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2 What is the interest of 917/ 1Gs. annum for 7 years?

at 5 per cent. per answer 2211 4s 7d. per cent. what will ans. 17 12s 7d4+

3 If my correspondent be to have 4 his commission on 391/ 175, come to? 4 What will be the interest and amount of 5671 10s. in

9 years, at 6 per cent. per annum ?

answer

S3061 9s. Interest. 1873 19s. Amount.

5 What is the interest of 4726 185 6d. for 31 years, at

7 per cent. per annum?

answer 1158/ is rid.

answer 180291 35 2d.

6 What will 9526/ 125 9d. amount to in 12 years and 9 months, at 7 per cent. per annum?

ALLIGATION.

LLIGATION is a rule for adjusting the prices and simples of compound quantities.

CASE 1.

When several simple quantities, and their prices, are given, and a mean price of any part of the compound is required. RULE.

As the sum of the several quantities,

Is to their total value;

So is any part of the composition,
To its value.

EXAMPLES.

If 19 bushels of wheat at 6s, the bushel, 40 of rye at 4. and 12 of barley at 3s. be mixt together; what is a bushel of this mixture worth?

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S. d. )310(4

44 answer.

C wt. at 43s. of this mixture answer 7l 135.

2 A grocer mixed sugars; 2C.t. at 56s. and 2C.wt. at 50s. per C.wt. what is 3C.wt. worth?

3 If 40%. of silver, worth 5s. the bunce, be melted with 80%. at 4s. what is one ounce of this mixture worth?

answer 4s 4d. 4 A wine merchant mixes 12 gallons of wine at 4s 10d. the galloa, with 24 gallons, at 5s 6d. and what is a gallon of this mixture worth?

16 at 6s 3d.4; answer 58 7d.

5 A goldsmith melted together Soz. of gold of 22 carats fine, 1 8oz. of 21 carats fine, and 10 oz. of 18 carats fine; what is the quality or fineness of the composition?

B answer 20 carats fine. 6 A refiner melted 5 of silver bullion of 8ox. fine, with 10lb of 70%, and 15lb. of 6oz fine; of what fineness is 1lb. 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 I. If all the given prices be greater, or less than the mean rate, they must be linked to a cipher.

Different modes of lirking will produce different answers.

EXAMPLES.

1 How much rye at 4. the bushel, barley at 35. and oats at 25. will make a mixture worth 2s 6d. the bushel?

48

Mean rate 30 36

6 at

6 3 answer.

18+6=24 2

2 Canary at 25. a quart, Sherry at 16d. and Malaga at 15. how much of each must be taken, that the mixture may be worth is 6d. the quart?

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

lb. s.p.lb.

2 at 12

1 I

1b.-s.p.lb.

lb. s.p.lb.

I at 12

II

3 at 12

21 11

2

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3 ans.

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lb. sp.lb.

3 at 12

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4 How much sugar at 4d.

8

of each sort.

at 6d and at 11d. per pound, must be mixed together, so that the composition may be worth 7d. per ib.

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 35. 58. and 75. per gallon, with water, that the mixture may be worth 45. per gallon; how much of each sort must the mixture consist of?

answer 1 gal. wine at 3s. I ditto at 5s. 4 ditto at 75. and 3 gals. water.

CASE 3.

one of

When the rate of all the simples, the quantity 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.

EXAMPLES

EXAMPLES.

1 A merchart har 4cb. of tea, at 6s. per . which he would mix with some at 5s 8d. at 5s 2d and 4s 6d. per lb. how much of each sort must he take, to mix with the 40%, that he may sell the raixture at 5s 5d. per lb.

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347=10

3+7=10

JI:3-14

11+3=14 against the price of the quantity

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40 at 5s.8.

per lb.

2 How much Larky at 25 6d. rye at 35. and wheat at 4. per bushel, must be mixed with 12 bushels of oats, at 18. ! per bushel, that the whole may rate at is 10d. per bushel? ans wer1 bushel of each.

3 How much gold of 16, 20, and 24 carats fine, and how much alloy, must be mixed with rooz. of 18 carats fine, that the composition may be 22 carats fire?

answer 100% of 16 carats fine, 10 of 20, 170 of 24 and io of alloy.

4 Ten bushels of wheat, at 4. per bushel, with rye at 3 barley at 25. and oats at 1s. what quantity of these must be mixed with the wheat to rate at 2s 4d. per bushel?

2bu. 2p. of rye,

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f40bu of rye,

barley,

2 ans.

50

oats.

8bu. of rye,
barley,

oats.

12bu. 2p. of rye,

10

14

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barley,

oats.

barley,

oats.

20

barley,

oats.

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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.

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. 1 630:4 to 20 at 6d.

7d.

{

87

6 JJ 3+1=4

6

answer.

2 A druggist compounds medicines, at 4s. 5s. and 8s. per lb. to make two parcels, one of 21. at 6s. the other of 35lb. at 7s. per lb. what quantity of each must be taken?

5lb. at 4s.

6lb at 4s.

answer 6

5

21b. at 6s, &

9

8

{

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25

8

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%. what quantity of each must he take, so as to sell at 16d. per 16?

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 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.

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