Answer
The amount of the 20% alcohol solution to be used is approximately 5.3 pints, and the amount of the 50% solution to be used is approximately 2.7 pints.
Work Step by Step
Let X represent the amount of the 20% alcohol that we will use.
Since a 8 pint solution will be obtained, the amount of the 50% alcohol solution is equal to 8 - X.
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.
20% $\times$ X + 50% $\times$ (8 - X) = 30% $\times$ 8
$ .2 \times X + .5 \times (8-X)= .3 \times 8$
0.2X + 4 - 0.5X = 2.4
-0.3X = -1.6
Divide both sides by -0.3.
X $\approx$ 5.3 pint.
The amount of the 20% alcohol solution to be used is approximately 5.3 pints, and the amount of the 50% solution to be used is approximately 8 - 5.3=2.7 pints.
