How many men? 75 5×8=40 men Ans. $ 100 8 3 63 612 2 920 men. 8 40 men Ans. 5. If of a yard of cloth, yd. wide, cost £3, what is the value of yard, 13 yard wide, of the same quality? 6. If a man travel 240 miles in 12 days, when the days are 12 hours long, how far can he travel in 27 days, when the days are 16 hours long? Art. 183.-In Proportion, both Simple and Compound, the terms in the supposition and demand may be distinguished by cause and effect, or producing and produced terms. That which causes any thing, or produces an effect, as men, time, length, breadth, depth, etc., may be denominated a producing term. Thus, in the foregoing question, among the terms of supposition, one man, 12 days, 12 hours long, are the joint cause, or producing terms, and miles the effect, or produced term. Among the terms of demand, 27 days, 16 hours long, are the joint cause, or the producing terms, and the rods required are the effect, or the produced term. In all questions in Proportion the answer required will be either cause or effect, (a producing or produced term.) Hence, Art. 181.-When the term required is a produced term, Draw a perpendicular line, and place all the terms of demand on the right of the line, and all the corresponding terms of the condition on the left, closing the statement by placing the name of the answer on the right. QUESTIONS.-1. What is meant by producing and produced terms? 2. Rule, when the term required is a produced term? OBS. 1.-All questions under the foregoing head will be found to be in Direct Proportion. 7. If 4 students spend £19 in 3 months, how many pounds will 8 students spend in 9 months? Operation. How many £?8 students. Ans. £114. Producing terms of Students 49 months. of the demand. the supposition. Months 3 Producing terms £19. Produced term of the supposition. £114 Ans. 8. 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? Ans. 1162 acres. 9. If 8 reapers receive £3 4s. for 4 days' work, how much ought 20 reapers to receive for 15 days' work? Ans. £30. 10. If 3 men receive £8.9 for 19.5 days' labor, how much ought 20 men to receive for 100.25 days' labor? Ans. £305 Os. 8d. 1qr. 11. If 20 cwt. may be carried 80 miles for $35, how much will it cost to transport 40 cwt. 100 miles? Ans. $87. 12. 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? OBS. 2.-Hundred weight and distance are the producing terms, and the money received, the produced term. 5 13. If 24 yards of cloth, 13 yards wide, cost £33, how much will 36 yards, 1 yards wide, cost? Ans. £542. 14. 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? 136 bushels 4. $ bushels 245 months. 3 men 158 persons. 4 persons Ans. Art. 185.-When the term required is a producing term, Draw a perpendicular line, and place the produced term of the demand and the produciny terms of the supposition on the right, and the remaining terms on the left of the line, and procced as before. OBS.-This head will be found to correspond with Inverse Proportion, and may be applied to both Simple and Compound. 15. 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? Ans. 96 days. 16. 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 8 feet deep, in 27 days, when the days are 12 hours long? Ans. 18 men. 17. 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? Ans. 56 days. 18. If 98 lbs. of bread be sufficient to serve 7 men 14 days, how many days will 63 lbs. serve 21 men? Ans. 3 days. 19. 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? Ans. 15 hours. 20. 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 ? Ans. 15 days. 21. If 16 compositors set 150 pages of types, each page QUESTION.-3. Rule, when the term required is a producing term? 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? Ans. 120 compositors. SUPPLEMENT TO THE RULES OF PROPORTION. EXAMPLES. Art. 186.-1. If I can hire 30 horses pastured 7 weeks for £6, how many weeks may 5 horses be pastured for £4 58. 84d.? 2. If 8 men build 48 rods of fence in rods will 24 men build in the same time? 3. If 24 men build 144 rods of fence in rods will 8 men build in the same time? Ans. 30 weeks. 1 day, how many Ans. 144 rods. 1 day, how many Ans. 48 rods. 144 rods of fence 4. How many men will it require to build in 1 day, if 8 men build 48 rods in the same time? Ans. 24 men. 5. If 20 men build a mill in 160 days, in how many days could 25 men build the same mill? Ans. 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 23 cords cost $6 ? Ans. 531 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? Ans. 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? Ans. § 1600 cents. 33 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? Ans. 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 for $934. What was the value of the ship? Ans. $36. of his share Ans. $3736, 13. How many guineas will 83 yards of cloth cost, if 7 of a yard cost of a dollar? Ans. 12 guineas. 32 1 1 3 15 14. If of a pound of sugar cost of a shilling, what will of a pound cost? 1657 Ans. 4d. 3185 grs. 15. If 21 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 12 oz., what ought it to weigh when wheat is $.50 per bushel ? Ans. 18 oz. 17. How many yards of cloth, yd. wide, are equal in measure to 30 yds. 14 yds. in width? Ans. 60 yards. 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. 3 4 3 19. How far may 30 cwt. be transported for $8, if 21 cwt. be carried 180 miles for the same money? Ans. 15 miles. 20. How many yards, of yd. wide, will it take to line 850 suits of clothes, each suit to contain 31 yards of cloth, 13 yds. in width? Ans. 6941 yds. 2 qrs. 23 nails. 21. If 30 horses consume 600 bushels of oats in 8 months, how much will each horse consume per day? Ans. 2 quarts. 22. A man owns of a ship, which ship is valued at of the ship and cargo--the latter worth $96000. What is the value of of his share? Ans. $4000. 23. If 12 men consume of of of 4 of 30 bushels of wheat, in 1 of 14 of of of 20 months, how much will 4 men con 39 15 sume in 3 of of 16 of 38 of 14 of 40 months? 26 19 7 15 Ans. 12 bushels. 9 13 24. If 4 men spend of of of 1 of £30 in 71 of 1s of 29 of 11 of 9 days, how many dollars will 21 men spend in 3 of 14 of 9 of 12 of 45 days? 27 15 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 17 lbs. be worth £10224 ? Ans. 27068. |