5. If $100 gain $6 interest in one year, how much will $57 gain in the same time? Ans. $3.42. 6. What is the value of 751⁄2lb. of pork, at $.08 or 8cts. per pound? Ans. $6.04. 7. If 42cwt. of flour be packed in 24 barrels, what quantity is that per barrel? Ans. 1cwt. 3qrs. 8. What is the value of 26 yards of cloth, at $1 25 cents per yard? Ans $32.50. of gold be coined into 380 9. If 8lb. 3oz. 15dwt. English guineas, what is the weight of each? Ans. 5dwt. 6grs. 10. If 15 bushels of wheat cost $14 25 cents, what will Ans. $6.65. steel, at 7 bushels cost at the same rate? Ans. $22.75. 12. If 8 yards of cloth cost $20, what will 96 yards cost at the same rate? Ans. $240. 13. If 135 bushels of wheat cost $74.25, what is the value of 25 bushels? Ans. $13.75. of work in 15 Ans. 12 days. of the United 14. If 20 men can accomplish a piece days, in what time will 25 men perform it? 15. The yearly income of the President States is $25000-how much is that per hour, the year consisting of 365 days 6 hours? Ans. $2.85+ 16. If $1.00 contains 371.25 grains of pure silver, what is the value of 8.25lbs. of pure silver? Ans. $128. 17. How much must I pay for the carriage of 10.5cwt. at the rate of 1cts. per pound? Ans. $17.64. 18. If 4cwt. of lead cost $13.44, what will 1lb. cost? Ans. $.03, or 3cts. 19. Required the value of 120 yards of cloth, at 30 cents per yard. Ans. $36. 20. If a footman perform a journey in three days, when the days are 16 hours long, how many days will it require, of 12 hours long, to perform the same journey? Ans. 4 days. 21. If a man take five steps in walking four yards, how many steps will he take in walking from Philadelphia to Lancaster, the distance being 64 miles, and each mile equal to 1760 yards? Ans. 140800 steps. 22. If 425 bushels of salt cost $263.50, what is it per bushel? Ans. 62cts. 23. If a man spend 8 cents per day, how much is that in a year? Ans. $29.22. 24. Bought 17cwt. 3qrs. 17lb. of tobacco, at one cent per oz.-what did it cost? Ans. $320.80. 25. If a staff 6 feet long, cast a shade on level ground 4.5 feet long, what is the height of a steeple, whose shade at the same time is 186 feet? Ans. 248 feet. 26. If a man ride 162 miles (or any other distance, the distance being arbitrary) in 4 days, when the days are 15 hours long, how many days of 12 hours will he require to perform the same journey? Ans. 5 days. 27. If 200 dollars in 12 months, bring 12 dollars interest, what sum will bring the same in 8 months? Ans. $300. 28. A lady asked me how many yards of nankin, 9 inches broad, it would take to cover or line 3 quilts, 10 feet long, and 9 feet broad. Ans. 120 yards. 9in.=.75ft. 3=2.25ft. in one yard of nankin. 10ft. × 9ft.=90ft. in one quilt× 3=270 feet in three. 29. A person purchased 120 gallons of rum for $78, and by adding water to it, he was enabled to sell it at 60 cents a gallon, without loss-how much water did he add? 60c.: 7800c. :: 1gal.=130gals. sold. 30. If lcwt. of iron be worth $4.25, what is the value of 33cwt. 1qr. 22lbs. ? Ans. $142.147 31. A bankrupt compounds with his creditors at 65cts. in the dollar-what is the dividend on $1256, at that rate? Ans. $816.40. 32. What is the value of 1cwt. of iron, at 8cts. per lb. ? Ans. $8.96. 33. If the daily expenses of the U. S. Senate be $324, and they sit five hours in the day, how much does a speech in that assembly, of 3 hours in length, cost the public? Ans. $194.40. 34. What is the value of 120 yards of muslin, at 30cts. per yard? Ans. $36. 35. The sentinel's cry, "all's well," at the fort of Gibraltar, is said to have been heard, under favorable circumstances, on the African shore, at the distance of 12 mileshow long was the sound in moving this distance, at the rate of 1142 feet per second? Ans. 55sec.+ 37. A gun being fired on one side of a river, an observer directly opposite counts ten pulsations at his wrist, between seeing the flash and hearing the report-what was the breadth of the river? Ans. 9136 feet=1m. 5f. 33p. 3.5y. 1ft. 38. There is a cistern having one pipe which will empty it in 10 hours-how many pipes of the same cavity or capacity, will empty it in 24 minutes? Ans. 25 pipes. 39. If 3 horses and 4 oxen be worth 9 cows, how many cows will 6 horses and 8 oxen be worth? Ans. 18 cows. 40. If the moon move 13deg. 10min. 35sec. in one day, in what time does it perform one revolution? Ans. 27 days 7 hrs. 43sec.+ 41. A goldsmith sold a tankard for £10 12s. at the rate of 5s. 4d. per ounce-I demand the weight of it. I Ans. 39oz. 15dwt. 42. If I can get 5lb. of almonds for 1 dollar, what must for 75lb.? pay Ans. $15. 