A movie club charges a one-time membership fee of $25. It allows members to purchase movies for $7 each. Another club does not charge a membership fee and sells movies for $12 each. How many movies must a member purchase for the total cost of the two clubs to be equal?

Let's solve this problem by setting up an equation to find the number of movies where the total cost for both clubs will be the same.

### Step 1: Define the variables
Let $ x $ represent the number of movies purchased.

### Step 2: Write the total cost for each club
- For the first club (with the membership fee): 
  \[
  \text{Total cost} = 25 + 7x
  \]
  Here, $25 is the membership fee and $7 is the cost per movie.
  
- For the second club (no membership fee): 
  \[
  \text{Total cost} = 12x
  \]
  Here, $12 is the cost per movie.

### Step 3: Set the two total costs equal to find when they are the same
\[
25 + 7x = 12x
\]

### Step 4: Solve for $ x $
Subtract $ 7x $ from both sides to isolate $ x $:
\[
25 = 12x - 7x
\]
\[
25 = 5x
\]

Divide both sides by 5:
\[
x = 5
\]

### Conclusion
A member must purchase **5 movies** for the total cost of both clubs to be equal.

Would you like more details or have any questions?

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Here are 5 related questions you might find interesting:
1. What happens if the price per movie in the first club decreases?
2. How do you solve problems involving break-even points?
3. What is the concept of opportunity cost in similar scenarios?
4. How would the equation change if there was a discount on the membership fee?
5. What if a third club offered a different pricing model—how would you compare them?

**Tip:** When comparing costs in similar scenarios, setting up equations and looking for where they are equal can help you determine the break-even point.

Learn how to solve the equation comparing total costs between a movie club with a membership fee and one without. This problem involves linear equations and cost analysis. Suitable for students in Grades 6-8.

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