21. 1. If 6 men receive 72 dollars for building a barn, how many dollars will each man receive? ANALYSIS. If 6 men receive 72 dollars, 1 man will receive as many dollars as 6 is contained times in 72, which is 12 times. Therefore, if 6 men receive 72 dollars for building a barn, each man will receive 12 dollars. NOTE. If the pupil is sufficiently acquainted with Fractions, the following Analysis is often preferred.* ANALYSIS. If 6 men receive 72 dollars, 1 man, which ist of 6 men, will receive of 72 dollars, which is 12 dollars. Therefore, &c. 2. If 81 cents be paid for 9 dozen of eggs, what will be the cost of 1 dozen? 3. A mechanic sold a wagon for 77 dollars, and took his pay in hay, at 11 dollars a ton; how many tons did he receive? 4. How long will it take 12 men to perform a piece of work that 1 man can do in 48 days? 5. Paid 108 dollars for 9 thousand feet of lumber; what was the cost of a thousand feet? 6. How many barrels of flour can be bought for 56 dollars, at 7 dollars a barrel? at 8 dollars? 7. How many cows, at 12 dollars a head, can be bought for 60 dollars? for 96 dollars? for 120 dollars? 8. When steak is 10 cents a pound, how many pounds can be bought for 50 cents? for 80 cents? for 100 cents? 9. At 11 cents a pound, how many pounds of sugar can be bought for 88 cents? for 99 cents? * When any number or thing is divided into two equal parts, each of the parts is called one half; when into three equal parts, each of the parts is called one third; when into four equal parts, each of the parts is called one fourth; when into five equal parts, each of the parts is called one fifth; two of the parts, two fifths, &c.; when into six equal parts, each of the parts is called one sixth; two of the parts, two sixths, three of the parts, three sixths, &c. 10. A man planted an orchard of 132 trees, and put 11 trees in a row; how many rows in the orchard? 11. A farmer sold a horse for 120 dollars; how many cows at 12 dollars each would pay for the horse? How many young cattle at 8 dollars each? How many sheep at 5 dollars each? 12. If 25 sheep cost 75 dollars, what will 1 sheep cost? 13. If a boy read 7 pages a day, how long will it take him to read 56 pages? to read 84 pages? 98 pages? 14. At.15 cents a pound, how many pounds of coffee can be bought for 45 cents? for 60 cents? for 90 cents? 15. If 1 man can do a piece of work in 72 days, in what time can 6 men do it? 8 men? 9 men? 12 men? 16. If a certain quantity of provision will last 1 man 36 days, how many days will it last 4 men? 9 men? 12 men? 17. A man earns 66 dollars in 11 weeks; how much does he earn in 1 week? how much in 1 day? 18. If a painter receive 100 dollars for painting 5 carriages, how much does he receive apiece? 19. How many lots containing 12 acres each can be sold from a farm of 120 acres? how many lots of 20 acres each? 20. If a steamboat run 11 miles an hour, how long will she be in running 44 miles? 88 miles? 110 miles? 21. How many men, at 8 dollars a month, can be hired one month for 96 dollars? how many at 12 dollars? how many at 16 dollars? 22. If I travel 120 miles in 6 days, how many miles do I travel in 1 day? 22. 1. If 3 pounds of coffee cost 27 cents, what will 6 pounds cost? ANALYSIS. If 3 pounds of coffee cost 27 cents, 1 pound, which is 1 third of 3 pounds, will cost 1 third of 27 cents, or 9 cents. If 1 pound cost 9 cents, 6 pounds, which are 6 times 1 pound, will cost 6 times 9 cents, or 54 cents. Therefore, if 3 pounds of coffee cost 27 cents, 6 pounds will cost 54 cents. Or thus: 6 pounds will cost 6 times 1 third of 27 cents; 1 third of 27 cents is 9 cents, and 6 times 9 cents are 54 cents. Therefore, &c. Or 6 pounds, which are 2 times 3 pounds, will cost 2 times 27 cents, &c. 2. If 4 yards of broadcloth cost 20 dollars, what will 9 yards cost? 3. If 6 barrels of flour cost 54 dollars, what will 7 barrels cost? 4. If 9 yards of ribbon cost 72 cents, what will 4 yards cost? 5. If a man travel 40 miles in 8 hours, how far will he travel in 6 hours? in 9 hours? 