#### Answer

We will use 7.5 quarts of the 30% alcohol solution and 10 - 7.5 = 2.5 quarts of the 50% alcohol solution.

#### Work Step by Step

Let X represent the amount of the 30% alcohol that we will use.
Since a 10 quart solution will be obtained, the amount of the 50% alcohol solution is equal to 10 - 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.
30% $\times$ X + 50% $\times$ (10 - X) = 35% $\times$ 10
$.3 \times X+.5\times (10-X)=.35 \times 10$
0.3X + 5 - 0.5X = 3.5
- 0.2X = - 1.5
Divide both sides by -0.2
X = 7.5
We will use 7.5 quarts of the 30% alcohol solution and 10 - 7.5 = 2.5 quarts of the 50% alcohol solution.