36. A merchant bought 14 pipes of wine, and is allowed 6 months credit, but for ready money gets it 8 cts. a gallon cheaper; how much did he save by paying ready money? Ans. $141, 12 cts. Examples promiscuously placed. 37. Sold a ship for 5371. and I owned of her; what was my part of the money? Ans. £201 7s. 6d. 38. If of a ship cost 781 dollars 25 cents, what is the whole worth? As 5: 781,25:: 16 : $2500 Ans. 39. If I buy 54 yards of cloth for 317. 10s. what did it cost per Ell English? Ans. 14s. 7d. 40. Bought of Mr. Grocer, 11 cwt. 3 qrs. of sugar, at 8 dollars 12 cents per cwt. and gave him James Paywell's note for 197. 7s. (New-England currency) the rest I pay in cash; tell me how many dols. will make up the balance? Ans. $30, 91 cts. 41. If a staff 5 feet long cast a shade on level ground 8 feet, what is the height of that steeple whose shade at the same time measures 181 feet? Ans. 1131 ft. 42. If a gentleman have an income of 300 English guineas a year, how much may he spend, one day with another, to lay up $500 at the year's end? Ans. $2, 46 cts. 5 m. 43. Bought 50 pieces of kerseys, each 34 Ells Flemish, at 8s. 4d. per Ell English; what did the whole cost? Ans. £425. 44. Bought 200 yards of cambrick for 901. but being damaged, I am willing to lose 77. 10s. by the sale of it; what must I demand per Ell English? Ans. 10s. 3 d. 45. How many pieces of Holland, each 20 Ells Flemish, may I have for 231.8s. at 6s.6d. per Ell English? Ans. 6 pcs. 46. A merchant bought a bale of cloth containing 240 yds." at the rate of $7 for 5 yds. and sold it again at the rate of $111 for 7 yards; did he gain or lose by the bargain, and how much? Ans. He gained $25, 71 cts. 4 m.+ 47. Bought a pipe of wine for 84 dollars, and found it had leaked out 12 gals. ; I sold the remainder at 12 cts. a pint; what did I gain or lose? Ans. I gained $30. 48. A gentleman bought 18 pipes of wine at 12s. 6d. (New-Jersey currency) per gallon; how many dollars will pay the purchase? Ans. $3780. 49. Bought a quantity of plate, weighing 15 lb. 11 oz. 13 17 pwt. gr. how many dols. will pay for it, at the rate of 12st 7d. New-York currency, per oz.? Ans. $301, 50, ets. 2m. 50. A factor bought a certain quantity of broadcloth and drugget, which together cost 817. the quantity of broadcloth was 50 yds., at 18s. per yd., and for every 5 yds. of broadcloth he had 9 yards of drugget; I demand how many yds. of drugget he had, and what it cost him per yard?› ‹ Ans. 90 yds. at 8s. per yd. 51. If I give 1 eagle, 2 dols. 8 dimes, 2 cts. and 5m. for 675 tops, how many tops will 19 mills buy? Ans. 1 top. 52 Whereas an eagle and a cent just threescore yards did buy, How many yards of that same cloth for 15 dimes had I? Ans. 8 yds. 3 qrs. 3 na. 53. If the legislature of a state grant a tax of 8 mills on the dollar, how much must that man pay who is 319 dols. 75 cents on the list? Ans. $2, 55 cts. 8 m. 54. If 100 dols. gain 6 dols. interest in a year, how much will 49 dols. gain in the same time? Ans. $2, 94 cts. 55. If 60 gallons of water, in one hour, fall into a cistern containing 300 gallons, and by a pipe in the cistern 35 galons run out in an hour; in what time will it be filled? Ans. in 12 hours. 56. A and B depart from the same place and travel the same road; but A goes 5 days before B, at the rate of 15 miles a day; B follows at the rate of 20 mile a day; what distance must he travel to overtake A? Ans. 300 miles. RULE OF THREE E INVERSE. THE Rule of Three Inverse, teaches by having three numbers given to find a fourth, which shall have the same proportion to the second, as the first has to the third. If more requires more, or less requires less, the question belongs to the Rule of Three Direct. But if more requires less, or less requires more, the question belongs to the Rule of Three Inverse; which may always be known from the nature and tenor of the question. For example: If 2 men can mow a field in 4 days, how many days will require 4 men to mow it? men days men 1. If 2 require 4 how much time will 4 require? Answer, 2 days. Here more requires less, viz. the more men the less time is required. men days men 2. If 4 require 2 how much time will 2 require? Answer, 4 days. Here less requires more, viz. the less the number of men are, the more days are required-therefore the question belongs to Inverse Proportion. RULE. 1. State and reduce the terms as in the Rule of Three Direct. 