RULE.-1. State the question; that is, place the numbers so that the first and third terms may be of the same 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 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; multiply the quotient into the second, and the product will be the answer. 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? Here 20 yards, which moves the question, is the third term; 6 yds. the same kind, is the first, and 9 dollars the second. 2. If 20 yards cost 30 dols. what cost 6 yards? Yds. $ Yds. 20: 30 :: 6 Yds. $ Yds. 6:9: 20 9 6)180 Ans. $30 3. If 9 dollars will buy 6 yards, how many yards will 30 dols. buy? $ yds. $ 9 6::30 6 2,0)18,0 Ans. $9 9)180 Ans. 20yd 4. If 3 cwt. of sugar cost 81. 8s. what will 11 cwt. I qr. 24 lb. cost? 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 517. 6s. what will one pair cost? Ans. 4s. 6d. 7. At 10 d. per pound, what is the value of a fir'in c 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 de they come to at 21. 5s. 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. 371⁄2 tuns. 12. If a man's yearly income be 2087. Is. what is that a day? Ans. 11s. 4d. 3-73 qrs. 13. If a man spend 3s. 4d. per day, how much is that a year? Ans. £60 16s. 8d. 14. Boarding at 12s. 6d. per week, how long will 324 10s. last me? Ans. 1 year. 15. A owes B 34751. but B compounds with him for 13s 4d. on the pound; pray what must he receive for his debt! Ans. £2316 13s. 4d. 36 per 16. A goldsmith sold a tankard for 87. 12s. at 5s. 4d. 07..what was the weight of the tankard? Ans. 2 lb. 8 oz. 5pwt. 17. If 2 cwt. 3 qrs. 21 lb. of sugar cost 67. Is. 8d. what cost 35 cwt. ? Ans. £73. 18. Bought 10 pieces of cloth, each piece containing 93 yards, at 11s. 4;d. per yard; what did the whole come to? Ans. £55 9s. 03d. 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 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 su 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 1 qr. 9 lb. sugar come to, at 6 dollars 45 cts. per lb. qr. cwt. ? lb. cts. 1 9 As 112: 645:37 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 middle 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 23. If a man lay out 121, 23 in merchandise, and thereby gaius $39 51 cts. how much will he gain by laying out $13 at the same rate? Cents. Cents. Cents. As 12123: 3951 : : 1200 13230 12123 1107 24. If the wages of 15 weeks come to $64 19 cts. what is e year's wages at that rate? Ans. $222, 52 cts. 5m. 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. $341. 27. When a tun of wine cost 140 dollars, what cost a quart? Ans. 13 cts. 8 m. 28. A merchant agreed with his debtor, that if he would pay him down 65 cts. on a dollar, he would give him up a note 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 bushels will serve 45 horses the same time? Ans. 112 bush. 30. Bought a piece of cloth for $48 27 cts. at $1 19 cts. per 7d.; how many yds. did it contain? Ans.40 yds. 2 grs. 3. 31. Bought 3 hhds. of sugar, each weighing 8 cwt. I qr. 12 lb. at $7 26 cts. per cwt. what come they to? 30 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=95 yds. 33. Bought 3 hhds. of brandy, containing 61, 62, 621⁄2 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, Łow 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? Ans. $S03. |