Wayne bought blueberries. He uses three eighths
 of the blueberries to make blueberry​ bread, one sixth
 of the blueberries to make​ pancakes, and five twelfths
 of the blueberries to make jam. If Wayne uses 69 ounces of the blueberries he​ bought, how many ounces of blueberries did he​ buy?

Let the total number of ounces of blueberries Wayne bought be \( x \).

We know the fractions of blueberries used for different purposes:
- \( \frac{3}{8} \) for blueberry bread
- \( \frac{1}{6} \) for pancakes
- \( \frac{5}{12} \) for jam

The total amount of blueberries used is the sum of these fractions:
\[
\frac{3}{8} + \frac{1}{6} + \frac{5}{12}
\]

To combine these fractions, we first find the least common denominator (LCD) of 8, 6, and 12, which is 24.

Now we rewrite each fraction with a denominator of 24:
\[
\frac{3}{8} = \frac{9}{24}, \quad \frac{1}{6} = \frac{4}{24}, \quad \frac{5}{12} = \frac{10}{24}
\]

Adding these fractions:
\[
\frac{9}{24} + \frac{4}{24} + \frac{10}{24} = \frac{23}{24}
\]

Wayne used \( \frac{23}{24} \) of the blueberries, and this amount is given as 69 ounces. Therefore, we can set up the equation:
\[
\frac{23}{24} \times x = 69
\]

To solve for \( x \), multiply both sides of the equation by \( \frac{24}{23} \):
\[
x = 69 \times \frac{24}{23} = \frac{1656}{23} = 72
\]

Thus, Wayne bought **72 ounces** of blueberries.

Would you like further details on this? Here are some related questions to expand your understanding:

1. How can you determine the total amount of blueberries used for each recipe?
2. How would you solve a similar problem with different fractions?
3. What if Wayne had used a different portion of blueberries for one recipe—how would that change the calculation?
4. Can you explain how to simplify fractions to make adding them easier?
5. How do you check if the fractions of blueberries used sum to less than or more than the total amount?

**Tip**: Always simplify fractions before adding them for easier calculations.

Wayne bought blueberries. He uses three eighths of the blueberries to make blueberry​ bread, one sixth of the blueberries to make​ pancakes, and five twelfths of the blueberries to make jam. If Wayne uses 69 ounces of the blueberries he​ bought, how many ounces of blueberries did he​ buy?

Learn how to solve a real-world math problem involving fractions and algebra. Wayne uses parts of the blueberries he bought for different recipes. Find out the total ounces of blueberries he bought given the ounces used and the fractions involved. This problem covers fraction addition, finding the least common denominator (LCD), and solving equations, suitable for students in Grades 5-7.

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