The Fun Guys game rental store charges an annual fee of $5 plus $5.50 per game rented. The Game Bank charges an annual fee of $35 plus $2.50 per game. For how many game rentals will the cost be the same at both stores? What is that cost?

10 games; $60

9 games; $55

4 games; $27

8 games; $49

Answer:10 games; $60

Step-by-step explanation:

Let x represent the number of games rented at either stores. Let y represent the cost of renting x games at Fun guys rental.

Let z represent the cost of renting x games at Games bank.

The Fun Guys game rental store charges an annual fee of $5 plus $5.50 per game rented.

The cost of x games will be

y = 5 + 5.5x

The Game Bank charges an annual fee of $35 plus $2.50 per game.

The cost of x games will be

z = 35 + 2.5x

Since we want to determine the number of games that will be played for the costs to be the same, we would equate y to z. It becomes

5 + 5.5x = 35 + 2.5x

5.5x - 2.5x = 35 - 5

3x = 30

x = 30/3 = 10

They will make 10 games rentals before the costs become the same.

To find the cost of 10 games, we will substitute x = 10 into one of the equations, it becomes

5 + 5.5 * 10 = 5 + 55 = $60