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Algebra problem

  1. Nov 3, 2008 #1
    1. The problem statement, all variables and given/known data

    A lab has a 20% acid solution and a 50% acid solution. How many liters of each are required to obtain 600 liters of a 30% acid solution?

    2. Relevant equations



    3. The attempt at a solution
    .20x + .50(600 - x) = .30(600)
    .20x + 300 - .50x = 180
    -0.3x + 300 = 180
    - 300 -300
    -0.3x = -120
    ----- -----
    -0.3 -0.3
    x = 400 liters

    I am sure that the answer is wrong. Can anyone tell what im doing wrong, or how to set the problem up properly?
    Thank you
     
  2. jcsd
  3. Nov 3, 2008 #2

    gabbagabbahey

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    Homework Helper
    Gold Member

    Your solution for x looks good to me, what does that mean the quantity of the 20% solution is? How about the 50% solution?
     
  4. Nov 3, 2008 #3

    HallsofIvy

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    Staff Emeritus
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    The only thing I see wrong with it is that you haven't yet answered the question.

    "x= 400 liters" does not answer "How many liters of each are required to obtain 600 liters of a 30% acid solution?" For one thing, there is no "x" in the question and, for another, there are obviously two quantities required, not just one.

    I presume that x represents the amount of 20% acid solution used. It is very good practice to SAY that at the beginning of the solution (if nothing else, it will really shock your professor!). You also have (600- x) in your formula and that, I guess, is the amount of 50% acid solution used. Well, 600- 400= 200, so your answer should be "400 liters of the 20% acid solution and 200 liters of the 50% acid solution must be used to make 600 liters of 30% acid solution."

    Now, let's see if that is correct. Certainly 400+ 200= 600 liters so that gives the correct amount of solution. 400 liters of 20% acid solution contains .20(400)= 80 liters of pure acid. 200 liters of 50% acid solution contains .5(200)= 100 liters of pure acid so the 600 liters of mixture contains 180 liters of acid. 180/600= 18/60= 3/10= .30. Yes, that is a 30% solution.
     
  5. Nov 3, 2008 #4
    thanks soo much!
     
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