Question

One month Dante rented 2 movies and 3 video games for a total of$22 . The next month he rented 4 movies and 8 video games for a total of$57 . Find the rental cost for each movie and each video game.

Answer 1

x = $1.25; y = $6.50

Explanation:

Let x be the cost of movies and y be cost of video games.

Month 1 has 2x+3y = 22

So here x = (22-3y)/2 and y = (22-2x)/3

Month 2 has 4x+8y =57

Here x = (57-8y)/4 and y = (57-4x)/8

Now you have two options: Find the y or the x. I will demo the x and you can try the y if you wish.

(22-2x)/3 = (57-4x)/8

176-16x = 171-12x

-4x = -5

x = 1.25

Now with the x found, you plug it into either of the y equations to figure out the other variable.

y = (22-2(1.25))/3

y = 6.5

And to double check:

y = (57-4(1.25))/8

y = 6.5