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Thread: "Cans of Paint" Word Problem

  1. #1
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    "Cans of Paint" Word Problem

    Hey guys, this problem has been giving me a headache for the last hour, and its the last problem I need to do before my homework is due in an hour and a half! Help!

    I have two cans of paint. Can A has 9 parts of blue paint to one part of yellow paint. Can B is 20 percent blue paint and the rest is yellow paint. How much paint should I use from each can to obtain 2 liters of paint which is half blue and half yellow.


    amount of can A= ___________________ liters
    amount of can B= ___________________ liters
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  2. #2
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    The farthest I keep getting is that A + B= 2L, but I have no idea what other equation to set up, I've tried a bunch.
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  3. #3
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    Quote Originally Posted by Togechu64 View Post
    Hey guys, this problem has been giving me a headache for the last hour, and its the last problem I need to do before my homework is due in an hour and a half! Help!

    I have two cans of paint. Can A has 9 parts of blue paint to one part of yellow paint. Can B is 20 percent blue paint and the rest is yellow paint. How much paint should I use from each can to obtain 2 liters of paint which is half blue and half yellow.


    amount of can A= ___________________ liters
    amount of can B= ___________________ liters
    1. Can A: \frac9{10} blue + \frac1{10} yellow

    Can B: \frac2{10} blue + \frac8{10} yellow

    2. Let x denote the amount of cans A and y the amount of cans B. Of each color you need exactly 1 litre.

    3. Solve the system of equations for x, y:

    \left|\begin{array}{rcl} \frac{9}{10} x + \frac{2}{10} y &=& 1 {\color{blue}\bold{blue}}\\  \frac{1}{10} x + \frac{8}{10} y &=& 1 {\color{yellow}\bold{yellow}}\end{array}\right.

    Spoiler:
    I've got x = \frac67~\vee~y=\frac87
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  4. #4
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    PERFECT!!! I worked it out and got exactly the right answer, thank you so much, you're an incredible life saver! I've made sure to write down your explanation so I have a practice problem to review for the midterm, thank you very much again for all your help!!!
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