Chapter 3 - Equations and Problem Solving - 3.5 - Problem Solving - Problem Set 3.5 - Page 132: 33

There is 16.25 percent of grapefruit juice in the resulting mixture.

Work Step by Step

Let X represent the amount of grapefruit in the mixture. Since the first mixture is 30 ounces and the second mixture is 50 ounces, the resulting mixture will be 30 + 50 = 80 ounces. To find X, the amount of grapefruit in the mixture, we use the following guideline: Amount of grapefruit in the first solution + amount of grapefruit in the second solution = Amount of grapefruit in the final solution. 10% $\times$ 30 + 20% $\times$ 50 = X $.1 \times 30 + .2 \times 50 =X$ 3 + 10 = X X = 13 There are 13 ounces of grapefruit in the 80 ounce mixture. Since we need to calculate the percentage of grapefruit juice, we proceed: $\frac{13}{80}$ $\times$ 100% = 16.25%

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