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RULE.-1. State the question; that is, pl.ce the numbers so that the first and third terms may be of the sain 3 kind; and the second lerin of the same kind with the answer, or thing sought.

2. Bring the first and third terms to the same denomination, and l'educe the second term to the lowest name mentioned in it.

3. Multiply the second and third terms together, and divide their product by the first term; and the quotient will be the answer to the question, in the same denomination you left the second term in, which may be brought into any other denomination required.

The method of proof is by inverting the question. [NOTE.-The following methods of operation, when they can be used, perform the work in a much shorter manner than the general rule.

1. Divide the second term by the first; multiply the quotient into the third, and the product will be the answer. Or,

2. Divide the third term by the first; múltiply the quotient into the second, and the product will be the answer. 'Or,

3. Divide the first term by the second, and the third by that quotient, and the last quotient will be the answer. Or,

4. Divide the first term by the third, and the second by that quotient, and the last quotient will be the answer.)

EXAMPLES. 1. If 6 yards of cloth cost 9 dollars, what will 20 yards cost at the same rate ?

Yds. $ Yds. Here 20 yards, which moves the 6:9 :: 20 question, is the third term; 6 yds.

9 the same kind, is the first, and 9 dollars the second.

6)180

Ans. $30 2. If 20 yards cost 30 dols. 3. If I dollars will buy 6 what cost 6 yards ?

yards, how many yards will Yds. *

Yds. 30 dols. buy? $ yds. $ 20 : 30 : : 6

9: 6:: 30 6

6 2,0)18,0

9)180 Ans. $9

Ans. 20yd 4. If 3 cwt. of sugar cost él. 8s. what will 11 cwt. I qr. 24 lb. cost? 3 cwt. El. 8s. C. gr. lb.

1b. 112 20 11 1 24 As 336 : 168 :: 1284 16. 4

168 336 16. 1685,

45 (Carrted ap.) 10272

45
28

364
92

10272 7704 1284

(2,01 336)215712 64,2 2016

-321. 2s 1411 Ans 1344

1284

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672

672 5. If one pair of stockings cost 4s. 6d. what will 19 do zen pair cost ?

Ans. £51 6s. 6. If 19 dozen pair of shoes cost 511. 6s. what will cne pair cost ?

Ans. 4s. 6d. 7. At 10 d. per pound, what is the value of a fir'ain cl butter, weight 56 pounds ?

Ans. £2 9s. 8. How much sugar can you buy for 231. 2s. at 9d. per pound?

Ans. 5 C. 2 qrs. 9. Bought 8 chests of sugar, each 9 cwt. 2 qrs. what do they come to at 21. 58. per cwt. ?

Ans, £171. 10. If a man's wages be 751. 10s. a year, what is that it calendar month?

Ans. £6 5s. 10d. 11. If 41 tans of hay will keep 3 cattle over the winter; how many tuns will it take to keep 25 cattle the same time!

Ans. 37; tuns. 12. If a man's yearly income be 2081. Is. what is that a day?

Ans. 11s. 4d. 3.45 qrs. 13. If a man spend 3s. 4d. per day, how much is that a year?

Ans. £60 16s. 8d. 14. Boarding at 128. 6d. per week, how long will 32% 10s. last me?

15. A owes B 3475l. but B compounds with him for 13s 4d. on the pound; pray what must he receive for his debt

Ans. £2316 13s. 4d. 16. A goldsmith sold a tankard for 81. 12s. at 5s. 4d. per 07.. what was tne weight of the tankard? Ans. 2 lb.8 oz. 5 put.

17. If 2 cwt. 3 qrs. 21 lb. of sugar cost 67. Is. 8d. what cust 35) cwt. ?

Ans. £73.

Ans. 1 year,

18. Bought 10 pieces of cloth, each piece containing 9: yards, at lls. 4 d. per yard; what did the whole come to ?

Ans. £55 9s. 0 d.

