The Single Rule of Three Dire&. THE Single Rule of Three Direct teaches, from three numbers given, to find a fourth, that shall be in the fame proportion to the third as the second is to the first. If more require more, or lefs require lefs, the proportion is direct, RULE. 1. Make the number that is the demand of the questions the third term, the number that is of the same name or quality, the first term, and the remaining number will be the middle term. Reduce the first and third numbers into the fame, and the second into the lowest denomination mentioned. 2. Multiply the second and third numbers together, and divide the product by the first, and the quotient (if there be no remainder) is the answer, or fourth number required. If, after division, there be remainder, reduce it to the next denom. ination below that to which the second number was reduced, and divide by the fame divifor as before, and the quotient will be of this last denomination. Proceed thus with all the remainders till you have reduced them to the lowest denomination, which the second number admits of, and the several quotients taken together will be the answer required. The method of proof is by reversing the question. EXAMPLES. 1. If z yards of cloth cost 4 fhillings, what will 125 yds.come to? yds. yds. yds. f yds. : 4:1 125 Proof if 125:12 10 :: 2 4 IF 2 20 Ans. £.12 10 125)500(4 shillings. 500 If : bushel of corn cost 75 cents, what will 257 bushels come to ? bufh. cis. bush. If I: 75 :: 257 2. per yard ? bushel can per cwt, ? What will 931 yards of shalloon come to at 55 cts. 4 ms. Anf. 515 dols. 77 cts. 4 ms. 4. How many bushels of wheat at i dol. 12 cts. per I have for 81 dols. 76 cts. ? Anf. 73 bushels. 5. What will 94 cwt. of iron come to at 4 dols. 97 cts. 2 ms. Ans. 467 dols. 36 cts. 8 ms. 6. What will 349 lbs. of beef come to at 2d. per pound ? Anf. £.2 18 2. 7. At 38. per yard what will 59 yards of cloth come to ? Anf. £.8 17 0 Prove this answer to be right. 8. How many lbs. of beef at 5 cts. per Ib. may be bought for 29 dols, 85 cts. ? cts. Ib. dols. cts. If 5 : 1 :: 29,85 905)29,85 597 Anf. 597 lb. 9. How many hogsheads of salt at 4 dols. go cts. per hhd. can I have for 392 dols. ? Ans. 8o hhds. 10. How many lbs. of Coffee at 187 per lb. may be bought for £.8 12 7? Ans. iog lb. 11. When 25 yards of cloth coft £.2 12 1, what is it per yard ? yd. £. S. d. yd. If 25:2 12 1 :: 1 If 56 bufhels of corn cost 42 dols. 56 cts, what is it per bushel ? bush. dols. cts. bush. If 56 : 42,56 :: 1 1 56)42,56(,76 392 336 gallon ? 18. quintal ? 50 cts. Anf. 76 cts, 13. If 112 pounds of beef cost 185. 8d. what is it per lb, ? Anf. 2 penee. 14. If 673 bushels of rye coft 769 dols. 23 cts. 9 mills, what is one bushel worth ? Anf. i dol. 14 cts. 3 mills. 15. What is one yard of baize worth, when 97 yards cost £10 125. 2 d. ? Anf. 25. 21d. 16. When iron is sold at 5 dols. 4 cts. per cwt. what is it per pound ? Ans. 4 cts. 5 m. 17. If 891 gallons of molasses cost £.176 6 10], what is it per Anf. 35. 11d. Prove this answer to be right. What will 253 quintals of fish come to, at 175. 6d. per Ans. £.225 7 6 19. At 5 dols. 50 cts. per thousand, what will 37 thousand of boards come to ? Ans. 203. dols. 20. What will 4 hhds. of rum come to, containing viz. 79, 84, 101į, and 112 gallons, at 6s. gd. per gallon ? Anf. £.127 49 What will 327 hhds. of salt come to, at 5 dollars Anf. 1716 dols. 75 cts. 4 9, Ans. 23. If a chest of Hyson tea, weighing 79 lb. neat, cost £:32 11 g what is it per 1b. ? Ani. 8s. 3d. 24. B owes £.2119 17.6 and he is worth but £ 1324 18 54 ; if he delivers this to his creditors, how much do they receive on the pound? Anf. 125, 6d. 25. A owes B £.569 6 8, but failing in trade, he is able to pay but 155. 