a pigs are worth 30 sheep, how many sheep did he get for his horses? 9. If 200 men in 12 days of 8 hr. each can dig a trench 160 yd. long, 6 yd. wide, and 4 yd. deep, in how many days of 10 hr. will 90 men dig a trench 450 yd. long, 4 yd. wide, and 3 yd. deep? 10. 5 compositors, in 16 da. of 14 hr. each, can compose 20 sheets of 24 pages in each sheet, 50 lines in a page, 40 letters in a line. In how many days of 7 hr. each will 10 compositors compose a volume containing 40 sheets, 16 pages in a sheet, 60 lines in a page, 50 letters in a line? 11. At 6%, what principal will gain $27 in 9 months ? 12. If 12 horses eat 10 bu. of oats in 8 da., how many 8 bushels will 30 horses eat in 40 days? 13. If it takes 22 reams of paper to make 1000 copies of a book of 11 sheets, how many reams will be required to make 4500 copies of a book of 7 sheets ? 14. If a field 60 rods long and 20 rods wide cost $500, what will a field 15 chains long and 8 chains wide cost? 15. If a piece of iron 7 ft. long, 4 in. wide, and 6 in. thick weighs 600 lb., how much will a piece of iron weigh that is 16 ft. long, 8 in, wide, and 4 in. thick ? 16. If a 6-cent loaf weighs 8 ounces when wheat is $1.25 per bu., how much bread may be bought for 50 cents when wheat is $1.00 per bushel ? 17. A ship's crew of 32 men, at a daily allowance of 3 lb. to each man, have provisions enough for 45 days. If they now rescue a crew of 16 men, what can be allowed each man daily to make the provisions hold out 40 days ? 18. 4000 copies of a book, containing 420 pages, were printed from 650 reams of paper ; how paper would have been required to print 7000 copies, containing 528 pages, of the same size? 19. If $500 will gain $16.50 in 4 mo. 12 da., at 9%, how much will $750 gain in 2 yr. 9 mo. 8 da., at 6% ? 20. If 3280 42-lb. shot cost $3000, how many 32-lb. shot can be bought for $4200 ? 21. How many hours a day must 5 men work to mow a field in 8 days, that 7 men can mow in 6 days of 10 hours ? 22. If 25 horses can consume a bin of grain in 40 days, in what time will a bin of twice the size be consumed, if 7 horses are added when the grain is f eaten ? 23. $600 gains $72 in 2 years. In how many years at the same rate will $92 gain $54? CAUSE AND EFFECT. Since like causes produce like effects, we have the following general formula : 1st cause : 2d cause : : 1st effect : 2d effect. ILLUSTRATIONS. 1. If 4 men earn $144, how much will 6 men earn in the same time and at the same rate ? Process. Let x be the required effect, representing what 6 men will earn, and we have : 2. If 4 men earn $144 in 12 days, how much will 6 men earn in 10 days at the same rate ? NOTE.—Here there are compound causes, consisting of men and days. } X= Process. Let x dollars be the required effect of 6 men and 10 days, and we have : 5 36 6 x 19 x 144 $180. 12 : 10 4 x 12 2 PROBLEMS. 1. If 3 workmen can board 4 weeks for $54, how many can board 13 weeks for $585 ? ef. ef. Suggestion : :: 54 : 585. 3:3 } 13 2. If 36 men earn $1296 in 13 days, how much will 42 men earn in 87 days ? 3. If 12 horses consume 40 bu. of oats in 8 days, how long will 140 bu. of oats last 16 horses? Suggestion : Let x days be a cause. 4. If it cost $15 to carry 20 tons 17 miles, what will it cost to carry 400 tons } of a mile? 5. If A. can do it of a piece of work in 5 da., working 8 hr. a da., how long will it take him to do the whole piece, working 10 hr. a day? 6. If 12 horses in 5 da. draw 44 loads of stone, how many horses will draw 132 loads the same distance in 18 da. ? NOTE.-If additional practice is needed in applying the principle of cause and effect, any of the previous problems in proportion may be used. PROPORTIONAL PARTS. A number may be divided into parts which are proportional to two or more given numbers. ILLUSTRATIONS. 1. Divide the number 180 into three parts that shall be to one another as 3, 4, and 5. 2. Divide 940 in the proportion of }, }, 1: = Process. The L. C. D. of the fractions is 60. }= ; } = {f; = 4= 16 940 = 12 + 20 + 15 = 47 parts. 14 of 940 240. 940. . 12 parts 15 parts PROBLEMS. 1. Divide 60 into two parts that are to each other as 5 and 7. 2. Divide 1200 into parts proportional to 11, 12, 13, 14. 3. Divide 780 into parts proportional to 1, 3, 1. 4. Three men caught 120 fish. How many did each catch, their proportions being as 2, 13, and 1 ? 5. Divide a profit of $13,384 among three partners, the first owning 34, the second 34, the third 14. 6. Divide $9 into parts that are to each other as .05, .10, .25, and .50. 7. A house, a farm, and a store cost $18,000. The farm cost twice as much as the house, and the store three times as much as the house. How much did each cost ? 8. Three men agree to pay $60 rent for a pasture lot; the first pastures 3 cows, the second 5 cows, and the third 4 cows. How much should each pay ? 9. If gunpowder contains nitre, charcoal, and sulphur in the proportion of 15, 3, and 2, and if in a quantity of gunpowder there is 20 cwt. of charcoal, find the weight of nitre and sulphur therein. PARTNERSHIP. 1. Partnership is of two kinds,-Simple and Compound. 2. It is simple when the capital of the partners continues in the business for the same time. 3. It is compound when the capital of the partners continues in the business for different lengths of time. Time, therefore, has to be considered in the proportional division of gains or losses. ILLUSTRATIONS. 1. Two men, A. and B., enter into partnership, and gain in 1 yr. $500. What part of the gain did each own if A.'s capital was $3000 and B.'s $2000 ? Process. A.'s capital is to B.'s as 3 to 2. $500, of $500 = $300, A.'s share; of $500 = $200, B.'s share. 2. But suppose A. had $3000 in business for 3 yr., and B. had $2000 in business for 2 yr.; how would $1300 gain be divided proportionally ? Difference of time must be considered as well as difference of capital. 2 parts |