FEDERAL MONEY. Note l. You mus: state the question, as taught in the Rules foregoing, and after reducing the first and third terms to the same name, &c. you may multiply and divide according to the rules in decimals; or by the rules for multiplying and dividing Federal Money.

EXAMPLES. 19. If 7 yds. of cloth cost 15 dollars 47 cents, what will 12 yds cost?

Yds. $ cts. yds.
7: 15,47 : : 12

12

7)185,64

Ans. 26,52=$26, 52 cts. But any sum in dollars and cents may be written down as a whole number, and expressed in its lowest denomination, as in the following example: (See Reduction of Federal Money, page 62.) 20. What will l qr. 9 lb. sugar come to, at 6 dollars 45 cwt. ? qr.

16. cts,

16. i 9 As 112 : 645 ::37 28

37

cts. per

ib.

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Note 2. When the first and third 'numbers are federal money, you may annex ciphers, (if necessary,) until you make their decimal places or figures at the right hand of the separatrix, equal : which will reduce them to a like denomination. Then you may multiply and divide, as in whole nunibers, and the quotient will express the answer in the least denomination mentioned in the second, or midule term.

EXAMPLES. 21. If 3 dols. will buy 7 yds. of cloth, how many yds. can ) buy for 120 dols. 75 cts.? cts. yds. cts. As 300 : 7 : : 12075

7

-yds.

300)84525(2812 Ans. 22. If 12 lb. of tea cost 6 dols. 600 78 cts. and 9 mills, what will 5 lb. cost at the same rate ?

2452
18. mills. 1b.

2400
As 12 : 6799 :: 5
5

525

300 12)33945

$cts.m. 2:25 Ans. 2828+mills.--2,82,8.

4

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23. If u man lay out 121, 23 in merchandise, and thereby gaivs $39 51 cts. how much will he gain by laying out $13 at the same rate ? Cents. Cents. Cents. As 12123 : 3951 :

: 1200 1200

-cts. $ cts. 12123)4741200(391=3,91 Ans, 36369

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13230
12123

1107 24. If the wages of 15 weeks come to $64 19 cts. what is 2 year's wages at that rate ? Ans. $222, 52 cts. 5 m.

25. A man bought sheep at $1 11 cts. per head, to the amount of 51 dols. 6 cts.; how many sheep did he buy?

Ans. 46. 26. Bought 4 pieces of cloth, cach piece containing 31 yards, at 16s. 6d. per yard, (New-England currency;) what does the whole amount to in federal money? Ans. $311.

27. When a tun of wine cost 140 dollars, what cost a quart?

Ans. 13 cts. 8147 m. 28. A merchant agreed with his debtor, that if he would pay him dowa 65 cts. on a dollar, he would give him up a Mote of hand of 249 dols. 88 cts. I demand what the debtor Inust pay for his note?

Ans. $162 42 cts. 2m. 29. If 12 horses eat up 30 bush. of oats in a week, how many nushels will serve 45 horses the same time? Ans. 1121 bush.

30. Bought a picce of cloth for $48 27 cts. at $1 19 cts. per 7d.; how many yds. did it contain? Ans.40 yds. 2 qrs.

31. Bought 3 hhds. of sugar, each weighing 8 cwt. I qr. 12 lb. at $7 26 cts. per cwt. what come they to?

Ans. $182 1 ct. 8 m. 32. What is the price of 4 pieces of cloth, the first piece containing 21, the second 23, the third 24, and the fourth 27 yards, at 1 dollar 43 cents per yard?

Ans. $135 85.cts. 21+23+24+27=93 yds. 33. Bought 3 hhds. of brandy, containing 61, 62, 621 gallons, at I dollar 38 cts. per gallon, I demand how much They amount to?

Ans. $255 99 cts. 34. Suppose a gentleman's incoine is $1836 a year, and he spends $3 49 cts. a day, one day with another, low much will he have saved at the year's end? Ans.9502, 15 cts.

35. If my horse stand me in 20 cts. per day keeping, what will be the charge of 11 horses for the year, at thit rate ?

Ans. SSO:

30

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