6d. on the pound; how much is A to receive, and what is his loss ? Anf, he is to receive £:441 48 his loss is 128 20 26. A merchant failing in trade, owes in all 29475 dollars, and delivers up his whole property, worth 21894 dollars 3 cents; how much per cent does he pay, and what is B's loss, to whom he owed Ans, he pays 74 dols. 28 cts. per cent. and B loses 83 dols. 59 CES, 21. 25 cents per hhd. ? 22. 18. 325 dollars ? 27. How much will 4 cwt. I qr. 19 lb. of butter come to at gd. per lb.? If d. 9 :: 495 9 12)4455 20)371 3 Ans. £.18 115. 3d. 28. If 3 qrs. 26 lb. of steel cost 13 dols. 20 cts. what is it per pound? Anf. 12 cents. 29. If 16 cwt. 3 qrs. of steel cost 157 dollars 45 cents, what is I qr. worth ? Ans. 2 dols. 35 cts. Prove this answer to be right. 30. A captain of a ship is provided with 18000 lb. of bread for 150 seamen, of which each man eats 4 lb. per week, how long will it last them ? Ans. 30 weeks. 31. How long would 2295 lb. of beef last for 45 seamen, if they get i lb. each, and that three times a week ? Anf. 17 weeks. 32. Suppose 120 seamen are provided with 7200 gallons of water for a cruise of 4 months, each month 30 days ; how much is each man's share per day ? Ans. 2 quarts. 33. , A ship’s company of 16 men is on an allowance of 6 ounces of bread per day, when meeting with a vessel from which they are supplied with 2 cwt. of bread, what addition will this make to their daily allowance, if they suppose their voyage to last 28 days. Ans. 8 ounces. 34. If 17 tụns 2 hhds. of wine cost 5468 dols. 40 cts. how much is one pint worth? Anf. 15 cts. 5 mills. 35. How much will 4 pieces of linen, containing viz. 351, 36, 377 and 38 yards come to, at 79 cts. per yard ? Anf. 116 dollars 13 cents. 36. How many crowns of 110 cents each will pay a debt of £.82 16s. 7d. ? Ans. 251 crowns. 37. If 203 tons 9 cwt. 3 qrs. 3 lb. of tallow cost £ .4558 30 what does I ton cost. Anf. 2.22 8 38. How many cwt. of rice may be bought for 487 dols. 50 cts. when 7lb. coft 25 cents. Anf. 121 cwt. 3 qrs. 14 lb. 39. When 9 dols. 36 cts, is paid for 2 qrs, 22 lb. of sugar, what is 7 lb. worth ? Anf, 84 cts. 1 ounce ? cents. 40. When 47 cwt. 3 qrs. of sugar coft £.182 4.11, what is one quarter worth ? Anf. 195. 1d. 41. If 6 lb. 6 oz. Avoirdupois cost s dols. 10 cts. what is it per Anf. 5 42. Bought 40 tubs of butter, weighing 36 cwt. 2 qrs. 14 ib. neat, for 472 dols. 2 cents; paid cooperage 12 cts. per tub; salt and labour 4 dols. 83 cts. 8 mills ; storeage 6 dols. 48 cts. I would know what it stands me in per lb. Anl. 11 cts. 9 mills. 43. How much will a grindstone, 32 inches diameter and 6 inch. es thick, come to, at 5s. per cubic foot ? 32 the diameter. 48 288 768 cent? 6 Anf. 135. 4d. 44. What will a grindstone, 28 inches diameter and 31 inches thick, come to, at i dol. go cts. per cubic foot. Anf. 2 dols. 26 c. 45. When a man's yearly income is 949 dollars, how much is it per day? Ans. 2 dols. 60 cts. 46. At 41 per cent, what is the commission on 1525 dollars ? Ans. 68 dols. 62 cts. 5 mills. 47. What is the interest of 456 dols. for I year, at 6 per Ans. 27 dols. 36 cts. 48. At 5 dolls. 50 cts. per M. what will 21,186 feet boards come to ? Anf. 116 dols. 52 cts. 3 m. 49. When boards are sold at 18 dols. per M. what is it per Anf. I cent 8 mills. 50. What will 98 feet of boards come to at 4 cents per foot ? Anf. 3 cents. 51. What will 49 thousand 3 hundred and 25 casts of stave come to, at sy dollars per thousand ? Note. Staves are counted by casting three at a time ; 40 casts make a hundred, and 10 hundred I thousand. dols. M. h. C. 49 § 25 foot ? M. If I : 10 493 40 Casts 400 dols. cts m. Anf. 839 16 2 19745 |