RULE OF THREE DIRECT IN VULGAR FRACTIONS. RULE. PREPARE the fractions as before, then state your question 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. s. d. qrs. 1. If 4 of a yard cost of a pound, what will is of an Ell English ost? {yd.=of of }= or El English. EU. £. EU. As} ::: And *****=*£=10 3 14 Ans. 2. If of a yard cost 7 of a pound, what will 40 yds. come to? Ans. £ 59 8s. 6d. 3. If 50 bushels of wheat cost 1731. what is it per bushel ? Ans. 7s. Od. 1aqrs. 4. If a pistareen be worth 14 pence, what are 100 pistareens worth? 5. A merchant sold 54 pieces of cloth, each containing 24 yds. at 9s. fd. per yard; what did the whole amount to ? Ans. £60 10s. Od. 3qrs. 6. A person having of a vessel, sells of his share for 3121. ; what is the whole vessel worth? 7. If of a ship be worth of her cargo, valued at 87001. what is the whole ship and cargo worth? Ans. £10031 14s. 11 d. Ans. 56 Ans. 6780 INVERSE PROPORTION. RULE. PREPARE the fractions and state the question as before, then invert the third term, and multiply all the three terms together, the product will be the answer. EMAMPLES. 1. How much shalloon that is } yard wide, will line 51 yards of cloth which is 1+ yard wide ? Yds. yds. yds. Yds. As 11:51: And Xx+x=W=16,1 Ans. 2. If a man perform a journey in 31 days, when the day is 124 hours long; in how many days will he do it when the day is but 9 hours. Ans. 4 days. 3. If 13 men in 11 days, mow 214 acres, in how many days will 8 men do the same. Ans. 1841 days. 4. How much in length that is 7} inches broad, will make a square foot ? Ans. 20 inches. 5. If 254s. will pay for the carriage of an cwt. 1454 miles; how far may 64 cwt. be carried for the same mo. Ans. 22,8 miles. 6. How many yards of baize which is 14 yards wide, will line 187 yards of camblet | yd. wide ? Ans. 11yus. 1gr. lj na. 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. £. s. d. 1. If 7 of a yd. cost of a pound ; what will 15 yds. come to 1=,875 ;=,583+and 1=,75 Yds. Yds. £. grs. 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. ? Ans. £.378 8. If 4tyds. cost 3s. 410. what will 305 vds cont? Ans. fo.1 48 4d 247a. 4. If 1,4 cwt. of sugar cost 10 dols. 9 cts, what will 9 cwt. 3 qrs. cost at the same rate ? cut. 8 cwt. 8 As 1,4 : : 10,09 : : 9,75 : 70,269=$70, 26cts. 9m. + 5. If 19 yards cost 25,75 dols. what will 4354 yards come to ? Ans. 8590, 21cts. 7m. 6. If 345 yards of tape cost 5 dols. 17 cents, 5m. what will 1 yard cost ? Ans. ,015=1}cts. 7. If a man lays out 121 dols. 23 cts. in merchandize, and thereby gains 39,51 dols. how much will he 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 294 yds. cost 41 dollars ? Ans. 178} yards. 9. If 1785 yds. cost 254 dollars, what cost 297 yards ? Ans. 84+ 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. A TABLE OF RATIOS. Ratio is the simple interest of il. 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 5years, 5 per cent. per annum? 8 cts. ,05 Ratio 10,5725 Interest for one year. 5 Multiply by the time. per cent. 52,8625 Ans.=852, 86cts. 24in. 2. What is the interest of 6451. 10s. for 3 years, at 6 per cent. per annum ? 6645,5 X06x3=116,190=4116 Ss. 9d. 2,4qrs. Ans. 3. What is the interest of 1211. 83. 6d. for 4 years, at 6 per amnum? Ans. £S2 15s. 8d. 1,36grs. 4. What is the amount of 536 dollars 39 cents, for 13 years at 6 per cent. per annum: ins. $584,6651. 5. Required the amount of 648 dols. 50 cts. for 124 yrs. at 55 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 quotient will be the principal. 1. What principal will amount to 1235,975 dollars, in 5 years, at 6 per cent. per annum ? $ 8 ,06x5+1=1,30) 1235,975(950,75 Ans. 2. What principal will amount to 8731. 19s. in 9 years, at 6 per cent. per annum ? Ans. £,567 ios. 3. "What principal will amount to 626 dols. 6 cts. in 12 years, at 7 per cent. ? Ans. $340,25=8340, 25cts. 4. What principal will amount to 9561. 20s. 4,125d. in 87 years, at 55 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 prinápal, and the quotient will be the ratio. EXAMPLES. EXAMPLES. 1. At what rate per cent. will 950,75 dols. amount to 1235, 975 dols. in 5 years ? 950,75 X5=4753,75)285,2250,06=6 per cent. 285,2250 Ans. 2. At what rate per cent. will 5671. 10s. amount to 8731. 19s. in 9 years ? Ans. 6 per cent. 3. At what rate per cent. will 340 dols. 25 cts. amount to 626 dols. 6 cts. in 12 years ? Ans 7 per cent. 4. At what rate per cent. will 645l. 158. amount to 9561. 10s. 4,125d. in 87 years ? Ans. 53 per cent. CASE IV. The amount, principal, and rate per cent. given, to find the time. RULE. Subtract the principal from the amount; divide the remainder by the product of the ratio and principal ; and the quotient will be the time. 1. In what time will 950 dols. 75 cts. amount to 1235 dollars, 97,5 cents, at 6 per cent. per amnum ? 285,2250 EXAMPLES. Ans. 9 years. 2. In what time will 5671. 10s. amount to 8731. 19s. at 6 per cent. per annum ? 3. In what time will 340 dole. 25 cts. amount to 626 dols. 6 cents at 7 per cent. per annum ? Ans. 19 years. 4. In what time will 6451. 158. amount to 9561, 106, 4,125d. at 55 per ct. per annum ? Ans.8,75=8+ years. TO CALCULATE INTEREST FOR DAYS.' RULE. Multiply the principal by the given number of days, and that product by the ratio; divide the last product by 865 (the number of days in a year) and it will give the kterest required. |