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RULE FOR STATING, &c.* Set that term of supposition which is of the same kind as the term of demand in the first place, set the other term of supposition in the second place, and the term of demand in the third place; as in the following examples: yds. 8. yds.
bu. 2 : 4 :: 6
10 : 20 :: 5 Note.-In the former of these examples 2 and 4 are the terms of supposition, and 6 is the term of demand; in the latter, 10 and 20 are the terms of supposition, and 5 is the term of demand. The questions which they state are thus : Suppose 2 yards cost 4 shil lings, what will 6 yards cost ?-Suppose 10 shillings will pay for 20 bushels, how many bushels will 5 shillings pay for?
When a question is stated, consider whether the preportion be direct or inverse.
DIRECT PROPORTION. The proportion is direct when the third term is greater than the first, and the nature of the question requires that the fourth term, or answer, should be greater than the second; or when the third term is less than the first, and it is required that the fourth term be less than the second.
RULE. If the first and third terms be not of the same denomi. nation, reduce both to the lowest in either; and if the second term consist of several denominations, reduce it to the lowest thereof: then multiply the second and third terms together, and divide the product by the first; the quotient will be the fourth term, or answer, in the same denomination as the second, or that to which the second is reduced.
* The following rule for stating and solving questions in the Rule of Three, if adopted, would render the distinction of direct and in. verse proportion useless.
Or the three given numbers, set that which is of the same name or kind as the answer, for the third term ; then consider whether the answer will be greater or less than this third term; if greater, set the less of the two remaining numbers for the first term, and the other for the second; but if less, set the greater of those two numbers for the first term, and the other for the second. When the question is thus stated, if the first and second terms be not of the same denomination, reduce both to the lowest in either; and if the third consist of several denominations, reduce it to the lowest thereof: then multiply the second and third terms together, and divide the product by the first term: the quotient will be the answer in the same denomination as the third term.
PROOF. Invert the question, making the answer the second term, as in the following wrought examples.
EXAMPLES. 1. If 2 yards of muslin cost 4 shillings, what will 6 yards cost? yds. 8. yds.
yds. 8. yde. 2 : 4 :: 6
6: 12 : : 2
Proof 2. If 10 shillings will pay for 20 pounds of beef, het many pounds will 5s. pay for? 16.
8. 16. 10 : 20 :: 5
3 : 10 :: 10 5
Ans. 10 lb.
Proof 20 lb. 3. If i lbs of sugar cost 9d. what will 2 Cwt. 2 qrs. IDlb. cost? 10. d. Cwt.qrs.lb. Cwt.gra.lb. L. d. 26. 1:9 :: 2 2 10
2 2 10 : 10 17
4. Sold 125 bushels of wheat, at 11s. 3d. a bushel; what did it come to?
Ans. 70 L. 6s. 3d. bu.
bu. bu. L. d. bu, 1:11 3 :: 125 125 : 70 6
3 :: 1 12
210) 14016 3
625 Ans. 70L. 6s. 3d. 5. If 3 pounds of sugar cost 4 shillings, what will 6 pounds cost?
Ans. 8s. 6. If 8 yards of muslin cost 24 shillings, what will 96 yards come to?
Ans. 14 L. 8s. 7. If 12 bushels of wheat be worth 16 dollars, how much are 48 bushels worth?
Ans. 64 dols. 8. If 1 pound of butter bring 16 pence, what will 56 pounds bring?
Ans. 3L. 14s. 8d. 9. Sold 12 yards of cloth for 72 dollars : how much was it per yard?
Ans 6 dols. 10. If 12 yards of cloth cost 19 L. 16s. what will 192 yards come to ?
Ans. 316L. 16s. 11. If 96 pounds of sugar cost 3 L. 12s. what is it per pound?
Ans. 9d. 12. What will 421 bushels of wheat come to, at 1 doltar 35 cents per bushel?
Ans: $ 568.35 13. What will 128 pounds of pork come to, at 8 cents a pound?
Ans. 10 dols. 24 cts. 14. How much will 75 pounds of almonds come to, at 37į cents a pound?
Ans. $28.12 15. If 3 yards of cloth cost 5 L. 125. 6d. how much will 225 yards cost?
Ans. 421 L. 17s, 6d.
Ans. 5 d.
76. If i pound of rice cost 4 d. what will 48 pounds cost?
Ans. 18s. 17. Bought 230 bushels of coal for 26 L. 16s. 8d. how much was it per bushel ?
