We need to mix 12 gallons of the 15% salt solution.
Work Step by Step
Let X represent the amount of the 15% salt solution that is to be mixed. The second solution is 8 gallons. That means that the final solution will be 8 + X gallons. 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. 15% $\times$ X + 20% $\times$ 8 = 17% $\times$ (8 + X) $.15 \times X + .2 \times 8 = .17 \times (8+X)$ 0.15X + 1.6 = 1.36 + 0.17X 0.24 = 0.02X Divide both sides by 0.02 X = 12 We need to mix 12 gallons of the 15% salt solution.