## Elementary Algebra

Published by Cengage Learning

# Chapter 3 - Equations and Problem Solving - 3.5 - Problem Solving - Problem Set 3.5 - Page 131: 29

#### 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.

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