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.