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, ir. the same naine with the second or middle term.

EXAMPLES.

1. If of a yard cost of a pound, what will of an Ell English cost?

syd.= off of 1=2; or ¦ Ell English.

54

Ell. £. Ell. s. d. qrs. As ::: Aud 7×3×=£.=10 3 14 Ans. 2. If of a yard cost of a pound, what will 40 yards 'me to? Ans. £59 8s. 6d. 3. If 50 bushels of wheat cost 1737. what is it per bush Ans. 7s. Od. 13 qrs.

el? 4. If a pistareen be worth 143 pence, what are 100 pista Ans. £6 reens worth? 5. A merchant sold 5 pieces of cloth, each containing 241 yards at 9s. d. per yard; what did the whole amount Ans, £60 10s. Od. 33 qrs. 6. A person having of a vessel, sells & of his share for 3127.; what is the whole vessel worth?

to?

Ans. £780

7. If of a ship be worth 3 of her cargo, valued at 80007. what is the whole ship and cargo worth?

Ans. £10031 14s. 11d.

INVERSE PROPORTION.

RULE.

Prepare the fractions and state the question as before. hen invert the third term, and multiply all the three terins together, the product, will be the answer.

EXAMPLES.

1. How much shalloon that is yard wide, will line yards of cloth which is 13 yard wide?

Yds. yds. yds.

Yds.

As 1:54 And xx=w=16 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?

3. If 13 men in 11 days, mow 21 days will 8 men do the same?

4. How much in length that is 7 make a square foot?

days.

Ans. 4 acres, in how many Ans. 18 days. inches broad, will Ans. 20 inches.

5. If 253s. will pay for the carriage of a cwt. 145 miles; how far may 61 cwt. be carried for the same money

?

Ans. 22 mile.

6. How many yards of baize which is 14 yards wie, will line 187 yards of camblet yard wide?

Ans. 11 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 an swer, &c.

EXAMPLES.

1. Lf of a yard cost of a pound; what will 15; yard, come to ? 1,875,=,583+ and -,75 £. s. d. grs.

Yds.

£.

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 hlids?

Ans. £378

3. If 4 yards cost 3s. 44d. what will 30 yards cost? Ans. £1 4s, 3d. 3 gri.+

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

cut. As 1,4

10,09 :: 9,75: 70,269=$70, 26 cts. 9 m.+ 5. If 19 yards cost 25,75

come to?

dollars, what will 435 yards Ans. $590, 21 cts. 72 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 251⁄2 dols. if 03 yards cost 4 dollars? Ans. 178 yards. 9. If 178 yds. cost 25 dollars, what cost 293 yards?

Ans. 841 10. If 1,6 cwt. of sugar cost 12 dols. 12 cts., what cost 3 hds., each 11 cwt. 3 qrs. 10,12 lb. ?

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

SIMPLE INTEREST BY DECIMALS.

A TABLE OF RATIOS.

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 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 annum?

& cls.

211,45 principal.
,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 6457. 10s. for 3 years, at 5 per cent. per annum?

£645,5×06×3=116,190=£116 3s. 9d. 2,4 qrs. Ans. 3. What is the interest of 1217. 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 11 years, at 6 per cent. per annum? Ans. $584,6651. 5. Required the amount of 648 dollars 50 cents for 123 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? $ $

,66×5+1=1,30, 1235,975(950,75 Ans. 2. What principal will amount to 8737. 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. amount to 9567. 10s. 4,125d. 15 Ans. £645 15s.

4. What principal will 8 years, at 51 per cent.?

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?

950,75×5=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.

Ans. 51 per cent.

4. At what rate per cent. will 6457. 15s. amount to 9561. 10s. 4,125d. in 83 years?

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?

From the amount $1235,975

Take the principal

950,75

285,2250

950,75X06-57,0450)285,2250(5 years, Ans.

2. In what time will 5671. 10s. amount to 8737. 19s. at per cent. per annum?

3. In what time will 340 dols. 25 cts. ols. 6 cts. at 7 per cent per annum?

Ans. 9 years. amount to 626 Ans. 12 years.

4. In what time will 6457. 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; 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 3607. 10s. for 146 days, at 6 pr. ct.?