Video Store A charges $8 to rent a video game for one week. Although only members can rent from the store, membership is free. Video Store B charges only $4 to rent a video game for one week. Only members can rent from the store and membership is $92 per year. After how many video game rentals will the total amount spent at each store be the same?

a) Write an equation to model the problem. Let x represent the number of video game rentals.

To model the problem, let $ x $ represent the number of video game rentals.

**Store A** charges $8 per rental, with no membership fee. The total cost after $ x $ rentals is:
\[
\text{Cost for Store A} = 8x
\]

**Store B** charges $4 per rental, but there is an annual membership fee of $92. The total cost after $ x $ rentals is:
\[
\text{Cost for Store B} = 4x + 92
\]

We want to find when the total amount spent at each store is the same. Therefore, we set the two expressions equal to each other:
\[
8x = 4x + 92
\]

This is the equation that models the problem.

Would you like help solving this equation, or do you have any further questions?

### Related Questions:
1. What is the solution to the equation $ 8x = 4x + 92 $?
2. After how many rentals is Store B the cheaper option?
3. How much would be spent at each store after 10 rentals?
4. What is the total cost at Store A after 15 rentals?
5. How would the equation change if Store A had a membership fee?

**Tip**: When comparing costs over time, look for fixed fees and variable costs.

Video Store A charges $8 to rent a video game for one week. Although only members can rent from the store, membership is free. Video Store B charges only $4 to rent a video game for one week. Only members can rent from the store and membership is $92 per year. After how many video game rentals will the total amount spent at each store be the same? Write an equation to model the problem. Let x represent the number of video game rentals.

Learn how to compare costs between two video stores with different rental prices and membership fees. This algebraic problem involves setting up and solving linear equations to find when the total amount spent at both stores will be equal. Suitable for students in Grades 6-8.

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