RULE OF THREE DIRECT IN VULGAR FRACTIONS. RULE, 007 Prepare the fractions as before, then state your question 4 agreeable to the Rules already laid down in the Rule of Three in whole numbers, and invert the first term in the proportion; then inultiply all the three terms continually together, and the product will be the answer, ir: the same naine with the second or middle term. EXAMPLES. s. d. qrs. 1. If of a yard cost of a pound, what will is of an Ell | English cost ? byd.=of of 1=lf or | Ell English. Eli. £. Ell. As } ::: 1 And 1 x * Xp=fiz£.=10 3 14 Ans. 2. If } of a yard cost of a pound, what will 40% yards yime to? Ans. £59 8s. 61d. 3. If 50 bushels of whcat cost 1731, what is it per bush ed? Ans. 7s. Od. 14 qrs. 4. If a pistareen be worth 14; pence, what are 100 pista reens worth? Ans. £6 15. A merchant sold 51 pieces of cloth, each containing 14} yards at 9se jd. per yard; what did the whole amount Ans, £60 10s. Od. 3 qrs. 6. A person having f of a vessel, sells of his share for 312. ; what is the whole vessel worth ? Ans. £780 7. If 7 of a ship be worth of her cargo, valued at 80001. what is the whole ship and cargo worth? Ans. £10031 14s. 11 d. lo? INVERSE PROPORTION. RULE. Prepare the fractions and state the question as before. len invert the third term, and multiply all the threo terine Ingether, the product, will he the answer. EXAMPLES 1. How much shalloon that is yard wide, will line 51 yards of cloth which is 14 yard wide ? Yds. yds. yds. Yds. As 11:54::And 1 XY X=W=164 Ans . 2. If a man perform a journey in 3 days, when the day is 12; hours long; in how many days will he do it when the day is but 9 hours ? Ans. 44's days. 3. If 13 men in 11; days, mow 21 acres, in how many days will 8 men do the same? Ans. 1847 days. 4. How much in length that is 71 inches broad, will make a square foot ? Ans. 20 inches. 5. If 253s. will pay for the carriage of a cwt. 1454 miles; how far may 61 cwt. be carried for the same money ? Ans. 22.4 mile. 6. How many yards of baize which is 14 yards wijn will line 187 yards of camblet yard wide ? Ans. Il yds. 1 gr. 1; na. RULE OF THREE DIRECT IN DECIMALS. RULE. Reduce your fractions to decimals, and state your ques tion as in whole numbers; multiply the second and third to gether; divide by the first, and the quotient will be the art Swer, &c. EXAMPLES £. s. d. grs. 1. Lf 1 of a yard cost la of a pound; what will 15 yard, come to ? 1=,875,6=,583+ and =,75 Yils. £. Yds. £. As ,875: ,583 :: 15,75: 10,494=10 9 10 2,24 Ans 2. If i pint of wine cost 1,2s. what cost 12,5 hlids ? Ans. £378 3. If 41 yards cost 3s. 4fd. what will 304 yards cost ? Ans. £1 4$. 3d. 3 qrs. + 4. If 1,4 cwt. of sugar cost 10 dols. 9 cts., what will 9 cwt. 3 qrs. cost at the same rate ? cict. crot. As 1,4:: 10,09 :: 9,75 : 70,269=$70, 26 cts. 9 m. + 5. If 19 yards cost 25,75 dollars, what will 435, yards come to ? Ans. $590, 21 cts. 7* m. 6. If 345 yards of tape cost 5 dols. 17 cents, 5 m., what will one yard cost ? Ans. ,015=1} cts. 7. If a man lay out 121 dollars 23 cts. in merchandise, and thereby gains 39,51 dollars, how much will he gain in laying out 12 dollars at the same rate ? Ans. $3,91=$3, 91 cts. 8. How many yards of riband can I buy for 25, dols. if 20 yards cost 4 dollars ? Ans. 1781 yarıls. 9. If 1781 yds. cost 25 dollars, what cost 29% yards ? Ans. 841 10.' If 1,6 cwt. of sugar cost 12 dols. 12 cts., what cost 3 slids., each 11 cwt. 3 qrs. 10,12 lb. ? Ans. 269,072 dols.=$269, 7 cts. 2 m. + ,04 SIMPLE INTEREST BY DECIMALS. A TABLE OF RATIOS. Ratio. ,055 6 ,06 ,065 ,07 RULE. Multiply the principal, ratio and time continually toge. ther, and the last product will be the interest required. EXAMPLES: 1. Required the interest of 211 dols. 45 cts. for 3 years at 5 per cent. per annum? $ cts. ,05 ratio. 10,5725 interest for one year. 5 multiply by the time. 52,8625 Ans.=$52, 86 cts. 2} m. 2. What is the interest of 645l. 10s. for 3 years, at 5 per cent. per annum ? £645,5 x 06 X3=116,190=£116 3s. 9d. 2,4 qrs. Ans. 3. What is the interest of 1211. 8s. 6d. for 44 years, at 6 per cent. per annum ? Ans. £32 15s. 8d. 1,36 qrs. 4. What is the amount of 536 dollars, 39 cents, for 11 years, at 6 per cent. per annum ? Ans. $584,6651. 5. Required the amount of 648 dollars 50 cents for 123 years, at 5į per cent. per annum ? Ans. $1103, 26 cts. 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. EXAMPLES. 1. What principal will amount to 1235,975 dollars, in 5 years, at 6 per cent. per annum ? $ ,66 x 5+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 10s. 3. What principal will amount to $626, 6 cents in 19 years, at 7 per cent. ? Ans. $340,25=$340, 25 cts. 4. What principal will amount to 9561. 10s. 4,125d. 18 84 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 ro. mainder by the product of the time and principale and the quotient will bo the ratio. EXAMPLES. 1. At what rate per cent. will 950,75 dollars amount to 1230,975 dollars in 5 years ? From the amount 1235,975 285,2250 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 6451. 15s. amount to 9561. 10s. 4,125d. in 8 years ? Ans. 5) per cent. CASE IV. The amount, principa , 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. EXAMPLES. 1. In what time will 950 dols. 75 cts. amount to 1235 lollars, 97,5 cents, at 6 per cent. per annum ? Froin the amount $1235,975 950,75 x 06=57,0450)285,2250(5 years, Ans. 285,2250 2. In what time will 5671. 10s. amount to 8731. 19s. at Ans. 9 ycars. i per cent. per annum ? 3. In what time will 340 dols. 25 cts. amount to 026 ols. 6 cts. at 7 per cent per annum? Ans. 12 years. 4. In what time will 6451. 15s. amount to 9561. 10s. 4,125d, at 5per ct. per annum? Ans. 8,75=87 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 365 (the numper of days in a year) and it will give the interest required. EXAMPLES 1. What is the interest of 3601. 10s. for 146 days, at 6 pr. ct.) |