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3 If 4oz. of silver, worth 5s. 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.

5 A goldsmith melted together 8oz. of gold of 22 carats fine, ilb. oz. of 21 carats fine, and 10oz. 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. Sgr. 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 ? 48

6 at 4 Mean rate 20{ 36

6 at 3 answer. 24

18+6=24 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
6

Sherry, and
Malaga.

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3 A druggist had several sorts of tea, viz. at 12s. per . at 11s, at 9s. and at 8s. how much of each sort must be taken to be sold at 10s.

per

lb.
lb. s.p.lb. Ib. s.p.lb.

lb. s.p.lb.
2 at 12
3 at 12

(1 at 12
1 11
2 il

2 11
1 ans.
2 ans.

3 ans
1 9
2 9

2 9
2 8
3 8

8
lb. s.p.lb.
lb. s.p.lb.

1b. s.p.lb.
ri at 12
3 at 12

2 at 12 3 11

11

3 11
5 ans.

6 ans.
3 9
3 9

1 9
8

8

3 8 7 answer 3 lb. of each sort. 4 How much sugar at 4d. at 6d. and at 11d. per pound, must be mixed together, so that the composition may be worth 7d. per lb.

answer 1lb. or 1 C.wt. of each, or any other

weight of equal quantity. 5 It is required to mix several sorts of wine, at 3s. 5s. and 7s. per gallon, with water, that the mixture may be worth 4s. per gallon; how much of each sort must the inixture consist of ?

answer i gal. wine at 3s. 1 ditto. at 58. 4 ditto at 7s.

and s gals. water.

4 ans.

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;

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

02

Esi v

As 14:20

}

40 :

ans,

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per lb.

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EXAMPLES 1 A merchant has 40lb. of tea, at 6s. per

lb. which he would mix with some at 56 8d. at 5$ 2d. and at 4s 6d. per lb. how much of each sort must he take, to mix with the 40lb. that he may sell the mixture at 5$ 5d. per

lb. 54

3+7=10 62 653

3+7=10 68

11+3=14 72 11+3=14 against the price of the quantity given.

S 284 at 4s 6d. and 5s 2d. per lb. 2

40 at 5s 8d. 2 How much barley at 2s 6d. rye at 3s. and wheat at 4s. per bushel, must be mixed with 12 bushels of oats at-18d. per bushel, that the whole may rate at 1s 10d. per bushel ?

answer 1 bushel of each. 3 How much gold of 16, 20, and 24 carats fine, and how much alloy, must be mixed with 10oz. 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 10 of alloy. 4 Ten bushels of wheat at 4s. per bushel, with rye at 3s. barley at 2s. and oats at 1s, what quantity of these must be mixed with the wheat to rate at 2s 4ch

per

bushel ? 2bu. 2p. of rye, 1 ans. 5

barley, 2 ans. 50 barley, 12 2 oats.

20 oats. 8bu. of rye,

rye, S ans. 10 barley,

4 ans. 14 barley, 14. oats.

14

oats. 12bu. 2p. of rye, 5 ans. 5

barley,
6 ans.

14 barley,
17 2
oats.

10 oats.
50bu. of rye,
70

barley,
20 oats.

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

RULE.

40bu. of rye,

S 10bu. of

zbu. of rye,

7 ans.

RULE. Link the several prices, and place their differences as before; 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.

EXAMPLES

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.

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

answer.

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6

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-21lb. at 65. &c.?

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5

2 A druggist compounds medicines, at 4s. 5s. and 8s. per lb. to make two parcels, one of 211b. at 6s. the other of 35lb. at 7s. per lb. what quantity of each must be taken? 6lb, at 4s.

5lb. at 45. answer 6 5

5 9 8

25 8

351b, 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 36lb, at 8d. 12 at 12d. 24 at 18d. and 48 at 22d. 4 How many gallons of water must be mixed with wine. at 48. per gallon, so as to fill a vessel of 80 gallons, that may be afforded at 28 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.

P

POSITION.
OSITION is a rule for finding an unknown number, by

one or more 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;
So is the number given
To that required.

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 and of his money, bad 60). left; what had he at first ? £.

£ £. f
Suppose 24 As 10 : 24 :: 60 : 144 answer,

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2 B's age is 14 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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