In my fencing club, there are twice as many boys who are in high school as there are boys who are in middle school. Of the students in the club who are in middle school, there are three times as many girls as there are boys. Half of the girls in the club are in high school. If there are 72 people in my fencing club, how many are middle school boys?

Let's denote the number of middle school boys as \( x \).

### Step 1: Express the other quantities in terms of \( x \)
- **High School Boys:** Since there are twice as many high school boys as middle school boys, the number of high school boys is \( 2x \).
- **Middle School Girls:** The number of middle school girls is three times the number of middle school boys, so the number of middle school girls is \( 3x \).
- **High School Girls:** Half of the girls in the club are in high school. Since there are \( 3x \) middle school girls, the total number of girls is \( 3x \times 2 = 6x \). Therefore, the number of high school girls is \( \frac{6x}{2} = 3x \).

### Step 2: Set up the equation for the total number of students
The total number of people in the club is the sum of all these quantities:
\[
x + 2x + 3x + 3x = 72
\]
\[
9x = 72
\]

### Step 3: Solve for \( x \)
\[
x = \frac{72}{9} = 8
\]

### Conclusion:
The number of middle school boys is \( \boxed{8} \).

Would you like more details on any step or have additional questions?

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Here are some related questions you might be interested in:
1. How many girls are in the fencing club?
2. How many high school boys are there in the club?
3. How many students are in high school?
4. What percentage of the club members are middle school boys?
5. If three more middle school boys joined the club, how would that affect the total count?
6. How many more students would need to join to make the club 100 members strong?
7. What is the ratio of middle school girls to high school girls?
8. How many boys are there in total?

**Tip:** When solving word problems, carefully define variables and express all quantities in terms of these variables. This helps in setting up the equation correctly.

Learn how to solve a complex problem involving the number of middle school boys in a fencing club. This problem covers concepts of equations, algebra, and ratio and proportion. Suitable for students in Grades 7-9.

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