Question

A video game customers to rent games for $4.75 each. Customers can also buy a membership for $54 annually, and video games would only cost $2.50 each. Find the number of video games a customer would have to rent in a year in order for the two options to be equal

Answer 1

Given:

A video game customers to rent games for $4.75 each.

Customers can also buy a membership for $54 annually, and video games would only cost $2.50 each.

To find:

The number of video games a customer would have to rent in a year in order for the two options to be equal.

Solution:

Let x be the number of video games.

A video game customers to rent games for $4.75 each. So, the total cost is

`C_1(x)=4.75x`

Customers can also buy a membership for $54 annually, and video games would only cost $2.50 each. So, the total cost is

`C_2(x)=54+2.50x`

Now,
`C_1(x)=C_2(x)`, if the rent in a year for the two options to be equal.

`4.75x=54+2.50x`

`4.75x-2.50x=54`

`2.25x=54`

Divide both sides by 2.25.

`x=(54)/(2.25)`

`x=24`

Therefore, the rent in two options are equal for 24 video games.