Ans. 2s 4d. 18. Bought 120 bushels of corn for 58 dollars : how much is that a bushel?
Ans. 48cts. 19. If 891 gallons of molasses cost 176L. 6s. 10 d. what is it per gallon?
Ans. 3s. 11 d. 20. What must be paid for 45 bushels, 3 pecks of potatoes, at 2s. 3d. a bushel ?
Ans. 6L. 2s. 21. If I dozen of penknives cost 2 dollars 50 cents, how much will 4 dozen come to?
Ans. $10.00 22. If the price of 1 acre of land be 18 dollars, 25 cents, what will 50 acres, 2. roods, 20 perches, come to ?
Ans. $ 923.90 + 23. If i hundred weight of sugar cost 2L. 11s. 4d. what is the price of 1 pound?
24. If i hundred weight of iron be worth IL. 8s. what is the value of 33 Cwt. 1 qr. 22 lb. ? Ans. 46 L. 16s. 6d.
25. Sold 3 hundred weight of tobacco, at 13d. per pound, what did it amount to?
Ans. 25 L. 4s. 26. If 19 dozen pair of stockings cost 136 dols. 80 cents, what is the cost of 1 pair?
Ans. 60 cts. 27. Bought 6 Cwc. of sugar at 10 cents a pound: what does it amount to?
Ans. 8 67.20. 28. A silversmith bought 73 Ib. 5 oz. 15 dwt. of silver, for which he paid 5s. 9d. per ounce: what was the amount?
Ans. 253 L. 10s. 0 d. 29. A French crown is 8s. 3d. Pennsylvania currency, "how many pounds of that currency are 100 French crowns?
Ans. 41 L. 5s. 30. What must be paid for 53 English ells, I quarter of Holland, at the rate of 75.9 d. per yard ?
Ans. 25 L. 185. 1 d. 31. If 1 yard of muslin cost 21 cents, what will 43 yards cost?
Ans. 8.9.134 32. If lk yard of silk cost 2 dollars, 50 cents, what will i quarter, 2 nails cost?
Ans. 62, cts. 33. What is the value of 5į lb. of tea, at 9s. 4 d. per lb.
Ans. 2Lills. 6 d.
34. What is the value of 795 lb. of coffee, at 24 cents a pound?
Ans. $194.774 35. Calculate the amount of 1475 bushels of Indian corn, at 87 | cents a bushel ?
Facit 8 1290.625. 36. What must be paid for 53 English ells, i quarter of Holland, at the rate of 7s. 9 d. per yard ?
Ans. 25L. 188. 1d. 37. What will a hogshead of sugar come to, weighing 7Cwt. 3qrs. at 10 dollars 62 cents per hundred weight?
Ans. $82.344. 38. If 5 yards of cloth cost 28s. 4d. what is the value of 18 pieces, each containing 21 yards, 1 quarter ?
Ans. 108 L. 75.-60. 39. What must be paid for 7 casks of prunes, each. weighing 4 Cwt. 3 qrs. at 2 L. 19s. 8d. per Cwt.?
Ans. 99 L. 3s. 11d. 40. If I buy 20 pieces of cloth, each 20 ells, for 125. 6d. per ell, what is the amount of the whole? Ans. 250 L.
41. What will 4 pieces of cloth come to, containing 23, 24, 25, and 27 yards, at 72 cents per yard? Ans. $71.28.
42. Bought 3 pipes of wine, containing 120, 124, 126 gallons, at 5s. 6d. per gallon ; what did they amount to?
Ans. 102 L. Is. 10 d. 43. Bought four pieces of linen, two of which contained 27 yards each, and the other two, 25 yards each, at 62 cents per yard; what was the cost? Ans. $ 66.561
44. If the price of 1 yard of muslin be 3s. what number of yards may be bought with 1L. 175. 6d. ?
Ans. 121 yards. 45. What quantity of sugar will 23L. 10s. buy, at 26s. 8. per hundred weight? Ans. 17 Cwt. 2 qrs. 14 lb.
46. A person bought a piece of cloth for 16 L 10s. the price of which, pér yard, was 15s. how many yards did it contain?
Ans. 22 yards. 47. If a person have a salary of 1333 dollars a year, and spend daily 2 dollars, 14 cents, how much will he save each year?
Ans. 8.551.90. 148. If a person's income be 890 dollars 50 cents, a year, how much may he spend each day, to save, every year, 120 dols. 35 cts, ?