43. If 9 pence be equal to 10 cents, how many pence are there in 9 dollars, or 900 cents? Ans. 810d. 44. What is the half-year's rent of 547 acres of land, at 15s. 6d. per acre? Ans. £211 19s. 3d. 45. What is the value of a pipe of wine, at 10 cents per pint? Ans. $100.80. 46. A and B depart from the same place, and travel the same road, but A goes 4 days before B, at the rate of 35 miles per day, B follows at the rate of 40 miles per day— in what time and distance will he overtake A ? 29 153 Ans. 28 days, at 1120 miles' distance. 47. Bought a cask of wine, at 76cts. 5m. per gallon, for $125-how much did it contain? Ans. 163gal. 1qt. 1,2%. 48. What is the value of 18 yds. of muslin, at 18cts. 5m. per yard? Ans. $3.46875. 49. If 160 square rods make one acre, in a lot of land 100 rods long, how many rods wide must it be to contain 60 acres? Ans. 96 rods in breadth. 50. If 30 yards of cloth, 5 quarters broad, be required to hang a bed, how many yards, 3 quarters broad, will serve the same? Ans. 50 yards. 51. I paid a man $78 for ten cords of hickory wood; wanting another cord, what must I pay for it at the same rate? Ans. $7.80. 52. If one pound ten, and forty groats* will buy a load of (A groat 4d., and a crown = 58.) hay, how many pounds and nineteen crowns sterling, for twenty loads will pay ? Ans. £38 11s. 8d. 53. There is a cistern which has 4 spigots; the first will empty it in 10 minutes, the second in 20 minutes, the third in 40 minutes, and the fourth in 80 minutes-in what time will all four running together empty it? M. M. Cist. Cist. In one hour the four spigots would empty 11.25 cisterns. Cist. Cist. M. Then, if 11.25: 1 :: 60: 5.333+ M. nearly 5 M. 54. How many yards of matting that is half a yard wide, will cover a room that is 18 feet wide, and 30 feet long? Ans. 120 yards. 55. How many barrels of corn will a Delaware farmer make from one fifty acre field, allowing it is quite smart, say fifteen barrels per acre? Ans. 750. 56. When butter is 16 cents per pound, how much can be bought with eight hundred cents? Ans. 50lb. 57. In a parlor that is 30 feet long, and 18 feet wide, how many yards of carpeting of 1 yard, of 2, and of width, respectively, will it require to cover the floor? yard in Ans. 60yds. of lyd. wide, 80yds. of 3qr., and 120yds. of half yard wide. 58. If 20 men can accomplish a piece of work in 15 days, in what time will 25 men perform it? Ans. 12 days. 59. The parallel of latitude passing through Philadelphia, is about 19150 miles, and the earth performs one rotation in 23 hours, 56 minutes, 4 seconds-how far then are the Philadelphians carried in an hour, by this motion? Ans. 800m. 32p. 3y. 2ft. 3,11-in. 60. If a field will feed 6 cows 91 days, how long will it Ans. 26 days. feed 21 cows? 61. At 80 cents per week, how many months' board can I have for $120? Ans. 37.5 months. 62. If 4 men can build a wall in 4 days, how many men can do it in 8 days? Ans. 2 men. 63. A cistern, containing 48 cubic feet of water, may supply an engine during 3 hours-how long can it supply 10 engines, in case of a fire? Ans. 18 minutes. 64. If 20 horses eat 70 bushels of oats in three weeks, how many bushels will six horses eat in the same time? Ans. 21 bushels. 65. How many bushels of wheat, at $1.12 per bushel, can I purchase for $81.76? Ans. 73 bushels. 66. Find a fourth term or proportional to 16 : 24 :: 36. 67. If a gentleman, whose annual income is 1200 dollars, spends $21 a week, will he save money, or run in debt; and how much in a year? Ans. save $108. 68. If three men or 4 women do a piece of work in 56 days, how long will one man and one woman be in doing the same? Ans. 96 days. 69. The imperial canal, which intersects China from north to south, employed 30,000 men 43 years in its construction -how many men must have been employed to have completed it in one year? Ans. 1290000 men. THE DOUBLE RULE OF THREE, OR COMPOUND PROPORTION. IT is composed generally of five given terms to find a sixth. These terms are distinguished into three supposition terms, including one which is of the same name or kind with the answer; the other two are terms of demand. RULE. Place the term which is of the same kind with the required answer, for the third term. With this third term, and each pair of similar terms, complete a statement in the Single Rule, as already taught. Reduce the similar terms to like denominations, and the third to its lowest given denomination. Multiply the two quantities in the second term together; and likewise the two quantities in the first term together. It is then reduced to the Single Rule of Three. Multiply the second and third terms together, and divide by the first, the quotient will be the answer. PROOF-The same as in the Single Rule. |