https://file.aiquickdraw.com/mathbot/file/1728327705253cltq9hg9.jpg

Let's solve the problem from the image:

We have two scenarios to consider:

- **Members** pay a $10 membership fee plus $2 per aerobics class.
- **Nonmembers** pay $4 per aerobics class with no membership fee.

We need to find the number of classes $ x $ where the total cost for both members and nonmembers is the same.

### Step 1: Write the equations
- For members: $ \text{Cost} = 10 + 2x $
- For nonmembers: $ \text{Cost} = 4x $

### Step 2: Set the equations equal to each other
\[ 10 + 2x = 4x \]

### Step 3: Solve for $ x $
\[
10 + 2x = 4x
\]
\[
10 = 4x - 2x
\]
\[
10 = 2x
\]
\[
x = 5
\]

### Answer
For 5 aerobics classes, the cost will be the same for members and nonmembers.

Would you like more details on how this solution was reached, or do you have any questions?

Here are 5 related questions to deepen your understanding:

1. What would the cost be for members and nonmembers if they took 3 aerobics classes?
2. How much money would a member save compared to a nonmember if they took 8 aerobics classes?
3. At what number of classes is it more economical for a member to take a membership versus paying the nonmember price?
4. How does the membership fee impact the cost-effectiveness of being a member?
5. What happens to the cost comparison if the class price for nonmembers increases to $5 per class?

**Tip:** When solving word problems, always translate the words into algebraic equations to better understand the relationships between variables.

At a local fitness center, members pay a $10 membership fee and $2 for each aerobics class. Nonmembers pay $4 for each aerobics class. For what number of aerobics classes will the cost for members and nonmembers be the same?

Learn how to determine the number of aerobics classes where the cost is the same for members and nonmembers at a fitness center. Members pay a $10 membership fee and $2 per class, while nonmembers pay $4 per class. Suitable for students in Grades 6-8.

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