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.