Case II.-When the two first terms are of different denominations reduce them to the same. 8. lb. 3: 112: 2: To 1 oz., 112 lbs., and 2s., find a fourth proportional. RULE WITH EXAMPLE.-Multiply the 112 lbs. by 16, to bring them to the same as the first term-viz., to ounces. this is done the numbers stand thus 3 oz. 1792 oz. 2s. When 16 672 112 1792 2 3)3584 1194,2 Find the fourth proportional to the following numbers :-- To 2 qrs., 240 yds., 12s........ Ans. .5760s. .320 yds. To 5 cwt., 6000 lbs., 8s...... ..85s. 400 remains. ..50 yds. 60 remains. ...9 yds. Case III.-When the third term is of a different denomination reduce it to the lowest. To 2 lbs., 112 lbs., and 5s. 6d., find a fourth proportional. RULE WITH EXAMPLE.-Multiply the lbs. lbs. 8. d. 5s. by 12 adding the 6d. It then stands 2: 112 :: 5 6: thus: 2 lbs. 112 lbs. 66d. Proceed as formerly. Find the fourth proportional to the following numbers : To 2 tons, 14 tons, 287. 10s....... Ans. .3990s. .4440d. .588 farthings. If 24 lbs. of butter cost £1 8s., what is the price of 3 lbs.' 8. 24: 3 :: 1 8 20 28 24 { 2)84 12)42 3s. 6d. RULE WITH EXAMPLE.-In this ques- lbs. lbs. £ tion there are two things mentioned butter and money. Is the answer to the question to be given in butter or money? You see at once it is to be given in money. Put down the money, 17. 8s., for the third term. Having done this, you have now to consider where you are to place the 24 lbs. and the 3 lbs. Read over the question, and you will see that the answer must be less than the third term; for 3 lbs. will not cost so much as 24 lbs. If, then, the answer is to be less, put the less number for the second term, and the greater for the first. In all questions let the third term be the same as the answer; and if the answer is to be greater than the third term, put the greater second; if it is to be less, put the less second 1. If 2 lbs. of tea cost 9s., what will 24 lbs. cost? 2. If 4 lbs. of coffee cost 8s. 8d., what will 36 lbs. cost? 3. If 8 yds. of cloth cost 47. 16s. 6d., what will 74 yds. cost? 4. Bought 2 pair of boots for 17. 18s. 8d.; what will 46 pair ⚫ost? 5. Bought 2 oz. of tea for 7ąd.; what is that per lb.? 6. Bought 15 lbs. of sugar for 9s. 10d.; what was the price per cwt.? 7. A person spends 21. 16s. 8d.; per week; how much is that per annum? 8. 3 qrs. 24 lbs. of sugar cost 41. 16s. 8d.; how much is that per cwt.? 9. If 9s. 3 d. will buy 14 lbs. of sugar; how much will 3. 6d. buy? 10. If 24 yds. cost 31. 14s. 7d; how much must I give for 1 yd. 3 qrs. 2 nls.? 2 11. What cost 5 hogsheads of sugar each weighing 14 cwt. 24 lbs., at 27. 13s. 6d. per cwt.? qrs. 12. If for 7s. 8d. I can buy 9 lbs. of raisins; how much ean I purchase for 567. 16s.? 13. A bankrupt owes 49687.; but he has only money suffieient to pay 9s. 7d. for every pound he owes: how much money has he to pay his debts? 14. A pole 6 feet high throws a shadow of 5 feet 8 inches; what is the height of a spire which throws a shadow of 156 feet? 15. If 54 men can build a house in 90 days; how many men would it require to do it in 12 days? 16. A grocer bought 6 cwt. 3 qrs. 26 lbs. of sugar, for which he paid 247. 16s. 8d.; at what rate per pound must he sell it to gain 47. 10s. 4d. on the whole? 17. A person reaches a certain place in 18 days by walking 8 hours a day; what number of days would he have taken had he walked 12 hours a day? 18. If 14 men could make a ditch in 18 days; in what time could 34 men do it? 19. A ship was provisioned for a crew of 40 for 3 months; how long would these provisions last, if the crew were reduced to 32 men? 20. If 8 horses can subsist on a certain quantity of hay for 2 months; how long would 12 horses subsist on the same quantity? 21. A field of corn was to be cut down by 40 men in 10 days; ten of the men, however, did not make their appearance: in what time would the field be cut down? 22. If for 24s. I can have 1200 lbs. carried 36 miles; how many pounds can I have carried 24 miles for the same money? 23. A tea dealer bought 4 chests of tea, each weighing 37 lbs 7 oz., for 631. 14s. 6d. ; what did the tea cost him per ounce ? 24. If 74 gallons of wine cost 521. 17s. 94d.; how much will 16 gallons cost? 25. If 4 lbs. of tea cost 24s. 8d.; how much may be bought for 421. 7s. 8d.? 26. If 3 cwt. 2 qrs. 16 lbs. of sugar cost 131. 17s. 9d.; what is the value of 19 cwt. 3 qrs. 14 lbs. ? COMPOUND PROPORTION. When, in order to find a fourth proportional, several circumstances require to be considered, it is called Compound Proportion. If 14 horses eat 56 bushels of oats in 16 days; how many bushels will be required for 20 horses for 24 days? days bush. 20 :: 56: 16 : 24 224 480 56 2880 RULE WITH EXAMPLE.-Write horses 14 : 2400 224)26880(120 bus. 224 448 448 Ο horses. Take the other two terms and proceed in the same manner. After all the terms have been put down, multiply the two first terms, 14 and 16, together; do the same with the two second terms, 20 and 24, and proceed as in Simple Proportion. CONTRACTION.-Let the question be the same as in the last example. 10 3 After the terms have been properly arranged, the operation may often be greatly shortened by using the following method: Draw a line, and place the first terms, 14 and 16, under it, and the second and third terms, 20, 24, and 56, above it; then divide any number above the line and any below by any number which will divide both without leaving a 2 2 remainder. Thus, 14 below and 56 above may both be divided by 7; divide by it, and place the figures obtained below and above the 14 and 56, drawing your pencil at the same time through the 14 and 56. Again, you see that 16 and 24 may be divided by 8; draw your pencil through them, and write the numbers above and below; then cancel the 20 and the 2; then the 8 and the other 2. Multiply all the figures that remain above the line and divide the product by the product of all the figures under the line, if any, for the answer: thus, 10X3X4 120. This is the answer as there are no figures " below the line by which to divide. 1. If 15 men build 37 roods of wall in 27 days, how many roods will 74 men build in 63 days? 2. If 8 men for 5 days' work get 40s. ; how much ought 32 men to get for 24 days' work? 3. If 4 men can mow 20 acres of grass in 7 days, how many acres can 12 men mow in 28 days? 4. If 6 tailors can make 10 suits of clothes in 4 days; how many suits can 20 make in 7 days? 5. A wall, 28 feet in height, was built in 15 days by 68 men; how many men working at the same rate could build a wall 32 feet high in 8 days? 6. If 12 horses in 5 days draw 44 tons of stones from a quarry; how many horses would it require to draw 132 tons in 18 days? 7. A garrison of 1500 men has provisions for 12 weeks, at the rate of 20 ounces per day to each man; how many men will the same provisions maintain for 20 weeks, allowing each man only 8 oz. per day? 8. If 50 men can do a piece of work in 100 days, working 8 hours per day; in what time will 120 men do it, working 6 hours per day? 9. What is the interest of 3307. 10s. for 2 years at 4 per cent per annum? 10. If 6001. gain 451. in 18 months; how much will 1037. gain in 12 months? |