* A star or asterisk used in this manner, denotes the addition of decimal ciphers as has been noted before. 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, the 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 ai 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 that 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. 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 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. As 95 bushels, or simples, are to 6650 cents; so is 1 bushel to its value: 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 + 0 = 35. Many and various operations may be wrought in Alligation Alternate, and Alternation Total; but these examples must suffice for an introduction. More useful matter claims a preference, and the want of room forbids the insertion of several curious subjects. |
