Final answer:
To determine for how many game rentals the cost will be the same at both The Fun Guys and The Game Bank, we set up an equation based on the rates provided and solve for the number of games. The costs will be the same when 6 games are rented, with the total cost being $54.
Step-by-step explanation:
The question asks about determining the number of game rentals for which the costs from two different rental stores, The Fun Guys and The Game Bank, would be the same. To solve this, we can set up an equation that equals the total costs from both stores and solve for the number of games rented.
Step 1: Set up the equation based on the given information.
Let x be the number of games rented. The total cost for The Fun Guys is given by the annual fee of $15 plus $6.50 per game, which can be written as 15 + 6.50x. The total cost for The Game Bank is the annual fee of $27 plus $4.50 per game, which is 27 + 4.50x.
Step 2: Equate the costs to find the number of games where the costs are the same.
Setting the total costs equal to each other, we get:
15 + 6.50x = 27 + 4.50x
Step 3: Solve for x.
We subtract 4.50x from both sides to get 2x = 12, and then divide both sides by 2 to find x, which gives us x = 6. This indicates that renting 6 games will yield the same cost at both stores.
Step 4: Determine the total cost.
Substituting x = 6 into any of the total cost equations gives us 15 + 6.50(6) = $54. So the cost at which both stores charge the same amount for renting 6 games is $54.