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: 26

Answer

10 liters of alcohol must be added in the solution.

Work Step by Step

Let p represent the amount of alcohol to be added. After p is added, we obtain a 60% solution. We use the following guideline to solve this problem: Amount of pure alcohol in original solution + Amount of pure alcohol to be added = Amount of pure alcohol in final solution. So: 20 $\times$ 40% + p = 60% (20 + p) $20 \times .4 +p =.6(20+p)$ 8 + p = 12 + $\frac{3p}{5}$ 4 = p - $\frac{3p}{5}$ 4 = $\frac{5p}{5}$ - $\frac{3p}{5}$ 4 = $\frac{2p}{5}$ Multiply both sides by 5. 20 = 2p Divide both sides by 2: p = 10 10 liters of alcohol must be added in the solution.
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