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To solve the problem, let's find the values of \( x \), \( y \), and \( z \) in terms of \( m \) and then determine their average.

1. **Calculate \( x \):**
\[ x \text{ is the average of } m \text{ and } 9. \]
\[ x = \frac{m + 9}{2} \]

2. **Calculate \( y \):**
\[ y \text{ is the average of } 2m \text{ and } 15. \]
\[ y = \frac{2m + 15}{2} \]

3. **Calculate \( z \):**
\[ z \text{ is the average of } 3m \text{ and } 18. \]
\[ z = \frac{3m + 18}{2} \]

4. **Find the average of \( x \), \( y \), and \( z \):**
\[ \text{Average of } x, y, \text{ and } z = \frac{x + y + z}{3} \]

Substitute the values of \( x \), \( y \), and \( z \):

\[ \frac{\frac{m + 9}{2} + \frac{2m + 15}{2} + \frac{3m + 18}{2}}{3} \]

Combine the fractions:

\[ \frac{\frac{(m + 9) + (2m + 15) + (3m + 18)}{2}}{3} \]

Combine like terms in the numerator:

\[ \frac{\frac{m + 2m + 3m + 9 + 15 + 18}{2}}{3} \]
\[ \frac{\frac{6m + 42}{2}}{3} \]

Simplify inside the fraction:

\[ \frac{3m + 21}{3} \]

Simplify the entire expression:

\[ m + 7 \]

Therefore, the average of \( x \), \( y \), and \( z \) in terms of \( m \) is:
\[ \boxed{m + 7} \]

If you have any questions or want more details, please let me know.

Here are 5 questions you might ask:
1. Can you explain another example of finding the average of averages?
2. How do you find the mean of a set of numbers?
3. What is the difference between arithmetic mean and geometric mean?
4. How can I solve equations with multiple variables?
5. What are some common mistakes to avoid when calculating averages?

**Tip:** When combining fractions, always look for a common denominator to simplify the calculations.

Learn how to find the average of averages in algebra with a step-by-step solution. This problem involves calculating the average of three expressions and is suitable for students in Grades 7-9. Understand key concepts like averages and arithmetic mean through clear examples.

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