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Note. In reducing the common fractions in this example, it will be sufficiently exact if the decimal be extended to three places.
Ans. 1084 lb,
1089 4. At 123 cents per lb. what will 374 lbs. of butter cost?
Ans. $47184. 5. At $17'37 per ton for hay, what will 11s tons cost?
Ans. $201'923. 6. The above example reversed. At $201'923 for 113 tons of hay, what is that per ton ?
Ans. $17'37. 7. If '45 of a ton of hay cost $9, what is that per ton? Consult TT 65.
Ans. $20. 8. At '4 of a dollar a gallon, what will 625 of a gallon of molasses cost ?
Ans. $1. 9. At $9 per cwt., what will 7 cwt. 3 qrs. 16 lbs. of sugar cost?
Note. Reduce the 3 qrs. 16 lbs. to the decimal of a cwt., extend. ing the decimal in this, and the examples which follow, to four places.
Ans. 71'035 + 10. At $69-875 for 5 cwt. 1 qr. 14 lbs. of raisins, what is that per cwt. ?
Ans. $13. 11. What will 2300 lbs. of hay come to at 7 mills per lb. ?
Ans. $16'10. 12. What will 765} lbs. of coffee come to, at 18 cents per lb. ?
Ans. $13779. 13. What will 12 gals. 3 qts. 1 pt. of gin cost, at 28 cents per
Note. Reduce the whole quantity to quarts and the decimal of a quart.
Ans. $14'42. 14. Bought 16 yards 2 qrs. 3 na. of broadcloth, for $100ʻ125; what was that per yard?
Ans. $6. 15. At $1'92 per bushel, how much wheat may be bought for $72.
Ans. I peck 4 quarts. 16. At $92'72 per' ton, how much iron may be purchased for $60 268 ?
Ans. 13 cwt. 17. Bought a load of hay for $9'17, paying at the rate of $16 per ton; what was the weight of the hay? Ans. 11 cwt. 1 qr. 23 lbs.
18. At $302'4 per tun, what will i hhd. 15 gals. 3 qts. of wine cost?
Ans. $94'50. 19. The above reversed. At $94'50 for 1 hhd. 15 gals. 3 qts. of wine, what is that per tun?
Ans. $302'4. Note. The following examples reciprocally prove each other, excepting when there are some fractional losses, as explained above, and even then the results will be sufficiently exact for all practical purposes. If, however, greater exactness be required, the decimals must be extended to a greater number of places.
20. At ?!'80 for 3] qts. of wine, 21. At $2'215 per gal., what what is that per gal. ?
cost 3] qts.? 22. If ik of a ton of potashes 23. Ai 96'72 por ton for potcost $60-45.what is that per ton ? jashes, what will g of a ton cost ?
24. If '8 of a yard 25. If a yard of cloth) 26. At $2'5 per yard, of cloth cost $2, what cost $2'5, what will 8 how much cloth may is that per yard? of a yard cost ? be purchased for $2 ?" 27. It 14 cwt. of pot 28. If a ton of pot
29. At 27 £. 10 s., ashes cost 19 £. 5 s., ashes cost 27 £. 10 s. a ton for potashes, what is that per ton ? what will 14 cwt. what quantity may be cost?
bought for 19 £. 5's.? Note. After the same manner let the pupil reverse and prove the following examples :
30. At $18'50 per ton, how much hay may be bought for $12'025 ? 31. What will 3 qrs. 2 na. of broadcloth cost, at $6 per yard ? 32. At $22'10 for transportation of 65 cwt. 46 miles, what is that
33. Bought a silver cup, weighing 9 oz. 4 pwt. 16 grs., for 3 £. 2 s. 3 d.
33 9. ; what was that per ounce ? 34. Bought 9 chests of tea, each weighing 3 cwt. 2 qrs. 21 lbs., at 4 £. 9 s. per cwt. ; what came they to?
35. If 5 acres 1 rood produce 26 quarters 2 bushels of wheat, how manfy acres will be required to produce 47 quarters 4 bushels ?
Note. The above example will require two operations, for which consult | 65, ex. 1.
36. A lady purchased a gold ring, giving at the rate of $20 per ounce; she paid for the ring $1625; how much did it weigh ?
per ton ?
REDUCTION OF CURRENCIES.
178. Previous to the act of Congress, in 1786, establishing federal money, all calculations in money, throughout the United States, were made in pounds, shillings, pence and farthings, the same as in England. But these denominations, although the same in name, were different in value in different countries.
Thus, 1 dollar is reckoned in
called Canada currency.
s. 6 d., called Pennsylvania currency.
} 4 s. 8 d., called Georgia currency. 1. Reduce 6 £. 11 s. 61 d. to federal money. Note. To reduce pounds, shillings, pence and farthings, in either of the above-named currencies, to federal money,-First, reduce the shillings, pence and farthings (if any be contained in the given sum) to the decimal of a pound by inspection, as already taught, IT 76.
