« ΠροηγούμενηΣυνέχεια »
Rule 1. Stato the question; that is, pl ce the numbers so that the first and third terms may be of the sam: kind; and the second term of the same kind with the answer, or thing sought.
2. Bring the first and third terms to the same denomination, and reduce 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 ito any other denomination required.
The method of proof is by inverting the question. (NOTE.–The following methods of operation, when hey 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; multiply 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. 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.
Ans. $30 2. If 20 yards cost 30 dols. 3. If 9 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
Ans. $9 4. If 3 cwt. of sugar cost 81. 8s. what will 11 cwt. I qr. 24 lb. cost? 3 cwt. El. 8s. C
lb. 112 20 11 1 24 As 336 : 168 :: 1284 16. 4
168 336 lb. 168s.
45 [Carried up. 1.0272
10272 7704 1284
-(2,0) 336)215712(64,2 2016
-$21.2s. 1411 Ans. 1344
672 5. If one pair of stockings cost 4s. 6d. what will 19 dozen pair cost ?
Ans. £51 6s. 6. If 19 dozen pair of shoes cost 511. 6s. what will one pair cost?
Ans. As. 6d. 7. At 10d. per pound, what is the value of a firiin of 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 nf 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 a calendar month?
Ans. £6 5s. 10d. 11. If 4 tuns of hay will keep 3 cattle over the winter; how many tuns will it take to keep 25 cattle the same time?
Ans. 371 tuns. 12. If a man's yearly income be 2081. Is. what is that a day?
Ans. 11s. 4d. 3.6 qrs. 13. If a man spend 3s. 4d. per day, how i. uch is that a
Ans. £60 16s. 8d. 14. Boarding at 12s. 6d. per week, how long will 321. 10s. last me?
15. A owes B 3475l. bu' 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 oz.what was the weight of the tankard? Ans. 216.8 oz. 5pwt.
17. If 2 cwt. 3 qrs. 21 lb. of sugar cost 6l. Is. od. what CC: 3:55. cwt. ?
Ans. 1 year,
18. Bought 10 pieces of cloth, each piece containing 9 yards, at 11s. 4 d. per yard; what did the whole come to?
Ans. £55 9s. 0 d.
FEDERAL MONEY. NOTE 1. You must 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 doilars 47 cents, what will 12 yas. cost?
Yds. $ cts. yds.
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 lqr. 9 lb. sugar come to, at 6 dollars 45 cts. per cwt ? qr. lb. 16. cts. 16.
1 9 As 112 : 645 ::37 28
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 numbers, and the quotient will express the answer in the least denomination mentioned in the second, or midule term.
21. If 3 dols. will Luy 7 yds. of cloth, how many yds.can I buy for 120 dols. 75 cts.? cts. yds. cts.
As 300 : : 12075
23. If a man lay out 121, 23 in merchandise, and thereby gai is $39 51 cts. how much will he gain by laying out $12 at the same rate ? C'ents. Conts. Cents. As 12123 : 3951 :
: 1200 1200
-cts. $ rts. 12123)4741200(391=3,91 Ans. 36369
1107 24. If the wages of 15 weeks come to $64 19 cts. what is a year's wages at that rate ? Ans. $2:22, 52 cts. 5 m.
25. A man bought sheep at $1 Il 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, each piece containing 31 yards, at 16s. 6d. per yard, (New-England currency ;) what does the whole amount to in federal inoney? Ans. $341.
27. When a tun of wine cost 140 dollars, what cost a quart?
Ans. 13 cts. 86. m. 28. A merchant agreed with his debtor, that if he would pay him dowj 65 cts. on a dollar, he would give bim up a note of hand of 249 dols. 88 cts. I demand what the debtor must pay for his note?
Ans. $162 42 cts. 2m. 29. If 12 horses eat up 30 bush. of oats in a week, how many bushels will serve 45 horses the same time? Ans. 112; bush.
30. Bought a piece of cloth for $45 27 cts. at $i 19 cts. per yd. ; how many yds. did it contain? Ans. 10 yds. 2 qrs. 36.
31. Bought 3 hhds. of sugar, each weighing 8 cwt. 1 qr. 12 lb. at $7 26 cts. per cwt. what come they to?
Ans. $182 I 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 13 cents per yard ?
Ans. $ 135 85 cts, 2123 + 24+27=95 yds. 33. Bought 3 hl. s. 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 income is $1836 a year, and he spends $3 49 cts. a day, one day with another, tow much will he have saved at the year's end? Ans.$562, 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 that rate ?