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Hello! I know the answer to this word problem; however, I want to know HOW to solve it. Any help is much appreciated!

Q:
A store sells used and new video games. New video games cost more than used video games. All video games cost the same. All new video games cost the same.

Omar spent a total of $84 on 4 used video games and 2 new games. Sally spent a total of $78 on 6 used video games and 1 new video game. Janet has $120 to spend.

What is the number of used video games Janet can purchase after she purchases 3 new video games?

(The answer for anyone who wants to know, is 5.) I would love to know how to solve this for an upcoming test. Thank you!

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  1. My main problem is trying to figure out the cost of the video games (both used and new). Their giving hints "Omar spent a total of $84 on 4 used video games and 2 new games. Sally spent a total of $78 on 6 used video games and 1 new video game." But I'm not sure how it can be of any use to me.

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  2. you can look at this website that i just posted

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  3. Ghost, you are the absolute best! Thank you so much!

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  4. They say how much Omar and Sally spent. So, let's say that
    x is the cost for a used game
    y is the cost for a new game.
    Then we know that
    4x+2y = 84
    6x+y = 78
    That is, since y = 78-6x,
    4x+2(78-6x) = 84
    8x = 72
    x = 9
    So, the used games cost $9 and the new games cost $24
    Sally has 120-78=$42 left to spend.
    At $9 per used game, she can buy another 4 games, and have $6 left over.

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  5. Oobleck, thank you so much too. Both of these were great help to solving the problem! I really appreciate it!

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