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The method of proof in this rule is the same as in the single rule, as may be seen above.

Qu. 2. A, B, and C rent a pasture in common, at 40l. per annum ; A puts in it z oxen for 8 months in the year, B puts in 7 for 4 months, and C puts in 2 for the whole year; what must each person pay towards the rent? Answer, A 121. 125. 712. &; B 141. 145.81d. 28; C 121. 125.714.44.

Example 3. A, B, and C make a stock for 12 months, A put in at first 7281. at the end of 2 months he put in 20!. more; B put in at first-200l, and at the end of 5 months he took out 150l.; C put in at first 40l. and at the end of 6 months 50l. more, and at the end of 10 months rol. niore; at the year's end they find they have gained sool. ; what is each person's profit?

In these examples, and all others of the like nature, where the different parts of the stack of each person are employed for a different time, the different parts of each person's stock are to be mukiplied by their own separate times, and these products added together to make up the product of each person; and then each person's, product added together to make the total product.

1456

Thus, in the last example, I first multiply the 7281.

put in by A, by 2, the number of months it is

employed alone, and the product is
Then A put in 20l. more, which, added to the 728!.

is 7481. and which multiplied by 10 months, the
product is
And which two added together gives A's product

7450 89,5

1000

350

B put in 200l, for 5 months, which product is
At the end of 5 months he took out 150l. and then

there remained only sol. which 'multiplied by 3 months, the product is The two products of B-added together are his true one 1350 C put in at firft 401. which continued alone 6 mönths, that produièt therefore is

240 At the end of 6 months he put in sol. more, which,

added to the former 40l. is gol, which multiplied by 4 months, gives

360 The last 2 months he had 100l. in the stock, wlich, multiplied by 2 months, gives" :

200 Therefore the product of C is

800 The total sum of all the products 11086

Then the work is wrought as before, saying, as 11086 (the sum of the products). is to sool. (the total gain), so is 8936le (the produ&t of A) 10,403). Os. 712, 4160703, the share of A of the profits; and repeat the operation twice more, to find the Ihares of B and C.

B b 2

Antzer.

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The rule of alligation teacheth how to mix différerit fub. Stances together, and to discover the value of any part of such mixture; or to make a mixture from known substances of

any value,

Alligation is either medial or alternate.

Alligation medial is that which teacheth how to find the rate or price of any mixture or compound, from having the rates or prices, and the quantities of the several substances given.

Rule. Multiply each quantity by its rate or price, and add the products together for a dividend; add the sums of the several quantities together for a divisor; and divide the sum of the products by the sum of the qdantities, and the quotient will be the rate or Price of the componnd. :::

Example'i. A mealman mites 26 buthels of flour, worth ss. per Buthel, with 12 Buthels worth 35. 48. per busfiel; what is : bushel of this mixture worth?

20

12

1200

Price of a bushel 6od. Price of a bustel 404.

Quantities. No. of bushels No. of bushels 12

20
450
- 1200
32) 1680szt...06 45. 44. per bufhely: .
160

for the Answer.
80
64

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In this example the price of the bushel is reduced into pence (as it mostly hould). The anfwer is the price of the quantity, which is of the fame denomination with the divisor, which here is bushels. i

Proof. Find the value of the whole mixture from the value of any part, and if it be equal to the value of the original fiimples, the work is right.

Thus, to prove the foregoing example, I multiply the price of one bushel of the mixture by 4 and 8, or 32, the number of bushels in the whole, and the product, I find, is 71.; then I find the value of the several fimples, by multiplying the number of bushels in each by the number of pence in a bushel (which is already done in the example), and the product 1680 brought into pounds, gives 7l as follows:

The Proof The Number of Bushels

The Price of a Bumel of the multiplied by the

Mixture multiplied by the
Pence in a Bushel.

Number of Bushels.

d. 12)1680 pence

4 41 2,0) 14,0 Thillings

2

pounds

17. 6

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Qua 2. A grocer mixed the following teas together, viz. 15lbs. at 8s. per lb. 20lbs at 75. 4d. per lb, rolbs, at 6s. 8d. per lb. and 24lbs. at 4s. per lb. what is one pound of this mixture worth? - Answer 6s. 2 d. 48.

Qu. 3. A vintner mixes - 5 gallons of wine at 75. per gallon), with 9 gallons at 8s. 6d. per gallon, and 141 gallons at 55. 10d. per gallon ; what is one gallon of this mixture worth? - Answer 6s. 1011.

Qu. 4. A goldsmith melts 1011 ounces of gold bullion, of 14 carats * fine, with 152 { ounces of 18 carats fine, how many carats fine is this mixture ? - Answer 1638 carats fine,,,

Alligation alternate is the method of finding what quantity of simples, whose rates or prices are given, will form a. mixture of a certain given rate or price. .

. Rute 1. Write the rates or prices of the several simples under each other. 2. Connect with a curve line the rate or price of each simple that is lets than the rate or price of the mixture, with one or more of these rates or prices that are greater than that of the mixture; and each greater rate with one or more that are less : and place the rate or price of the mixture on the left hand of the rates or prices. : 3. Write the difference between the rate of the mixtures and the rate of each fimple oppofite the rate with which such fimple is connected or linked.

Then these differences which stand opposite any rate is the quantity which that rate requires to form a mixture of the given rate ; but if there is more than one difference opposite any simple, their fum is the true difference.

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Gold is generally mixed with copper or some other base metal, which is called the allay; and the gold is said to be so many carats fine as it contains pure gold : thus, if an article weighs 24 carats, and contains 22 carats of gold, and 2 of allay, it is said to be 22 carats fine. What a carat is may be seen, page 135.

Example

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