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3 If 4oz. of silver, worth 58. the ounce, be melted with Soz. at 4s. what is one ounce of this mixture worth
answer 48 4d. 4 A wine merchant mixes 12 gallons of wine at 4s 10d. the gallon, with 24 gallons, at 58 6d. and 16 at 6s 3d.; what is a gallon of this mixture worth? answer 5s. 7d. 1.5 A goldsmith melted together 8oz. of gold of 22 carats fine, ilb. oz. of 21 carats fine, and 10 oz. of 18 carats fine; what is the quality or fineness of the composition ?
answer 20 carats fine. 6 A refiner melted 5lb. of silver bullion of 8oz. fine, with 10lb. of 7oz. and 15lb. of 6oz. fine; of what fineness is ilb. of this mass?
. answer 6oz. 13dwt. 8gr. fine.
.- CASE 2. When the prices of several simples are given, to find how much of each, at their respective rates, must be taken to make a compound at any proposed price;
RULE. Write the rates of the simples under each other ;-link each rate, which is less than the mean rate, with one or more that is greater; the difference or sum of the differences, between each rate and the mean price, placed opposite the respective rate or rates, with which it is linked, will be the several quantities required." Note 1. If all the given prices be greater, or less than the mean rate, they
*must be linked to a cipher. 2. Different modes of linking will produce different answers.
- EXAMPLES. 1 How much rye at 4s. the bushel, harley at Ss. and oats :. at 2s. will make a mixture worth 2s 6d. the bushel ?
- -. 6 at 47 Mean rate 20 36') .
6 at 3 answer. (24- 18+6=24 2 2 Canary at 2s, a quart, Sherry at 16d. and Malaga at is. how much of each must be taken, that the mixture may be worth is 6d. the quart?
8 quarts of Canary,
CASE 3. When the rate of all the simples, the quantity of one of them, and the compound rate of the whole mixture are given; to find the several quantities of the rest;
Place the mean rate, and the several prices, and take their differences, as in case 2 ; then, ..
As the differences of the same name with the quantity given
Is to the rest of the differences respectively; ..
RULE. Link the several prices, and place their differences as before; then,
As the sum of the differences
. 2 A druggist compounds medicines, at 4s. 5s. and 8s.
per lb. to make two parcels, one of 21lb. at 6s. the other of 35lb. at 7s. per lb. what quantity of each must be taken? rolb. at 4s.)
? 5lb. at 4s. answer 6 5 s=2ilb. at 6s. &c. 5: 5 .
( 98 8 s.
:: = 35lb, at 7s. per lb. 3 A merchant had 4 sorts of coffee, at 8d. 12d. 18d. and 22d. per lb. the worst would not sell, and the best was too dear, he therefore concluded to mix 120 lb. what quantity - of each must he take, so as to sell at 16d. per lb.
answer 361b. at 8d. 12 at 12d. 24 at 18d. and 48 at 22d. 4 How many gallons of water must be mixed with wine, at 4s. per gallon, so as to fill a vessel of 80 gallons, that may be afforded at 2s 9d. per gallon ?
answer 25 gallons of water with 55 of wine. 5 A goldsmith has gold of 15, 17, 20, and 22 carats fine, and would melt together of each of these so much, as to make a mass of 40oz. of 18 carats fine; how much of each sort is necessary. answer 16oz. of 15,4 of 17, 8 of 20, & 12 of 22 carats fine.
POSITION.. HOSITION is a rule for finding an unknown number, by
I one or more supposed numbers; and is either single or double.
SINGLE Positioning Single position' teaches to resolve such questions as re. quire only one supposed number.
- RULE. FI Work with a supposed number according to the tenor of the question; then,
As the result of that operation
: : PROOF.. Work with the answer according to the tenor of the ques. tion, and the result must equal the given number. : Note. If the results of two or more supposed numbers be in the same pro.
portion as the number supposed : or, If upon working with two supposed numbers, and multiplying each of them
by the result of the other, the products be equal, then the question may be solved by single position, otherwise not
EXAMPLES 1 A person, after spending 1 and 4 of his money, had 601. left; what had he at first ?