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As 30 articles, or gallons,

are to 8800 cents combined value; So is 1 gallon,

to its particular value.

cents.
30 : 8800 ::1

30)8800(293.33+

60

280 270

. 100

90

100*
90

100*
90

A star or asterisk used in this mamier, denotes the addition of decimal ciphers as has been noted before.

10

1

ALLIGATION ALTERNATE, Operates to the reverse of Alligation Medial, because the rate and prices are given to find the quantities to be mixed.

RULE. 1. Place the prices of the simples in a column, beginning with the least uppermost, increasing with the next least, till you come to the foot of the column with the greatest.

2. Place the given rate or mean price on the left of the column.

3. Connect, with a circular line, the price of a simple, which is less than the mean rate, with one which is greater than the mean rate; and so to the contrary, a greater with a lesser.

4. Take the difference between the mean rate and each simple, and place to the right, opposite to that other simple with which it is connected.

5. Carry out to the right, in a column, ihe amount of that difference, at the price which stands opposite in the first column,

EXAMPLE 1. A tobacconist has four sorts of tobacco; one at 10 cents, another ač 20 cents, a third at 30 cents, and a fourth at 40 cents a pound : he wishes to know what quantity of each may be mixed, so thai he can afford to sell at 25 cents a pound ?

Here we will call 25 cents, the given or mean rate, and 10, 20, 30, 40, prices of the simples.

OPERATION.
106 cents,
15 lb. at 10 cents,

150 cents.
5 do. at 20
20)

100 25 cents.

5 do. at 30
40
15 do. at 40

600

150

Mean rate,

Х

40 No. of lbs. 25 mean rate.

$ 10.00 Amount of the

[simples.

Proof, $10.00 The answer is 15 lb. at 10 cents, 5 lb. at 20 cents, 5 lb. at 30 cents, and 15 lb. at 40 cents.

EXAMPLE 2. Sugar at 10 cents a pound, at 20 cents, at 30 cents and at 40 cents, being ready for a mixture, required how many pounds of each to make a composition worth 25 cents a pound? Ans. 5lb at 10 cents, 15lb. at 20, 15lb. at 30, and 5lb. at 40

OPERATION.
Simples.
107

5 lb. at 10 cts. 50
20

15 lb. at 20 Mean rate 25.

300 30.

15 lb. at 30 450 40

5 lb. at 40 200

Am't of articles or simples, 40 lb.

$10.00 am't of the simples, PROOF BY ALLIGATION MEDIAL, Ib. cts. Ib. Ş If 40 lb. simples cost 10 dollars, what - 40 : 1000 ::1 > will 1 lb. cost ?

80 (25 lb. answer.

200 200

EXAMPLE 3. A farmer mixing oats at 40 cents a bushel, with peas at 75 cents a bushel, and corn at 100 cents a bushel, required how much of each sort to make. a mixture worth 70 cents a bushel ? Ans. 35 bushels at 40 cents, 30 at 75 cents, and 30 at 100 cents.

OPERATION. 40

5 + 30 = 35 at 40 c. – 1400 c. 70

30 at 75 c. =%250 C. 100

30 at 100 c. = 3000 c.

No. of bushels or simples, 95

6650 c. amount of simples

PROOF. As 95 bushels, or simples, are to 6650 cents ; so is 1 bushel to its values

* 95 : 6650 :: 1

665 (70 answer in cents.

...0 NOTE.—When more differences than one happen against any simple, as at 40, then such differences must be added together, as 5 + 30 = 35.

Many and various operations may be wrought in Alligation Alternate, and Alternation Total; but these examples must suffice for an introduca tion. More useful matter claims a preference, and the want of room forbids the insertion of several curious subjects.

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