SINGLE RULE OF THREE DIRECT. The Single Rule of Three Direct is known from Inverse Proportion by more requiring more, or less requiring less, i. e. if the third term be greater than the first, the fourth term or answer must be greater than the second or middle term, and contrary wise, if the third term be less than the first, the fourth must be less than the second or middle term. The third term must be that which makes the demand, and is known by these and the like expressions; how many, how much, how far, what will, what cost, &c. The third term being ascertained, the first must be of the same kind or quality; and the middle or second term must be always of the same kind, or quality of the answer. Having stated the terms as above, if they are of several denominations, reduce the first and third terms to the lowest mentioned in either; also reduce the middle term to the lowest denomination mentioned in it. Having thus prepared the terms for a solution, multiply the second and third together, and divide the product by the first, the quotient will be the answer in the same denomination the middle term was reduced to. If any remain, reduce it to the next lower denomination, and divide again by the first term, the quotient of this will be so many of the dénomination you last divided, &c. Questions in this rule are proved by inverting their order. EXAMPLES. 1. If 6 yards of cloth 2. If 12 yards of cloth cost $9, what will 12 yards | cost 18, what will 6 cost? yards cost? NOTE. These four examples prove cach other by inverting or varying their order, as do many of the following. 5. If a hogshead of wine cost $ 31, 50, how much will a quarter cask cost containing 31 gallons? 6. If a quarter cask of wine, containing 31 galIons, cost $15, 75, how much is it per hogshead? 63: 31,50 :: 31 ga. 2 qts. | 31 : 15,75 :: 63 Note. In the 5th example the gallons in the first and third terms are reduced to quarts; in this last they are reduced to half gallons, the result will always be the same, let the denominations of those two terms be greater or less, provided they are both of one denomination. K 14. If 3C. 1 qr. 10 lb. of sugar cost £7 19 1, how much will buy 1 C. 2 qrs. 19lb. ? Ans. 3 19.6 15. If 3 C. 1 qr. 10lb. of sugar cost £7 19 1, how much can I buy for £3 19 64. ? Ans. 1C. 2qr. 19lb. 16. If i C. 2 qrs. 19 lb. cost £3 19 6, how much for £7 19 1? Ans. 3C. 1 qr. 10lb. 17. If $1,50, will buy 6 yards of cloth, how many yards for 3 dols. ? Ans. 12 yards. 18. If 12 yards of cloth cost 3 dols. how many yards for $1,50? Ans. 6 yards. 19. If 12 yards of cloth cost 3 dols. how much will 6 yards cost? Ans. $1,50. 20. If 6 yards of cloth cost $1,50, how much will 12 yards cost? Ans. 3 dols. 21. If 2 yards of linen cost 1 dol. what will 15 yards cost? 22. If 15 yards of cloth cost $7,50, cost? 23. If 2 yards of cloth cost 1 dol. can I buy for $7,50 ? 24. If $7,50 buy, 15 yards of linen, for 1 dol.? Ans. $7,50. what will 2 yards Ans. 1 dol. how many yards Ans. 15 yards. how many yards Ans. 2 yards. 25. If a hogshead of rum, containing 108 gallons, cost $86,40, how much was it a pint ? Ans. 10 cts. 26. At 10 cents a pint, how many gallons of rum for $86,40 ? Ans. 108. 108 gallons of rum Ans. dolls. 86,40. $86.40, how much Ans. I pint. 27. At 10 cents a pint, what will cost? 28. If 108 gallons of rum cost can I buy for 10 cents? 29. If a man's yearly income be $2460, how much may he spend per day, (allowing the year to be 365 days) to lay up or save 1000 dols. at the year's end? Ans. 4 dols. 30. A man spent 4 dols. per day, and laid up $1000 at the year's end, what was his yearly income ? Ans. 2460 dols. 31. A man out of his yearly income of $2460, spent 4 dols. per day, how much was left at the year's end? Ans. 1000 dols. 32. A man spent $4 per day, out of his income, till he had spent $1460, and laid up $1000 in the same |