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 14:51 :: 1 And 1 x x==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. 4,0's days. 3. If 13 men in 11į days, mow 21 acres, in how many days will 8 men do the same? Ans. 1897 days. 4. How much in length that is 7} inches broad, will make a square foot ? Ans. 20 inches, 5. If 25 s. will pay for the carriage of a cwt. 145/ miles; how far may 61 cwt. be carried for the same money? Ans. 222 mile. 6. How many yards of baize which is 11 yards wi le, will line 187 yards of camblet | yard wide ? Ans. 11 yds. 1 qr. 1} 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 air SWCr, &c. EXAMPLES. S. 1. If 7. of a yard cost 11 of a pound ; what will 15% yards come to ? =,87511=,583+ and 3,75 Yds. £. Yds. £. £. d. qrs. 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 3. If 41 yards cost 3s. 4:1d. what will 30 yards cost ? Ans, £1 43. 3d. 3 qrs.t. 4. If 1,4 cwt. of sugar cost 10 dols. 9 cts., what will 9 cwt. 3 qrs. cost at the same rate ? cict. cwt. 5. If 19 yards cost 25,75 dollars, what will 435} yards come to ? Ans. $590, 21 cts. 77 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 293 yards cost 4 dollars ? Ans. 1781 yards. 9. If 178; yds. cost 25 dollars, what cost 29% 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, 7 cts. 2 m. + SIMPLE INTEREST BY DECIMALS. A TABLE OF RATIOS.' (Rate per Ratio. 5 6 ,03 ,055 41 ,045 ,065 5 ,07 Ratio is the simple interest of ll. for one year; or in feKeral money, of $1 for one year, at the rate per cent. agreed on. 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 5 years, at 5 per cent. per apnum? $ cts. ,05 ratio. 10,5725 interest for one year. 5 multiply by the time. 52,8625 Ans.=$52, 86 cts. 21 m. 2. What is the interest of 6451. 10s. for 3 years, at 5 per cent. per annum ? £645,5 x 06 X 3=116,190=£116 3s. 9d. 2,4 grs. Ans. 3. What is the interest of 1211. 8s. 6d. for 4 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 1} years, at 6 per cent. per annum? Ans. $584,6651. 5. Required the amount of 648 dollars 50 cents for 12 years, at 51 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 12 years, at 7 per cent. ? Ans. $340,25=8340, 25 cts. 4. What principal will amount to 9561, 10s. 4,125d. in 89 years, at 54 per cent. ? Ans. £645 15s. CASE III. The amount, principal and time given, to find the ratio. RULg.–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 dollars amount to 1230,975 dollars in 5 years ? From the amount 1235,975 285,2250 Ans. 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. 15s. amount to 9561. 10s. 4,125d. in 87 years? Ans. 5} 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. EXAMPLES. From the amount $1235,975 950,75 x 06=57,0450)285,2250(5 years, Ans. 285,2250 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 dols. 25 cts. amount to 626 dols. 6 cts. at 7 per cent per annum ? 4. In what time will 6451. 15s. amount to 9561. 10s. 4,125d. at 51 per ct. per annum ? Ans. 8,75=84 years. Ans. 12 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 pumber 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.3 61 311 891 A TABLE, showing the number of Days from any day of one month, to the same day of any other month. FROM ANY DAY OF 91 61 30 365 334 303 273 242 212 31 365 335 3041 274 911 61 30) 365 Ans. $10, 53 cts. + £ s. d. qrs. =865258 13 0 1,9 2. What is the interest of 640 dols. 60 cts. for 100 days, 3. Required the interest of 2501. 178. for 120 days, at 5 Ans. £4,1235=41. 2s. 5 d.+ 4. Required the interest of 481 dollars 75 cents, for 25 days, at 7 per cent. per annum ? Ans. $2,30 cts. 9m. + £ 360,5 x 146 x ,06 365 at 6 per cent. per annum ? per cent per annum ? 62 |