Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 3 - Equations and Problem Solving - 3.5 - Problem Solving - Problem Set 3.5: 30

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.
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