A mixture problem can involve mixing solutions containing different percents of a substance in order to obtain a solution containing a certain percent of the substance. This is usually present in real-world problems in chemistry and other related sciences.

Another kind of mixture problem for which the method of solving is similar involves mixing commodities of different values to obtain a combination worth a specific sum of money.
 

Problem:
Chemical Solutions

Determine how many liters of a 7% acid solution and how many liters of a 12% acid solution should be mixed by a chemist to obtain 6 liters of a 10% acid solution.

Solution
We need to determine the number of liters of each solution to be used. Therefore, we make the following representation:

$\mathbf{x:}$  the number of liters of the 7% acid solution
$\mathbf{6 – x:}$  the number of liters of the 12% acid solution

Draw a Diagram

Make a Table

From the last column in the table we see that the total number of liters of acid in the mixture can be represented by two ways: (1) 0.10(6) OR (2) 0.07x + 0.12(6 - x). Thus, we can derive an equation as follows:

\[0.07x + 0.12(6 - x) = 0.10(6)\]
\[0.07x + 0.72 - 0.12x = 0.60\]
\[-0.05x = -0.12\]
\[x = \frac{-0.12}{-0.05}\]
\[x = 2.4\]

AND

\[6 - x = 6 - 2.4\]
\[= 3.6\]

Therefore the chemist should use 2.4 liters of the 7% acid solution and 3.6 liters of the 12% acid solution.

CHECK

The 2.4 liters of the 7 percent acid solution gives 0.168 liter of acid and 3.6 liters of the 12 percent acid solution gives 0.432 liter of acid; and $0.168 + 0.432=0.60.$