7. Nake Sense and Persevere Wayne bought blueberries. He uses \( \frac{3}{8} \) the biueberries to make blueberry bread, \( \frac{1}{6} \) of the blueberries to pancakes, and \( \frac{5}{12} \) of the blueberries to make jam. If Wayne uses 69 ounces of the blueberries he bought, how many ounces of blueberries did he buy?

To find out how many ounces of blueberries Wayne initially bought, we need to sum the fractions of blueberries he used for different recipes and then set up an equation. First, we need a common denominator for the fractions \( \frac{3}{8} \), \( \frac{1}{6} \), and \( \frac{5}{12} \). The least common multiple of 8, 6, and 12 is 24. Now, we convert each fraction: - \( \frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24} \) - \( \frac{1}{6} = \frac{1 \times 4}{6 \times 4} = \frac{4}{24} \) - \( \frac{5}{12} = \frac{5 \times 2}{12 \times 2} = \frac{10}{24} \) Next, we sum these fractions: \[ \frac{9}{24} + \frac{4}{24} + \frac{10}{24} = \frac{23}{24} \] This means Wayne uses \( \frac{23}{24} \) of the blueberries. Since he used 69 ounces, we can set up the equation: \[ \frac{23}{24}x = 69 \] Now, solve for \( x \): \[ x = 69 \times \frac{24}{23} \] Calculating that gives: \[ x = 69 \times 1.043478 = 72 \] So, Wayne bought **72 ounces** of blueberries! 🍇