for 5 yards, and sold it again at the rate of 11 dollars for 7 yards; did I gain or lose in the purchase, and how much? Ans. I gained $46, 28c. 57m.+ 45. If a man have a salary of 327 English guineas (at 28s.) a year, how much may he spend one day with another, to lay up 625 dollars at the year's end? Ans. $2, 46c. 84 m. 46. A merchant bought 14 pipes of wine at 14s. 6d., (New York currency,) per gallon; how many dollars will pay the purchase? Ans. $3197,25. 47. A merchant bought 274 Ells Flemish of Holland, at 48 cents per Ell, and sold it again at 94 cents per Ell Enghow much did he gain on the whole ? lish; Ans. $23, 1c. 6m. 48. If 50 gallons of water in one hour fall into a cistern which will hold 230 gallons, and by a pipe in the cistern 35 gallons run out in an hour; in what time will it be filled? Ans. 15h. 20m. 49. A and B depart from the same place and travel the same road; but A goes 5 days before B at the rate of 20 miles a day; B follows at the rate of 25 miles a day; what distance must B travel to overtake A? Ans. 500 miles. RULE OF THREE INVERSE. 1. The Rule of Three Inverse teaches, from three given numbers to find a fourth, which shall have the same proportion to the second, as the first has to the third. 2. When more requires more, or less requires less, the question belongs to the Rule of Three Direct. 3. But if more requires less, or less requires more, the question belongs to the Rule of Three Inverse. [More requiring more is when the third term is greater than the first, and requires the fourth term to be greater than the second; less requiring less is when the third term is less than the first, and requires the fourth term to be less than the second.-Also, more requiring less is when the third term is greater than the first, and requires the fourth term to be less than the second; and less requiring more is when the third term is less than the first, and requires the fourth term to be greater than the second.] Thus, if 3 men can perform a piece of work in 6 days, how long will it take 6 men to do the same? It is evident that if three men require 6 days, 6 men will do it in half the number of days, that is, 3 days Here more requires less, viz. the more men the less time is required. If 6 men require 3 days, how many days will 3 men require? Ans. It is evident that 3 men will require as much again time as 6 men would, viz.: 6 days. Here less requires more, that is, the less the number of men is, the more days are required. RULE. 1. State the question, and reduce tne terms the same 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 that the middle term was reduced to. EXAMPLES. 1. If 10 men can dig a ditch in 18 days, how many men will do the same in 6 days? Ans. 30 men. 2. If a man perform a journey in 10 days, when the days are 12 hours long, in how many days will he perform the same when the days are but 10 hours long? Ans. 12 days. 3. If 20 bushels of grain, at 75 cents a bushel, will pay a debt, how many bushels, at 50 cents a bushel, will pay the same? Ans. 30 bushels. 4. What length of board that is 5 inches wide will make Ans. 27 inches. a square foot? 5. If when wheat is $1,25 per bushel the penny-loaf will weigh 9oz., what ought it to weigh when wheat is $1,00 bushel? Ans. 11oz. 5pwt. per 6. If $100 in 12 months gain $6 interest, what principal will gain the same in 8 months? Ans. $150. 7. If 5 dollars will pay for the carriage of 3cwt. 150 miles, how far may 15cwt. be carried for the same money? Ans 30 miles. 8. How many men must be employed to finish in 8 days what 18 men would do in 24 days? Ans. 54 men. 9. There was a certain building erected in 8 months by 120 workmen, but the same being demolished, it is required to be rebuilt in 2 months; I demand how many men must be employed to do it? Ans. 480 men. 10. Suppose 850 soldiers are placed in a garrison, and their provisions calculated to last but 2 months; how many must leave the garrison, that the same provisions may last those who remain, 5 months? Ans. 510. 11. How many yards of cambric, yard wide, will line 5 yards of cloth which is 14 yards wide? Ans. 9 yards Oqrs. 23 nails. 12. A regiment of soldiers, consisting of 652 men, is to be clothed, each suit to contain 3 yards of cloth which is 12 yards wide, and lined with flannel yard wide; how many yards of flannel will line the whole? Ans. 5324yds. 2qrs. 23 nails. Note. The foregoing are the common methods of solving questions in the Rule of Three Direct and Inverse, which we consider most applicable to general practice.-There is, however, another method of solving questions in these Rules, without making any distinction between Direct and Inverse proportion, and as some may have a preference for this method of operation, we therefore insert the following Rule, in which no distinction is made between Direct and Inverse proportion, together with some examples. RULE. Write that number for the 3d term which is of the same name or kind with the answer; then, if by the nature of the question the answer ought to be greater than the third term, write the greater of the two remaining numbers for the second term, and the less number for the first term. But if the answer ought to be less than the third term, place the least of the two remaining numbers for the second term, and the greater for the first term; then multiply the second and third terms together, and divide the product by the first term, and the quotient will be the answer in the same name of the third term. 3. If 8 men can build a wall in 20 days, how many men will do the same in 5 days? days. days. men. As 5 20:8: Ans. 32 men. 4. If 32 men can build a wall in 5 days, how many men will do the same in 20 days? days. days. mon. As 20:5: 32: Ans. 8 men. 5. If 8 bushels of wheat cost 11 dollars, what will 25 bushels cost? bush. bush. dols. As 8 25 :: 11 : 11 8)275 Ans. $34. 6. If a man perform a journey in 11 days when the days are 15 hours long, in how many days will he perform the same when the days are but 10 hours long? hours. hours. days. As 10 15 :: 11 : 11 10)165 Answer 16 days. 7. How many yards of cloth which is yard wide will line 9 yards of broadcloth, which is 14 yards wide? qrs. yds. yds. As 3: 19: Ans. 15 yards. Note. When the first and second terms are of different denominations, they must both be reduced to the same denomination. And if the third term be a compound number, reduce it to the lowest name mentioned. 8. If 3cwt. 1qr. of sugar cost $21, 6cts., what cost 35 qrs. cts. 140:: 2106: Ans. $226,80. 9. If 45 bushels of grain, at 75 cents per bushel, will pay a debt, how many bushels, at 1 dollar per bushel, will pay the same? cts. cts. bush. As 100 75: 45: Ans. 33bu. 3pks. The Latin term per centum, and its abbreviation per cent, signify by the hundred. Thus, 1 per cent of any number is of that number; 2 per cent is 10; 3 per cent 30; 4 per cent is 100; 5 per cent is so on. 1. What is 4 per cent of 1156 dollars? $1156 5 and 4 per cent is 100; therefore we multiply by 4 and divide by 100. To divide by 100, we need only cut off two figures from the right. Ans. 46 dollars 24 cents. $46,24 2. What is 5 per cent or 5, of $145 68 cents? $145,68 Ans. 7'28,40-$7 28cts. 4 mills. 3. What is 12 per cent of $250 ? 4. What is 7 per cent or 1 of $500? 7. What is 5 per cent of $956, 14? $ cts. mls. Ans. 30. Ans. 35. |