or those numbers which follow "HOW," &c., on the right of the line, and those which follow "IF," on the left, as in the Rule of Three Direct, closing the statement, in all cases, with that number which is of the same kind with the answer sought, and proceed to cancel as before instructed. NOTE. All questions under the foregoing head will be found to be in Direct Proportion. 6. If 4 students spend £19 in 3 months, how many £ will 8 students spend in 9 months? Answer, £114. Operation. How many Months 7. If 7 men can reap 84 acres in 12 days, 12 hours long, how many acres can 20 men reap in 5 days, 14 hours long? Answer, 116 acres. 8. If 8 reapers receive £3 4s. for 4 days' work, how much ought 20 reapers to receive for 15 days' work? Answer, £30. 9. If 3 men receive £8,9 for 19,5 days' labor, how mach ought 20 men to receive for 100,25 days' labor? Answer, £305 Ös. Sd. 1qr. 10. If 20 cwt. may be carried 80 miles for $35, how much will it cost to transport 40 cwt. 100 miles? Answer, $871. 11. If the freight of 9 hhds. of sugar, each weighing 12 cwt., 20 leagues, cost £16, what must be paid for the freight of 50 tierces, each weighing 24 cwt., 100 leagues? NOTE. Hundred weight and distance are the producing terms, and the money received, the produced term. 12. If 24 yards of cloth, 13 yard wide, cost £33, how much will 36 yards, 1 yard wide, cost? Ans., £543. 13. If 24 bushels of wheat be consumed by 8 persons in 5 months, how many persons will consume 36 bushels in 15 months? Operation. How many persons? 36 bushels 4 3 bushels 245 months. 3 men 158 persons. 4 persons, Answer. It is evident, that if 24 bushels are consumed by 8 per It sons in 5 months, that 1 person would consume § of 24=3, and in 1 month of a bushel, and in 15 months X15= 459 bushels. Then 36-9-4 persons, the answer. will be observed, that the answer required is a producing term; and, also, that the product of the 36 bushels, the produced term in the demand, and 8 persons, 5 months, the producing terms in the supposition, is divided by the product of 24 bushels and 15 persons, the produced and producing terms in the supposition. Hence the RULE : When the term required is a producing term, Draw a perpendicular line, and place the produced term of the demand and the producing terms of the supposition on the right, and the remaining terms on the left of the line, and proceed as before. NOTE. The above will be found to correspond with Inverse Proportion, and may be applied to both Simple and Compound. 14. If 6 men build a wall 20 feet long, 6 feet high and 4 feet thick, in 16 days, working 12 hours in a day, in how many days will 24 men build a wall 200 feet long, 8 feet high, and 6 feet thick, working 10 hours in a day? 15. If 3 men in 24 days, 9 hours long, can dig 328 rods of trench, 6 feet wide and 4 feet deep, how many men will it take to dig a trench 984 rods long, 9 feet wide and S feet deep, in 27 days, when the days are 12 hours long? Answer, 18 men. 16. If a man can travel 240 miles in 16 days, when the days are 14 hours long, how many days will it take him to travel 720 miles, when the days are 12 hours long? Answer, 56 days. 17. If 98 lbs. of bread be sufficient to serve 7 men 14 days, how many days will 63 lbs. serve 21 men? Answer, 3 days. QUESTIONS. 3. Rule, when the term required is a producing term? 18. If 40 men in 15 days, 12 hours long, build a wall 200 feet long, 12 feet high and 5 feet thick, how many hours long must the day be, that 20 men, in 12 days, may build a wall 100 feet long, 10 feet high and 6 feet thick? Answer, 15 hours. 19. If 20 men in 12 days, 15 hours long, can build a wall 100 feet long, 10 feet high and 6 feet thick, in how many days, of 12 hours long, can 40 men build a wall 200 feet long, 12 feet high and 5 feet thick? Answer, 15 days. 20. If 16 compositors set 150 pages of types, each page consisting of 48 lines, and each line of 50 letters, in 8 days, 10 hours long, how many compositors will be required to set 500 pages of 72 lines each, and 45 letters in a line, in 6 days, 8 hours long? Answer, 120 compositors. SUPPLEMENT TO THE RULES OF PROPORTION. EXAMPLES. 