A video game store charges a monthly membership fee of $7.50 but the charge to rent each movie is only $1.00 per movie. Another store has no membership fee but it costs $2.50 to rent each movie. How many movies need to be rented each month for the total fees to be the same from either company?
let n be the number of movies rented
solve
2.5n = n + 7.5
n = ....
To find the number of movies needed to be rented each month for the total fees to be the same from either company, we'll equate the total cost from both stores.
Let's assume the number of movies rented each month is 'x'.
For the first store (with a monthly membership fee of $7.50 and $1.00 per movie rental):
Total cost at the first store = Membership fee + (Cost per movie * Number of movies rented)
= $7.50 + ($1.00 * x)
= $7.50 + $1.00x
Total cost at the first store = $7.50x + $1.00x
For the second store (no membership fee and $2.50 per movie rental):
Total cost at the second store = Cost per movie * Number of movies rented
= $2.50 * x
Total cost at the second store = $2.50x
To find the number of movies needed for the total fees to be the same, we'll set the cost from both stores equal to each other:
$7.50x + $1.00x = $2.50x
We combine like terms:
$8.50x = $2.50x
We'll isolate 'x' by subtracting $2.50x from both sides:
$8.50x - $2.50x = 0
$6.00x = 0
Dividing both sides by $6.00:
x = 0
Since you can't rent zero movies, we conclude that the number of movies needed each month for the total fees to be the same from either company is 0. In other words, if you don't rent any movies, the total fees will be the same regardless of which store you choose.