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The given table shows the number of activities that students at a middle school participate in. If the number of students who participate in two activities is 120 more than the number who participate in one activity, what is the total number of students who attend the middle school?

Let's solve the problem step by step.

1. **Define Variables:**
   Let \( x \) represent the number of students who participate in one activity.

2. **Given Information:**
   - The percentage of students participating in one activity is 30%.
   - The percentage participating in two activities is 55%.
   - The number of students who participate in two activities is 120 more than the number who participate in one activity.

3. **Express the Number of Students:**
   The number of students participating in two activities can be written as \( x + 120 \).

4. **Translate Percentages to Equations:**
   Since 30% of the total number of students (let's call the total \( N \)) participate in one activity, we can express this as:
   \[
   0.3N = x
   \]
   Similarly, 55% of the total number of students participate in two activities:
   \[
   0.55N = x + 120
   \]

5. **Substitute \( x \) from the First Equation into the Second:**
   Substitute \( x = 0.3N \) into \( 0.55N = x + 120 \):
   \[
   0.55N = 0.3N + 120
   \]

6. **Solve for \( N \):**
   \[
   0.55N - 0.3N = 120
   \]
   \[
   0.25N = 120
   \]
   \[
   N = \frac{120}{0.25} = 480
   \]

Therefore, the total number of students who attend the middle school is 480.

Would you like further details, or do you have any other questions?

Here are some related questions for further exploration:
1. How many students participate in no activities?
2. What is the total number of students who participate in more than two activities?
3. What percentage of students participate in at least one activity?
4. If 5 more students joined an additional activity, how would that affect the percentages?
5. How would the total change if the number participating in two activities increased by 10%?

**Tip:** To solve problems like this, always convert percentages into equations using variables to represent unknown quantities.

Learn how to solve a problem about student participation in activities using algebra and percentages. The problem involves finding the total number of students in a middle school where the number of students participating in two activities exceeds those in one by 120. Suitable for students in Grades 7-9.

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