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EXAMPLES.

1. How much shalloon that is yard wide, will line 6 yards of cloth which is 1yard wido? Yds. yds. yds.

Yds. As 11:54 :: f And 7 XY Xf=W=16,1 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 days. 3. If 13 men in 11; days, mow 21 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 a cwt. 145; miles; how far may 6} cwt. be carried for the same money?

Ans. 22% mile. 6. How many yards of baize which is 11 yards wipe will line 187 yards of camblet yard wide ?

Ans. Il yds. I qr. 13 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 air

swer, &c.

EXAMPLES,

come to ?

1. If} of a yard cost is of a pound; what will 15 yards

15,875,45,583+ and 1,75 Yds. £. Yds. £.

£. s. 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?

Ars. £378 8. If 44 yards cost 3s. 414. what will 305 yards cost ?

Ans. £! 45, 3d. 3 grs. +

4. If 1,4 cwt. of sugar cost 10 dols. 9 cts., what will 9 swt. 3 qrs. cost at the same rate ? cuct.

cwt. 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 it 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 897 yards cost 4 dollars ?

Ans. 1781 yards. 9. If 1781 yds. cost 251 dollars, what cost 29 yards ?

Ans. $41 10. If 1,6 cwt. of sugar cost 12 dols. 12 cts., what cost 3 ihds., each 11 cwt. 3 qrs. 10,12 lb. ?

Ans. 269,072 dols.=$269, 7 cts. 2 m. +

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SIMPLE INTEREST BY DECIMALS.

A TABLE OF RATIOS.
\Rate
per cent. Ratio. \Rate per cent.

Ratio.
3
,03

,055
4

6

,06 4}

6)

,065
5
,05
7

,07 Ratio is the simple interest of 11. 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 toge.. sher, 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?

6

T

cts.
211,45 principal.

,05 ratio.
10,5725 interest for one year.

5 multiply by the time.
52,8625 Ans.=$52, 86 cts. 24 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 qrs. 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 13 years, at 6 per cent. per annum ? Ans. $584,6651.

5. Required the amount of 648 dollars 50 cents for 127 years, at 5; 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=8340, 25 cts.

4. What principal will amount to 9561. 10s. 4,1250. in 87 years, at 5} 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 re: mainder 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
Take the principal 950,75
950,75 x 5=4753,75)285,2250(,06=6 per cent.

285,2250 Ans. 2. At what rate per cent. will 5671. 10s. amount to 8731. 198. 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. 109. 4,125d. in 87 years?

Ans. 51 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 renainder 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 Jollars, 97,5 cents, at 6 per cent. per annum ?

From the amount $1235,975
Take the principal 950,75

950,75 x 06=57,0450)285,2250(5 years, Ans.

285,2250

2. In what time will 5671. 10s. amount to 8731. 198. at wper cent. per annum?

Ans. 9

years. 3. In what time will 340 dols. 25 cts. amount to 626 Acls. 6 cts. at 7 per cent per annum?

4. In what time will 6451, 15s. amount to 9561. 10s. 4,125d. at 5} per ct. per annum ? Ans. 8,758} 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 number 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.)

A TABLE, showing the number of Days from any aay of one

month, to the same day of any other month.

FROM ANY DAY OF

62

Ans. $10, 53 cts. +

£ s. d. qrs.

=8652=8 13 0 1,9 2. What is the interest of 640 dols. 60 cts. for 100 days, 3. Required the interest of 2501. 17s. for 120 days, at á

Ans. £4,1235=41. 2s. 5 d. + 4. Required the interest of 481 dollars 75 cents, for 28 days, at 7 per cent. per annum ? Ans. $2,30 cts. 9m. +

£ 360,5 X 146 ,06

365 at 6 per cent. per annum ? per cent per annum ?

Jan. Feb. Mar. Ap'l. May June July Aug. Scpt Oct. Nov./Dec.
Jan. 3651 334 306) 275 245 214 184 153 122 92 61 31
Feb. 31/ 365 337 306 276245 215 184 153 123

92
Mar. 59 28 365 334 304 273 243 212 181 151 120 901
Apoz. 90 59 31° 365 335 304 274 243 212 182 151 121
May 120

89 61 301 365 334 304 273 242 212 181 151
Junc151120 92 61 31 365 335 304 273 243 212 1821
Juiy 181 150 122 91 61 30 365 334 303 273 242 212
Aug. 212 181 153 122 92161 31 365/ 334 304! 273 243
Sept. 243 212 184. 153 123 91 62 31/ 365 335 304 274
Oct. 273 242 214 183 153 122

92! 61 30 365 334 304
Nov. 304 273 246 214 184 153 123 92 61311 365 335
Dec. 334 303 275 244 214 183 153 122 91 61 30] 3651

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