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The Mixture Problem

​
first solution volume x
45
second solution volume y
25
mixture concentration p
50
second solution concentration n
72
The mixture problem is a classic problem encountered in most algebra courses. It is solved by a simple application of linear equations.
The problem is stated as follows: given a solution of volume
x
with concentration
m
percent mixed with a solution of volume
y
with concentration
n
percent, we obtain a solution of volume
x+y
with concentration
p
percent. If
n
,
p
,
x
, and
y
are known, find
m
.
Concentrations out of the range 0–100% simply mean that the given mixture is not possible in practice.
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