## Elementary Algebra

Let X represent the amount of pure alcohol to be added. The second solutions is 10 liters. The resulting solution will be 10 + X liters. We use the following guideline to solve this problem: Amount of alcohol in the first solution + amount of alcohol in the second solution = Amount of alcohol in the final solution. The first solution is all alcohol; it has X liters of it. The second solution has 10 $\times$ 70% = 10 $\times$ 0.7 = 7 liters of alcohol. The resulting solutions is 90% alcohol, which means it has 90% $\times$ (10+X) = 0.9 $\times$ (10 + X) = 9 + 0.9X alcohol. We then solve the equation: X + 7 = 9 + 0.9X 0.1X = 2 Divide both sides by 0.1 X = 20 20 liters of alcohol must be added.