RULE OF THREE DIRECT IN VULGAR FRACTIONS RULE. PREPARE the fractions as before, then state your queson agreeable to the Rules already laid down in the Rule of Three in whole numbers, and invert the first term in the proportion; then multiply all the three terms continually together, and the product will be the answer, in the same name with the second or middle term. EXAMPLES. 1. If of a yard cost of a pound, what will of an Ell English cost? fyd. off of 12 or Ell Englisi.. Ell. Ell. £. s. d. qrs. As And 2××£.=10 3 11⁄2 Ans. 2. If of a yard cost of a pound, what will 40 yds come to ? Ans. £59 8s. 6d. 3. If 50 bushels of wheat cost 1737. what is it per bash el ? Ans. 78. Od. 133grs. 4. If a pistareen be worth 143 pence, what are 100 pis tareens worth? Ans. £6 5. A merchant sold 54 pieces of cloth each containing 24 yds. at 9s. d. per yard; what did the whole amount to ? Ans. £60 10s. Od 33qrs. 6. A person having of a vessel, selis & of his share for 3127.; wnat is the whole vessel worth? Ans. £780 7. If of a ship oe worth of her cargo, valued at 80007. what is the whole ship and cargo worth? Ans. £10031 148 11d. 78 INVERSE PROPORTION. RULE. PREPARE the fractions and state the question as be fore, then invert the third term, and multiply all the three terms together the product will be the answer. EXAMPLES. 1. How much shalloon that is yard wide, will line 5 yards of cloth which is 10 yard wide? Yds. yds. yds. Yds As 15 And xx-4=164 Ans. 2. If a man perform a journey in 3 days, when the day is 12 hours long; in how many when the day is but 9 hours. 3. If 13 men in 11 days, mow 12 days will 8 men do the same. 4. How much in length that is 73 make a square foot ? days will he do it Ans. 4days. acres, in how mary Ans. 1833 days. inches broad, will Ans. 20 inches. 5. If 95s will pay for the carriage of an cwt 1451 miles; how far may 61 cwt. be carried for the same money ? Ans. 22 miles. 6. How many yards of baize which is 11 yards wide, will line 183 yards of camblet 3 yd. wide? Ans. 11yds. 1qr. 1na. RULE OF THREE DIRECT IN DECIMALS. RULE. REDUCE your fractions to decimals, and state your question as in whole numbers; multiply the second and third together; divide by the first, and the quotient will be the answer, &c. EXAMPLES. 1 If of a yd. cost of a pound; what will 15 yds come to ? 7,875,7,583+ and 3,75 Yds. £. £. s. d. qrs. Yds. £. As ,875,583 :: 15,75: 10,494-10 9 10 2,24 Ans 2. If 1 pint of wine cost 1,2s. what cost 12,5 hhds? Áns. 878 3. If 4 yds. cost 3s. 44d. what will 30 yds. cost! Ans. 1 4s. 3d. 3grs. + 4. If 1,4 cwt. of sugar cost 10 dols. 9 cts. what will 9 cwt. 3 qrs. cost at the same rate? cit As 1,4: 10,09:: 9,75 : 70,269=$70, 26cts. 9m.† 3. If 19 yards cost 25,75 dols. what will 4351 yards come to ? Ans. $590, 21cts. 7m. 6. If 345 yards of tape cost 5 dols. 17 cents, 5m. what will one yard cost? Ans. ,015=14cts. 7. If a man lays out 121 dols. 23 cts in merchandize, and thereby gains 39,51 dols. how much will be gain in laying out 12 dollars at the same rate? Ans. 3,91 dols.=$3,91cts. 8. How many yards of ribbon can I buy for 25 dols. if 29 yds. cost 41 doliars ? 9. If 178 yds. cost 25 Ans. 1781 yards. dollars, what cost 293 yards? Ans. $41 10. If 1,6 cwt. of sugar cost 12 dols. 12 cts. what cost 3 hhds. each 11 cwt. 3 qrs 10,12 lb. ? Ans. 269, 072 dols.=$269, 7cts. 2m+ SIMPLE INTEREST BY DECIMALS. Rat is the simple interest of . for one year; or in federal money, of $1 for one year, at the rate per cent. agreed on. RULE. Multiply the Principal, Ratio and time continually to gether, and the last product will be the interest required. EXAMPLES. 1. Required the interest of 211 dols. 45 cts. for 5 years, at 5 per cent. per annum ? 52,8625 Ans.=$52, 86cts. 21m. 2. What is the interest of 6457. 10s. for 3 years, at 3 per cent. per «anum ? £645,5X06x3=116,190-£116 3s. 9d. 2,4grs. Ans. 3. What is the interest of 1217 8s. 6d. for 4 years, at 6 per cent. per annum ? Ans. £32 15s. 8d. 1,36qrs. 4. What is the amount of 536 dollars 39 cents, for 11 years at 6 per cent. per annunì? Ans. $584,6651. 5. Required the amount of 648 dols. 50 cts. for 123 yrs. at 5 per cent. per annum? Ans. $1103, 26cts. CASE II. The amount, time and ratio given, to find the principal. RULE. Multiply the ratio by the time, add unity to the product for a divisor, by which sum divide the amount, and the qnotient will be the principal. EXAMPLES. 1. What principal will amount to 1235,975 dollars, m 5 years, at 6 per cent. per annum ? $ at 6 $ ,06×5+1=1,30, 1235,975(950,75 Ans. 2. What principal will amount to 8737. 19s. in 9 years, per cent. per annum ? Ans. £567 10s. 3. What principal will amount to 626 dols. 6 cts in 12 years, at 7 per cent ? · Ans. $340,25-$340, 25ets. 4. What principal will amount to 9567. 10s. 4,125d. in 82 years, at 51 per cent. ? Ans. £645 15s. CASE III. The amount, principal and time given, to find the ratio. RULE.-Subtract the principal from the amount, divide the remainder by the product of the time and principal, and the quotient will be the ratio. EXAMPLES. 1 At what rate per cent. will 950,75 dols. amount to 1731975 tols. in 5 years? From the amount 1235,975 Take the principal = 950,75 950,75x5=4753,75)285,2250(,06=6 per cent. Ans. 285,2250 2. At what rate per cent. will 5677. 10s. amount to 8731. 19s. in 9 years ? 3. At what rate per cent. will 340 dols. 25 cts. amount to 626 dols. 6 cts. in 12 years? Ans. 6 per cent. Ans. 7 per cent. Ans. 5 per cent. 4. At what rate per cent. will 645l. 15s. amount to 9567. 10s. 4,125d. in 83 years? CASE IV. The amount, principal, and rate per cent. given, to find the time. RULE. Subtract the principal from the amount; divide the re mainder by the product of the ratio and principal; and the quotient will be the time. EXAMPLES. 1. In what time will 950 dols. 75 cts. amount to 1235 dollars, 97,5 cents, at 6 per cent. per annum ? From the amount Take the principal $1235,975 950,75 285,2250 950,75x06=57,0450)285,2250(5 years, Ans. 2. In what time will 5671. 10s. amount to 8731. 19s. at 6 per cent. per annum ? 3. In what time will 340 dols. 25 cts. dols. 6 cts. at 7 per cent. per annum ? Ans. 9 years. amount to 626 Ans. 12 years. 4. In what time will 645l. 15s. amount to 9567. 10s. 4,125d. at 51 per ct. per annum? Ans. 8.75=83 years. TO CALCULATE INTEREST FOR DAYS. RULE Multiply the principal by the given number of days, and that product by the ratio; livide the last product by 365 (the number of days in a year) and it will give the interest required. |