The Fun Guys game rental store charges an annual fee of $5 plus $6.50 per game rented. The Game Bank charges an annual fee of $37 plus $2.50 per game. For how many game rentals will the cost be the same at both stores? What is that cost?
Fun Guys:
total amount paid = 5 + 6.5×(no. of games rented)
v = 5 + 6.5x
Where, v = amount paid and x = no. of games rented
Game Bank:
total amount paid = 37 + 2.5×(no. of games rented)
y = 37 + 2.5x
Where, y = amount paid and x = no. of games rented
So we want to find out where the amount paid is the same at both stores.
So when, v = y
So, 5 + 6.5x = 37 + 2.5x
Now we need to solve this equation to find 'x':
5 + 6.5x = 37 + 2.5x
5 - 5 + 6.5x = 37 + 2.5x - 5
6.5x = 32 + 2.5x
6.5x - 2.5x = 32 + 2.5x - 2.5x
4x = 32
x = 8
So the game rental cost will be the same at both stores when x = 8 , i.e. when you rent 8 games.
So now we want to find out how much this will cost. Since the total cost should be the same for both shops when you rent 8 games it doesn't matter which equation we use.
So i'll chose the equation for Fun guys:
v = 5 + 6.5x so when x = 8
v = 5 + 6.5×8
v = 57
So the total cost is $57 .