Question

A gamestop you can buy a xbox one foe 150.00 and each game to go with it would cost 24.00 or you can buy a playstation 4 for 180.00 abd esch game for 20.00

Answer 1

Let's write two linear equations:

For the Xbox, we have:

Price per console (you pay it only once) = $150.

Price per game = $24

Then, the total price if you buy x games, you have:

P1(x) = $150 + $24*x

For the Playstation we have:

Price per console (again yo pay it only once) = $180

Price per game = $20

So if you buy x games, the total price is:

P2(x) = $180 + $20*x.

Now, we can find the number x such that both prices are equal

P1(x) = P2(x)

$150 + $24*x = $180 + $20*x.

let's solve this for x.

$24*x - $20*x = $180 - $150

$4*x = $30

x = $30/$4 = 7.5

What does this mean?

If you buy less than 7.5 games (7 or less) then the Xbox will be cheaper, because the y-intercept is smaller.

If you buy more than 7.5 games (8 or more) then the Playstation will be cheaper, because the price per game is smaller.