the numerator of a fractional part of the answer already found of which the divisor is the denominator, which bring to its equivalent value, as taught in reduction of fractions. OBSERVATIONS. 1. When the terms of the question are properly prepared and stated, if the numbers which compose the first and second, or first and third terms have a common divisor, the quotients of the numbers after dividing the terms thereby, will do just as well as the original numbers, by which the work may be often shortened. 2. When it can be done, always make use of compound multiplication or division, when the third term is divers denominations 3. It is not of any consequence whether he question be of that commonly called the Rule of Three Direct, or Inverse, state the terms according as the nature of the question requires, and proceed as before directed. If the ratio or analogy is compounded of several terms, multiply the corresponding terms into each other, and state and proceed with the products as with 3 terms. The heads of the foregoing rules and observations, may be comprised as follows:— Place as third term, that given quantity, which is of the same denomination as with the thing sought, consider from the nature of the question, whether the answer must be more or less than the given quantity and accordingly state the other 2 given terms. Having thus stated the terms, if the two first be mixed, fractional, or compound quantities, bring them to the same denomination; then altogether disregarding their denomination, multiply the second and third numbers together, and divide the product by the first, taking the advantage of any abreviations the numbers admit of. First Erample. If 8lbs of beef can be had for 3s. 6d. what is the price of a side, weighing 2ct 3qrs 16 lb? 2ct 3qrs 16 lb = 324 lbs Again-If 2ct. 3qr. 16b of beef is bought for 71 1s. 9d; what is the price of 8tb? à. If for 3s. 6d. I can buy 8fb of beef; what quantity can I purchase for 71s. 9d. ? 3s. 6d. 42d. and 71 1s. 9d. 1701 pence. 324 = 2ct. 3qrs. 16 If 71 1s. 9d. pay for 2ct. 3qrs. 16b tity can I purchase for 3s. 6d. ? of beef; what quanè Thus each question may be varied, and one answer will prove the truth of another. Second Example. If a mower can cut down the grass of a field in 5 days, working 10 hours each day; how many hours a day must he work, in order to have it done in 4 days? Here it is plain he must work a greater number of hours; therefore, the answer must be greater than the given third term 10 hours; hence, the two first terms must be thus stated, If a mower can cut down the grass of a field in 4 days, working 12 hours per day, in how many days will he complete it, working each day but 10 hours? h. h. Ds. 10 12:4 4 10)50 Answer, 5 days. If a mower, working 12 hours per day, can cut down the grass of a field in 4 days, how many hours each day may he work, and spend 5 days thereat? ds. ds. 5: 4 :: 121 4 -5)50 Answer, 10 hours. İf a mower can cut down the grass of a field in 5 days, working 10 hours each day; how many days will he spend thereat, if he work 124 hours each day? ..hs. 12 h. ds. 10:5 -5 4 days. Answer. Third Erample. If my friend lend me £150 for 6 months, interest free but afterwards expecting a like kindness from me, I have but £90 to spare; how many months may he keep my money to requite his good office? months. 90: 150: 6 If with £250 I gain £37 10s. in nine months; how much may I clear, by employing £400 fifteen months in like business? 250 X 9: 2250 and 400 15 Fifth Example. If 81 stone of oats are consumed by 7 horses in 9 days, in how many days will 16 horses consume 228 stone? 81 X 16 1296 and 228 x 7 = 2016, 1296: 2016:: 9 days Therefore, 14 days is the answer. Here the number of horses are inverse, and number of stones direct. QUESTIONS FOR PRACTICE. 1. If 4 yards of linen are bought for 10s. 3d. what will be the price of 50 yards at the same rate? 2. If 50 yards of linen are bought for 61 8s 1d, what will 4 yards of the same cost? 3. If 50 yards of linen are bought for 61 8s. 14d, how ma-, ny yards of the same can I buy for 10s. 3d.? 4. If 4 yards of linen are bought for 10s. 3d, how many, yards can I purchase for 61 8s 1d? 5. If yard of cloth cost 12s. 6d, what will 12 yards of the same cost? X yds 8 d 6. At same rate how many yards should I get for 101? 7. If 6 yards of cloth cost 50s. what will 84 yards cost? 8. At the same rate how many yards can I buy for 351? 9. If 9yds. 3qrs. cost 21 15s. Od. what will 3yds. 1qr. cost? 10. At the same rate what will be the price of 58yds, 2qrs. 11. What will be the price of a piece of muslin qt. 27 yds. of which lyd. cost 5s. 6d. ? 12. If 58yds. 2qrs. cost 167 10s. what will 9yds. 3qrs. cost 13. If an hhd. of sugar wt. neat Sct. 2qrs. cost 271 14s. 8d. what will be the price of 114ct. 3qrs? 14. If 114et. 3qrs. of sugar can be purchased for 3741 8s. what am I to pay for 8ct. 2qrs. of the same? 15. If 69yds. 1qr. of linen cost 127 13s. 11d. how much can I buy for 17 8s. 5d.? 16. If 11 8s. 5d. pay for 7yds. 3qrs. of linen, how many yards of the same can I have for 127 13s. 11d. ? 17. How many yards of muslin may be bought for 991 of which 11yds. cost 8s. 5d.? 18. If for 991 I buy 132 yards of muslin, what doth llyds of the same stand me in ? 19. What must be paid for 63bls. 11 stone of wheat at 18s. cwt. ? 20. If for 1421 19s. 9d. I can purchase 63bls. 11st. of wheat what doth one barrel stand me in? 21. What is the value of 1375 stone of oats at 2s. 81d. per bushel of 34 stone? 22. If 14lb of sugar are sold for 13s. 6d. what is the rate cwt.? 23. If 5 yards of cloth cost 21 7s. 6d. what will 3 yards cost? 24. What quantity of raisins can be bought for 63 pence of which 7b cost 1s. 9d.? 25. If 7b of sugar cost 5s. 6d. how many cwt of the same can I purchase for 165/? 26. If 7b of figs cost 1s. 9d. what quantity can I purchase for 5s. 3d.? 27. If in 365 days I spend 367 10s. what is that per week? 28. If 840 cost 217 what will 35t cost? 29. What will lcwt. stand me in if 7b are worth 1s. 4d. ? 30. If 112b of beef cost 42s. what will 7 cost? 31. If 802ct. 1qr. 17lb. of Merchandize cost 6501, what quantity of the same goods may be bought for 2001? 32. If 10 tuns of wine cost 800/ what quantity can be bought for 15001? 33. What will 6500 cost if 5600 of the same goods are bought for 7351? 34. How many tuns of brandy can I buy for 2133/ if 6 tuns cost 12967? 35. If 6cwt. of hops cost 321 what quantity can I have for 4601/? 36. If 63 gallons of brandy cost 451 16s. what will a jar containing 7 gallons cost? 37. Bought 2 chests of indigo wt. neat 7ct. 1qr. Of which stand me in 2991 12s. 8d. what is that p? |