Answer
20 liters of alcohol must be added.
Work Step by Step
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.
