5 liters of pure alcohol must be added to the solution.
Work Step by Step
Let x represent the amount of pure alcohol that must be added. We can use the following guideline to solve this problem: Original amount of alcohol + Amount of alcohol added = Final amount of alcohol. Original amount of alcohol = 20% $\times$ 15 = 0.2 $\times$ 15 = 3 liters. Amount of alcohol added = x Final amount of alcohol = 40% $\times$ (15 + x) = 0.4 $\times$ (15 + x) = 6 + 0.4x Substitute these values into the equation to obtain: 3 + x = 6 + 0.4x 0.6x = 3 Divide both sides by 0.6 x = 5 5 liters of pure alcohol must be added to the solution.