Answer
18 gallons of a 10% salt solution must be mixed.
Work Step by Step
Let X represent the amount of the 10% salt solution.
The amount of the final solution will be 12 + X
We use the following guideline to solve this problem:
Amount of salt in the first solution + Amount of salt in the second solution = Amount of salt in final solution.
The 10% salt solution has 10% $\times$ X = 0.1X gallons salt.
The 15% salt solution has 15% $\times$ 12 = 1.8 gallons of salt.
The final solution has 12% $\times$ (12 + X) = 1.44 + 0.12X gallons of salt.
We solve the following equation:
0.1X + 1.8 = 1.44 + 0.12X
0.36 = 0.02X
Divide both sides by 0.02.
X = 18
18 gallons of a 10% salt solution must be mixed.
