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3 If

40 of silver, vorth 5s. the owice, be melted with 8oz. at 45. what is one ounce of this mixture worth?

answer 45 4d. 4 A wine merchant mixes 10 gallong of wine at 45 10d. the gallon, with 24 gallons, at 55 6ch and 16 at 6s 3d. ; what is a gallon of this mixture worth? answer 55 7ch

5 A goldsmith melted together $os. of gold of 22 carats fine, 116. 8oz. of 21 carats fige, and 10 oz. of 18 carats fine; what is the quality or fineness of the composition ?

answer 20 carats fine, 6 A refiner melted 576. of silver bullion of 8oz. fine, with 10lb. of 70%, and 15lb. of 6oz. fine ; of what fineness is ille

. of this mass!

answer Gaz. Izdwt. 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 is

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 I. 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.

EXAMPLE S. I How niuch rye at 45. the bushel, barley at 3s. and oats at 2s. will make a inixture worth 2s 6d. the bushel ?

6 at 42

Mean rate 30








18+6=24 2 Canary at 25. 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?

quarts of Canary, 6

Sherry, and 6



at 12

1 at 12

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2 ans.

3 ans.



I at I2



6 ans.

3 A druggist has several sorts of tea, viz, at 125. per 1b. at 11s. at gs. and at 8s. how much of each sort must be taken, to be sold at 10s. per lb... 1bs.p.lb. 16. s.p.lb.

16. s.p.alb. 2 at 12

IL 9 9

9 8 8

8 Ib. s.p.io. 1b. sp.lb. 16. s.p.ls.

at 13

2 at 12 3 11


5 ans.
3 9

3 9

3 8 7 answer 3lb. of each sort. 4 How much sugar at 4d. at 6d. and at vid. per pound, must be mixed together, so that the composition may be worth 7d. per 1b.

answer ilb. or i Cowt. of each, or any other weight

of equal quantity. 5 It is required to mix several sorts of wine, at 35. 561 and 75. per gallon, with water, that the mixture


beworth 45. per gallon ; how much of each sort must the mix. ture consist of?

answer i gal: wine at 35. I ditto at 55.-4 ditto at 75,

and 3 gals. water.




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 ;

RULE. 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 rest of the differences respectively ;
So is the quantity given,
To the several quantities required.


Is 14 :



per lb.

EXAMPLE S. I A merchant has 4oib. of tea, at 6s. per 15. which he would mis with some at 55 8d. at 55 2d. and 45


per lb. how much of each sort must he take, to mix with the 40lb. that he may sell the raixture at 55 5d. per 16. 54

3+7310 62 65

3+7=10 11+3=14

*11+3=14 against the price of the quantity given. şio:

40 : {28+ at 4.5.6d, and 55.2d. per

} 2 How much barley at 2s Oil. rye at 3s, and wheat at 45. per bushel, must be mixed with 12 bushels of oats, at 18ch. per bushel, that the whole may rate at Is cod. per bushel ?

answer i bushel of each. 3 How much gold of 16, 20, and 24 carats fine, and how much alloy, must be mixed with rook. of 18 carats fine, that the composition may be 22 carats fine ?

answer 10oz. of 16 carats fine, 10 of 20, 170 of 24

and ro of alloy 4 Ten bushels of wheat, at 45. per busheł, with rye at 35+ barley at 2s. and çats at is. what quantity of these must be mixed with the wheat to rate at 2s 4d. per

bushel ?

Hobu. of rye,


barley, I 2 8bu. of rye,

1obu of rye, 3 15. 10 barley,

4 ans.

barley, 14 oats.


oats. 12bu. zp. of rye,

2bu. of rye, 5 5 ans. 5 barley,

6 ans 14 barley, 17 oats.


Qatsi sobu. of rye, og ans. 70 barley, 20


CASE 4. When the rates of the several simples, the quautity to be compounded, and the mean rate thereof are given, to find e quantity of each simple ;


of rye,

1 ans.






Link the several prices, and place their differences as be. fore, then,

As the sum of the differences,
Is to the quantity to be compounded ;
So is the difference opposite each rate,
To the required quantity of that price.



61b. at 45.

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1 A brewer had 3 sorts of beer, viz. at 10d. 8d. and 6d. per gallon ; how much of each sort must he take, to make 30 gallons, worth 7d. per gallon? 10

1 As 6. 30::1 to 5 gals. at 10d.&8d. 7d. 8

1 6. 30::4 to 20 at 6d. 3+1=4

6. 2 A druggist compounds medicines, at 45. 55. and 8s. per lb. to make two parcels, one of 211b. at Os. the other of 35lb. at 7s. per lb. what quantity of each must be taken?

5lb. at 4's. 6 5 +2113. at 6s. & 5 9 8


3516. at 73. 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 120lb. 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 fme, 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? aintzer 1607. of 15, 4 of 17, 8 of 20 & 12 of 22 carats fine




OSITION is a rule for finding an unknown number,

by one or inore supposed numbers; and is either single or double.

SINGLE Position. Single position teaches to resolve such questions as require only one supposed number.

RULE. Work with a supposed number according to the tenor of the question ; then,

As the result of that operation,
Is to the supposed number;
Sa is the number given,
To that required.

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 H upon working with two supposed numbers, and multiplying each of

them by the result of the other, the produsis be equal, then the quesa tion may be solved by single position, otherwise noto

EXAMPLE S. 1 A person, after spending and of his money, had 60l. left; what had he at first ?

Suppose 24. As 10. 24 :: 60 - 144 answer.




Result 10

60 Proof

2 B's age is 1{ A's; C's twice B's; both with A's make 132 years; how old is each of them? answer A 24, B 36, and C 72 years

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