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Math Help - Mixture Problem

  1. #1
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    Mixture Problem

    No matter what I try, I just cannot figure this one out. Like I mentioned on the other thread, I'm not having any trouble solving them, just modeling them.

    The radiator in a car is filled with a solution of 60% antifreeze and 40% water. The manufacturer of the antifreeze suggests that, for summer driving, optimal cooling of the engine is obtained with only 50% antifreeze. If the capacity of the radiator is 3.6 L, how much coolant should be drained and replaced with water to reduce the antifreeze concentration to the recommended level?
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  2. #2
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    Let x be the liters of 60% antifreeze coolant and y be liters of pure water.

    Then: x + y = 3.6
    .6x + 0y = .5(3.6)

    Solve the system for x and y, and of course your answer will be y.
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  3. #3
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    let x = number of liters to drain and fill ...

    3.6(60%) - x(60%) + x(0%) = 3.6(50%)

    solve for x
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  4. #4
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    Quote Originally Posted by icemanfan View Post
    Let x be the liters of 60% antifreeze coolant and y be liters of pure water.

    Then: x + y = 3.6
    .6x + 0y = .5(3.6)

    Solve the system for x and y, and of course your answer will be y.
    Thank you so much!

    I got the solution .6L. The only thing I don't quite understand is the set up. I mean, of course I know it's right. I was just wondering why you put everything where you did? I understand the x+y=3.6 just fine, it's the 0y I don't exactly understand. Because aren't you adding water? I don't know why I can't get this modeling down.. once I see it done it looks so easy.
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  5. #5
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    Quote Originally Posted by Chinnie15 View Post
    it's the 0y I don't exactly understand. Because aren't you adding water?
    No, because the water you are adding doesn't have any antifreeze in it. The second equation I wrote represents a relationship that equates the total amount of antifreeze (in liters) on both sides.
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