2. Multiply the first and second terms together, and divide the product by the third; the quotient will be the answer in the same denomination as the middle term was reduced into. EXAMPLES. 1. If 12 men can build a wall in 20 days, how many mon can do the same in 8 days? Ans. 30 men 2. If a man perform a journey in 5 days, when the day is 12 hours long, in how many days will be perform it when the day is but 10 hours long? Ans. 6 days. 3. What length of board 7 inches wide, will make a square foot? Ans. 19 inches. 4. If five dollars will pay for the carriage of 2 cwt. 150 miles, how far may 15 cwt. be carried for the same money? Ans. 20 miles. 5. If when wheat is 7s. 6d. the bushel, the penny loaf will weigh 9 oz. what ought it to weigh when wheat is 6s. per bushel? Ans. 11 oz. 5 pwt. 6. If 30 bushels of grain, at 50 cts. per bushel, will pay a debt, how many bushels at 75 cents per bushel, will pay the same? 7. If 100%. in 12 months gain 67. interest, what principal will gain the same in 8 months? Ans, £150. 8. If 11 men can build a house in 5 months, by working 12 hours per day-in what time will the same number of men do it, when they work only 8 hours per day? Ans, 7 months, Ans. 20 bushels. 9. What number of men must be employed to finish in 5 days, what 16 men would be 20 days about? Ans. 60 men, 10. Suppose 650 men are in a garrison, and their prov sions calculated to last but 2 months, how many men mus leave the garrison that the same provisions may be sufficient for those who remain 5 months? Ans. 390 men. 11. A regiment of soldiers consisting of 850 men are to be clothed, each suit to contain 31 yards of cloth, which is 1 yds. wide, and lined with shalloon yd. wide; how many yards of shalloon will complete the lining? Ans. 6941 yds. 2 qrs. 23 na. PRACTICE. PRACTICE is a contraction of the Rule of Three Direc when the first term happens to be a unit or one, and is & concise method of resolving most questions that occur in trade or business where money is reckoned in pounds, shilings and pence; but reckoning in federal money will ren der this rule almost useless: for which reason I shall no enlarge so much on the subject as many other writers have done. Tables of Aliquot, or Even Parts. Parts of a shilling. d. 6 S. Parts of a pound. 100 is Parts of a cwt. 12 The aliquot part of any number is such a part of it, as being taken a certain number of times, exactly makes that number. CASE I. When the price of one yard, pound, &c. is an even part of one shilling-Find the value of the given quantity as Is. a yard, pound, &c. and divide it by that even part, and the quotient will be the answer in shillings, &c. 2 100 Or find the value of the given quantity at 2s. per yd. &e. and divide said value by the even part which the given price is of 2s. and the quotient will be the answer in shillings, &c. which reduce to pounds. N. B. To find the value of any quantity at 2s. you need only double the unit figure for shillings; the other figures will be pounds. EXAMPLES. 1. What will 4612 yds. of tape come to at lid. per yd.? S. d. 11d. | | | 461 6 value of 4611 yds. at 1s, per yd 5,7 81 £2 17s. 8d. value at 11⁄2d, 2. What cost 256 lb. of cheese at Sd. per pound? £8 10s. 3d, value at 8d. per pound. 8d. Yards. per yard, 4861 at 1d. 862 at 2d. 911 at 3d. 749 at 4d. £. s. d. CASE II. When the price is an even part of a pound-Find the value of the given quantity at one pound per yard, &c. and divide it by that even part, and the quotient will be the an swer in pounds. EXAMPLES. What will 129 yards cost at 2s. 6d. per yard? s. d. £. S. 26 129 10 value at 1 per yard. Ans, £16 3s. 9d. value at 2s. 6d. per yard. Yds. s. d. 123 at 10 0 per yard 687 at 50 £. s. d. Answers. 61 10 0 171 17 6 |