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.