6 £. 11 s. 64 d. £6'576. English Money. Now, supposing the above sum to be English money,--1 £. is 20 s. = 240 pence, in all the above currencies. I dollar, in English money, is reckoned 4 s. 6 d. = 54 pence, that is,
of 1 pound. Now, as many times as % the fraction which; 1 dollar is of 1 pound, English ñoney, is contained in £6'576, so many dollars, it is evident, there must be; that is,-To reduce English to federal money,—Divide the given sum by dos tient will be federal money. £6'576 English money.
Note. It will be resollected, to divide by a
fraction, we multiply by 9 ) 263-040
the denominator, and di
vide the product by the 29*226federal money, Answer. numerator. CANADA CURRENCY. Supposing the above sum to be Canada currency, -1 dollar, in this currency, is 5 s. = 60 pence, that is, = of 1 pound. Therefore,—To reduce Canada currency to federal money,-Divide the given sum by 4, and the quotient will be federal money; or, which is the same thing, multiply the given sum by 4.
£6'576 Canada currency.
$26'304 federal money, Answer. New ENGLAND CURRENCY. 1 dollar, in this currency, is 6 s. = 72 pence, that is, *=, or of a pound. Therefore,—To reduce New England currency to federal moncy,Divide the given sum by '3.
13 ) £6'576 New England currency.
$21'92 federal money, Answer. NEW YORK CURRENCY. 1 dollar, in this currency, is 8 s. = 96 pence, that is, 6 = 4, or '4 of a pound. Therefore,-To reduce New York currency to federal money,-Divide the given sum by '4.
4) £6'576 New York currency.
$16'44 federal money, Answer. PENNSYLVANIA CURRENCY. 1 dollar, in this currency, is 7 s. 6 d. = 90 pence, that is 90 = of a pound. Therefore,—To reduce
240 Pennsylvania currency to federal money,-Divide by }, that is, mul. tiply the given sum by 8, and divide the product by 3.
£6'576 Pennsylvania currency.
3 ) 52'608
Answer. GEORGIA CURRENCY. i dollar, Georgia currency, is 4 s. 8 d. 56 pence, that is, o = 3% of a pound. Therefore, To reduce Georgia currency to federal money,—Divide by 3%, that is, multiply the given suin by 30, and divide the product by 7.
£6'576 Georgia currency.
7 ) 197'280
$28ʻ182ę federal money, Answer. From the foregoing examples, we derive the following genera RULE :-To reduce English money, and the currencies of Canada and the several states, to federal money, --First, reduce the shillings, &c., if any in the given sum, to the decimal of a pound; this being done, divide the given sum by such fractional part as 1 dollar, in the given currency, is a fractional part of 1 pound.
EXAMPLES FOR PRACTICE. 2. Reduce 125 £., in each of the before named currencies, to fede125 £. English money,
is $555-555&. 125 £. Canada currency,
$ 500. 125 £. New England currency,
$416-6667. Answers, 125 £. New York currency,
$ 312'50. 125 £. Pennsylvania currency,
$ 333'333}. 125 £. Georgia currency,
$535*7144. 3. Reduce 1 s. 6 d., in the several currencies, to federal money.
Answers, 1 s. 6 d. = '075 £. English money, is $'333}; Canada currency, it is $'30; New England currency, it is $'25 ; New York currency, it is $187}; Pennsylvania currency, it is $'20; Georgia currency, it is $321
213. 4. Reduce 75 £. 15 ş., in the several currencies, to federal inoney,
5. Reduce 18 £. O s. 89 d., in the several currencies, to federal money.
6. Reduce 45 d., in the several currencies, to federal money
7. Reduco 36 £. 3 s. 74 d., in the several currencies, to federal money.
119. To reduce federal money to any of the before named cur. rercies, reverse the process in the foregoing operations; that is,Multiply the given sum in federal money by such fractional part as 1 dollar, in that currency to which you would reduce it, is of 1 pound. The product will be the answer in pounds, and decimals of a pound, which must be reduced to shillings, pence and farthings, by inspection, as alrcady taught, 1 77.
EXAMPLES FOR PRACTICE. 1. Reduce $118-25 to the several before named currencies.
d. English money,
is 26 15.
0. Pennsylvania currency,
44 6 103. Georgia currency,
11 2. Change $250 to the several currencies. 3. Change 56 cents to the several currencies. 4. Change $45-123 to the several currencies.
9 80. It may sometimes be required to reduce one currency to the par, or equality of another currency.
1. Reduce 35 £. 6 s. 8 d., English money, to New England currency.
$1 is 4 s. 6 d.= 54 d. English money. $1 is 6 s. = 72 d. Nero England currency; that is, the value of any number of pounds, shillings, pence, &c., English money, is z = of the same in N. England currency; consequently,-To reduce English money to N. England currency-Multiply by , or, which is the same, increase it by $ part of itself. Thus,
£. 8. d. 9.
2 2 2 New England currency, answer. Hence we have this general Rule for finding a multiplier to reduce any currency to the par of another :
Make $1 in pence, of the currency to be reduced, the denominator of a fraction, over which write $1 in pence, of the currency to which it is to be reduced, for a numerator. This fraction may then be reduced to its lowest terms before multiplying.
On the same principles, let the pupil forın for himself multiplicrs, hy which To reduce English money to Canada, N. York, Pennsylvania, and
Pennsylvania, and Georgia currencies.