Elementary Algebra

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

Chapter 3 - Equations and Problem Solving - Chapter 3 Review Problem Set: 53

Answer

There will be 26% orange juice in the resulting mixture.

Work Step by Step

Let X represent the amount of orange juice in the resulting mixture. The amount of punch in the resulting mixture will be 20 + 30 = 50 ounces. We use the following guideline to solve this problem: Amount of orange juice in the first solution + amount of orange juice in the second solution = Amount of orange juice in the final solution. In 20 ounces of a punch containing 20% orange juice, there is 20% $\times$ 20 = 4 ounces of orange juice. In 30 ounces of a punch containing 30% orange juice, there is 30% $\times$ 30 = 9 ounces of orange juice. In the resulting mixture, there will be 4 + 9 = 13 ounces of orange juice. The total amount of punch in the resulting mixture will be 50 ounces. So, we calculate the percentage of orange juice in this punch. $\frac{13}{50}$ $\times$ 100% = 0.26 $\times$ 100% = 26% There will be 26% orange juice in the resulting mixture.
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