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: 27

Answer

15 centiliters of distilled water must be added.

Work Step by Step

Let X represent the amount of water to be added. After X is added, we obtain a 20% acid solution. A 20% acid solution has 80% water in it. A 50% acid solution has 50% water in it. We use the following guideline to solve this problem: Amount of water in original solution + Amount of water to be added = Amount of water in final solution. 50% $\times$ 10 + X = 80% $\times$ (10 + X) $.5\times 10 +X=.8 \times (10+X)$ 5 + X = $\frac{4}{5}$ $\times$ (10 + X) 5 + X = 8 + $\frac{4X}{5}$ 3 = $\frac{5X}{5}$ - $\frac{4X}{5}$ Multiply both sides by 5 X = 15 15 centiliters of distilled water must be added.
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