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Simple word problem

  1. Oct 10, 2008 #1
    1. The problem statement, all variables and given/known data
    When paper is recycled, water is added to break the paper up into its original wood fibers. If 100 kg of paper with a moisture content of 15% is to be recycled, how much water (kg) must be added to the recycled paper to create a solution that is 5% by dry weight fibers?

    2. Relevant equations
    100kg at 15% moisture is 6.6kg water and 85% dry is 93.4 kg fibers
    I want 95% moisture and 5% dry

    3. The attempt at a solution
    x=88.4 kg of water.
    Is it that simple or have i missed something?
  2. jcsd
  3. Oct 10, 2008 #2


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    Let's see. You have 93.4 kg fibers. To get a 5% solution, you would need X kg water. Since you already have 6.6 kg, you would have to add (X-6.6) kg water. Does that come out to be 88.4 kg?
  4. Oct 10, 2008 #3


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    How did you arrive at 15% of 100 kg is 6.6 kg and 85% of 100 kg is 93.4 kg?
  5. Oct 11, 2008 #4
    Sorry. Obvious mistake. 100kg at 15% moisture give 15 kg moisture and 85 kg solid. I had originally divided 100kg by 15.
    If I take my original solid mass of 85kg and add x amount of water, since I have 15kg of water already, its (x-15kg) I need to get a solution that is 5% or .05 water or 95% solid, so.

    It seems I am missing something. If everything that goes in must equal everything that goes out I don't think I am accounting for the added water in my final mass of 95kg solid.
    Last edited: Oct 11, 2008
  6. Oct 11, 2008 #5


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    Okay, you already have 15 kg of water and you add x kg of water. No, you don't "need" x- 15. You now HAVE x+ 15 kg. of water. You still have 85 kg of solid so you know have a total of x+ 15+ 85= x+ 100 kg total. The percentage of that that is water is (x+ 15)/x+ 100= 0.05.

    (If you wanted to add enough water to make a total of x kg of water, then you have to add x- 15 kg. But you said x is the amount of water you add (which is what the question asked), not the total amount of water.)
  7. Oct 11, 2008 #6
    First, thank you. I am not trying to be difficult, I am really trying to understand this.
    I tried the question again. I drew a diagram like this..

    A(w).15==> (re- )==>.05(s) C
    (s).85==> (cycler)==>.95(w)​

    1.Now I have a water(w) balance of...

    2.I have a solid(s) balance of...

    From equation 2, I get C=1700.
    Substituting 1700 into equation 1, I get B=1600

    From the question, 1600Kg of water must be added to the recycled paper to create a solution that is 5% fibers.
    Does that look reasonable or am I really out to lunch?
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