 days of 12 hours each, can build a wall 48 feet long, 8 feet high, and 3 feet thick, in how many days can 15 men, working 10 hours a day, build 440 ft. of wall 12 ft. high, and 4 ft. thick? Ans. 322 d. 12. How many men will be required, working 12 hours a day for 250 days, to dig a ditch 750 ft. long, 4 ft. wide, and 3 ft. deep, if it requires 27 men, working 13 hours a day for 62 days, to dig a ditch 403 ft. long, 3 ft. wide, and 3 ft. deep? Ans. 18 men 13. If 5 men, working 12 hours a day for 8 days, cut 44 loads of wood, each 8 ft. long, 4 ft. wide, and 4 ft. 6 in. high, in how many hours would 16 men cut 49 loads 8 ft. long, 4 ft. wide, and 5 ft. 6 in. high? Ans. 414 hours. 14. If 7 cases of boots can be made by 9 men laboring 12 hours a day for 7 days, what length of time will be required for 3 men and 4 boys (2 boys being equal to a man and a half), laboring 11 hours a day, to make 33 cases? Ans. 54 d. 15. If 421% rods of fence which is 4 feet high be built by 9 men in 10 days of 9 hours each, how many rods of a fence 5 ft. high will be built by 8 men in 6 days of 8 hours each? 16. What length of canal 27 ft. wide, 24 ft. deep, can be dug by 250 men in 100 days of 12 hours each, if 750 men in 3 months of 25 days each, working 11 hours a day, could dig 4 miles of a canal 30 ft. wide and 10 ft. deep? Ans. 7 fur., 7 rods, 5 ft., 23 in. 17. If the type for a book of 84 pages, 50 lines to a page, lines averaging 8 words, 14 syllables to a word, 2 letters to a syllable, was set by 2 men in 5 days of 12 hours each, how many pages of a book, each page containing 75 lines, averaging 5 words each, 2 syllables to a word, 3 letters to a syllable, would be set by 7 men, laboring 8 hours a day for the working days of a week? Ans. 142 pages. 18 If 12 men, in 2 months of 4 weeks each, working 6 days per week, 12 hours a day, can set the type for 12 books, of 600 pages each, 120 lines to a page, 20 words to a line, 10 letters to a word, in how many months of 4 weeks each will 7 boys, working 4 days per week, 16 hours a day, set the type for 6 books, of 500 pages each, 150 lines to a page, lines averaging 24 words, 4 letters to a word, each boy doing of the work of a man? Ans. 17 months. yd. wide, to line a cloak qrs. wide, how many yards 19. If it requires 15 yds. of silk, made of 12.25 yds. of cloth, 1 yd. 1 of silk, yd. wide, will be required to line a cloak made of 8.33 yds., 43 qrs. wide? Ans. 47 yds. 20* If 4 men dig a cellar 33.75 ft. long, 18 ft. wide, and 9.6 ft. deep, in 4.5 days of 11.25 hours each, in how many days of 11.7 hours will 15 men dig a cellar 15.2 yds. long, 7.8 yds. wide, and 10.8 ft. deep, the latter cellar being twice as hard to dig as the former? For Dictation Exercises, see Key. PARTNERSHIP, OR PARTITIVE PROPORTION. 376. Partnership is the association of two or more persons for the transaction of business. The persons thus associated are called Partners. The profits and losses are generally shared by the partners in proportion to the stock each has in trade, and the time it is employed. ILL. EX. A and B formed a partnership for one year. A put in $800, and B $700. They gain $375. What is the share of each? If $1500 gain $375, $1 will gain of $375, and $800 will gain 800 X 1300 of $375 $200, A's share, and $700 will gain 700 X 1500 of $375 $175, B's share. Hence the RULE FOR SIMPLE PARTNERSHIP. Apportion the gain or loss among the partners according to their stock in trade. EXAMPLES. 1. A and B form a partnership, A putting in $4000, and b $3000; they gain $3000; what is the share of each? Ans. A, $1714; B, $12855. 2. E, S, and Z invest in trade as follows: E $500, S $800, and Z $300; they gain $375.75; what is the share of each? Ans E, $117.42; S, $187.87; Z, $70.45. 3. Two traders, A and B, shipped coal from Philadelphia to Boston. A had on board 350 tons, and B 900 tons. It became necessary to throw overboard 250 tons. What was the loss of each? Ans. A, 70 tons; B, 180 tons. 4. Four persons, H, I, K, and L, engaged in an adventure H furnished $275; I, $640; K, $330; L, as much as H and K. They gained $4675. What was the share of each? Ans. H, $694.93; I, $1617.2937; K, $833.913; L, $1528.85. 5. A bankrupt owes to Q $800, to R $350, and to X and Y $500 each; his whole property sells for $1584.80, of which $158.48 are required to pay the expenses of the sale; what will Ans. Q receives $530.721; R, $232.1975; X and Y, each, $331.7019. 6. Gerry & Frost enter into a dry goods business. G puts in 250 pieces of cotton, 30 yds. each, at 10 cts.; 100 yds. broad cloth, at $3.25; and $918.75 in cash. F puts in 40 pieces linen, 12 yds. each, at 28 cts.; other goods to the amount of $500, and cash $565.60. On closing business, they find they have lost 40% of their investment. What is the loss of each? 7. Four persons, M, N, O, and P, engaged in partnership. M put in 700 bu. wheat, at $1.25; N, 1000 lbs. wool, at $.37; 0, 500 bbls. fleur, at $6.50; P, 2000 bu. corn, at $.90. Their whole stock being destroyed by fire, the firm received insurance on the goods, $4200; what was the loss to each partner? 8. Suppose the store occupied by the above persons, owned by A, B, and C, and valued at $80000, to have been insured for of its value. What would be the loss to each partner by the fire, the store being entirely consumed, A owning, B, and C the remainder? Ans. A, $5000; B, $66663; C, $83331. 9. Banks & Ward traded in company, and gained $975. It was agreed that B should have $8 of the gain as often as W had $7. What was the share of each? Ans. B, $520; W, $455. 10. Divide $1500 among three persons so that their shares shall be in the proportion of 3, 4, and 5. 11. Five persons, A, B, &c., hired a pasture for $275. A put in 250 sheep, B 300 sheep, C 200 sheep, D 15 yoke of oxen,' and E 10 yoke. One ox being equal to 10 sheep, what was due from each? Ans. A, $55; B, $66; C, $44; D, $66; E, $44. 12. F, G, H, and I are in partnership as stock brokers. F furnishes $2000, G $2500, H $1500, and I 75 shares of railroad stock. They gain $3300, of which I receives $1100; what was his stock per share, and what is the gain of each of the other partners? Ans. F, $7331; G, $916; H, $550; I, $ 40 a share. 13. Stewart & Mills traded in company for one year. Their gain was equal to 20% of their stock. S's share of the gain was |
