Question 1103699
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If you understand to use it, the method of alligation will get you to the answer to most "mixture" problems much faster than the traditional algebraic solution shown by most tutors.<br>
Here is how to solve this particular mixture problem using the method of alligation.<br>
{{{matrix(3,3,2.20,"",.25,"",2.95,"",3.20,"",.75)}}}<br>
The numbers in the third column give the ratio in which the dried apples and dried pears should be mixed.  Since that ratio is .25:.75, or 1:3, you need 5 pounds of dried apples and 15 pounds of dried pears to make 20 pounds of the mixture.<br>
Here is an explanation of how this method works...<br>
The first row of this diagram is for the dried apples, which cost 2.20 per pound; the last row is for the dried pears, which cost 3.20 per pound.  The middle row is for the mixture, which is to cost 2.95 per pound.<br>
The numbers in the third column are the differences, computed diagonally, between the numbers in the first and second columns: 3.20-2.95 = .25; 2.95-2.20=.75.<br>
Those numbers in the third column, calculated in that way, show the ratio in which the dried apples and dried pears need to be mixed.<br>
In this problem, that ratio is .25:.75, or 1:3.  That means 1/4 of the mixture must be dried apples and 3/4 must be dried pears.<br>
Since the mixture is to be 20 pounds, you need 5 pounds of dried apples and 15 pounds of dried pears.