1. If I can hire 30 horses pastured 7 weeks for £6, how many weeks may 5 horses be pastured for £4 5s. 84d.? Answer, 30 weeks. 2. If 8 men build 48 rods of fence in 1 day, how many rods will 24 men build in the same time. Ans., 144 rods. 3. If 24 men build 144 rods of fence in 1 day, how many rods will 8 men build in the same time? Answer, 48 rods. 4. How many men will it require to build 144 rods of fence in 1 day, if 8 men build 48 rods in the same time? Answer, 24 men. 5. If 20 men build a mill in 160 days, in how many days could 25 men build the same mill? Answer, 128 days. 6. If 25 men build a mill in 128 days, how many men will build the same mill in 160 days? Ans., 20 men? 7. How many cords of wood may be bought for £40, if 22 cords cost $6? Answer, 53 cords. 8. How many bushels of wheat may be bought for £40, if 1 bushel of wheat be worth 2 bushels of rye, and 4 bushels of rye be worth 5 bushels of corn, and 8 bushels of corn be worth 16 bushels of oats, and 1 bushel of oats be worth 2 shillings? Answer, 80 bushels. 9. If 18 cords of oak wood be worth 263 cords of hemlock, and a cord of hemlock 14 shillings, how much will 4 cords of oak cost in cents, and how many guineas? 1600 cents. Answer, 34 guineas. 10. How many stoves may be bought for 672 shillings, if 8 fire-frames are worth 3 stoves, and 16 fire-frames are worth 32 guineas? Answer, 5 stoves. 11. How much will $450 gain in a year, if 100 in the same time gain $8? 12. A merchant owning of a vessel, sold What was the value of the ship? share for $934. Answer, $36. of his Answer, $3736. 15. If 2 lbs. of tobacco cost 4s. 6d. how much will 180 lbs. cost in dollars? Ans., $54. 16. If when wheat is 4s. 6d. per bushel the penny loaf weigh 12oz., what ought it to weigh when wheat is $,50 per bushel? Ans., 18oz. 17. How many yards of cloth, 2 yd. wide, are equal in measure to 30 yds. 1 yard in width? Ans., 60 yds. 18. If 40 bushels of grain will pay a debt when the price is 60 cents per bushel, how many bushels will it take when the price is $1,20? Ans., 20 bushels. 19. How far may 30 cwt. be transported for $8, if 25 cwt. be carried 180 miles for the same money? Ans., 15 miles. 20. How many yards, of 2 yd. wide, will it take to line 850 suits of clothes, each suit to contain 3 yards of cloth, 12 yd. in width? Ans., 6941 yds., 2 qrs., 23 nails. 21. If 30 horses consume 600 bushels of oats in 8 mo. how much will each horse consume per day? 22. A man owns of a ship, valued and cargo-the latter worth $96,000. of of his share? 23. If 12 men consume Ans., 2 qts. of 3 of 2 of 4 of 30 bushels of wheat, in of 14 of 9 of 8 of 20 months, how much will 4 men consume in months? of of 18 of of of 38 of 1 of 40 Ans., 12 bushels. of 14 of £30 in of 24. If 4 men spend of 2 of 4 of 9 days, how many dollars will 21 men spend in of 1 of of of 45 days. Ans., $420. 25. If a man travel 336 miles in 14 days, when the days are 18 hours long, in how many days will he travel 672 miles, the days being 12 hours long? Ans., 42 days. 26. If a man travel 240 miles in 12 days, when the days are 12 hours long, in how many days will he travel 720 miles, when the days are 16 hours long? Ans. 27 days. 27. If a family of 9 persons spend $450 in 7 months, how much would be sufficient to maintain them 8 months, if 5 persons more were added to the family? Ans., $800. 28. What is the value of 1 grain of gold, if 173 lbs. be worth £10224 ? Ans., 2106. EXCHANGE. EXCHANGE teaches to find the relative value of money in different states and countries. When the United States were British colonies, the sterling value of the pound was the same in all the colonies; but the legislatures of the different colonies emitted bills of credit, which afterwards depreciated in their value—in some states more, and in others less. The following table exhibits the number of shillings in a dollar in each of the states. |