6. If 5 coats can be cut from 20 yards of cloth, how many yards would be required to cut 7 coats? 7. If 9 weeks' board cost 45 dollars, what will 4 weeks' board cost? 7 weeks'? 12 weeks' ? 8. If a boy earn 60 cents in 5 days, how many cents will he earn in 12 days? in 20 days? 9. What will be the cost of 10 cords of wood, if 6 cords cost 24 dollars? 10. What will be the cost of 14 dozen of eggs, if 12 dozen cost 120 cents? 11. If 18 apples are worth 6 peaches, how many apples are 15 peaches worth? 20 peaches? 12. If a stage coach run 48 miles in 8 hours, in how many hours will it run 60 miles? 13. If 15 yards of cloth cost 75 dollars, what will 40 yards cost? 14. How many melons can be bought for 100 cents, at the rate of 3 for 60 cents ? 15. What will 42 pounds of beef cost, if 7 pounds cost 56 cents? 16. When apples are sold at the rate of 4 barrels for 8 dollars, how many barrels must be given for 3 tons of coal at 6 dollars a ton? 17. How many dozen of eggs, at 12 cents a dozen, will pay for 15 pounds of sugar, at 8 cents a pound? 18. How many gallons of molasses, at 50 cents a gallon, will pay for 20 pounds of lard, worth 10 cents a pound? 19. If a farmer sell 5 firkins of butter, worth 12 dollars a firkin, for cloth worth 4 dollars a yard, how many yards will he receive? 20. If 5 barrels of cider are worth 15 dollars, how many hundred weight of pork,worth 6 dollars a hundred weight, would 8 barrels of cider buy? 21. If 6 bushels of wheat are worth 12 dollars, how many bushels of wheat must be given for 9 tons of hay, worth 10 dollars a ton? 22. At the rate of 3 for 4 cents, how many pears can be bought for 24 cents? ANALYSIS. Since 4 cents will buy 3 pears, 24 cents will buy as many times 3 pears as 4 cents is contained times in 24 cents, which is 6 times, and 6 times 3 pears are 18 pears. Therefore, if 3 pears can be bought for 4 cents, 18 pears may be bought for 24 cents. 23. A man paid 72 cents for some oranges, at the rate of 5 for 12 cents; how many oranges did he buy? 24. How many pounds of nails may be bought for 60 cents, at the rate of 4 pounds for 20 cents? 25. When eggs are sold at the rate of 9 for 11 cents, how many must be sold to receive 99 cents? 26. At the rate of 16 miles in 4 hours, how many miles would a man travel in 12 hours? 27. If 3 men can do a piece of work in 12 days, how many days will it take 9 men to do the same? ANALYSIS. If 3 men can do the work in 12 days, 1 man can do it in 3 times 12 days, or 36 days. 9 men can do it in 1 ninth as many days, (or as many days as 9 is contained times in 36,) which is 4 days. Therefore, &c. 28. If 6 men can build a wall in 8 days, how many men will be required to build it in 3 days? 29. If 4 men can dig a ditch in 10 days, how many days will it take 1 man to dig it? 5 men? 8 men? 30. How long will it take 7 men to reap a field, if it take 14 men 2 days to reap it ? 31. If 5 men can build a barn in 8 days, how many men would be required to build it in 1 day? in 2 days? in 4 days? 32. A man bought some oranges for 44 cents, at the rate of 5 for 11 cents, and divided them equally among his 4 children; how many did he give to each? · 33. If 15 days' work will pay for 10 cords of wood, at 3 dollars a cord, what is the price of 1 day's labor? 34. A man engaged to labor 5 months for 80 dollars, but by request continued 3 months longer, at the same rate; what amount will be due him for the whole time? 35. If you pay 60 cents for some lemons, at the rate of 6 for 10 cents, and sell them at the rate of 9 for 20 cents, how many cents will you gain by the operation? 36. If two ships are 120 miles apart, and sail directly toward each other, one at the rate of 9 miles an hour, and the other at the rate of 11 miles an hour, how many hours before they will meet? |