Solve Simple Word Problem: 100kg w/15% Moisture to 5% Dry Weight Fibers

[yoleven]

Homework Statement

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?

Homework Equations

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

The Attempt at a Solution

6.6kg+x=95kg
x=88.4 kg of water.
Is it that simple or have i missed something?

 

[dlgoff]

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?

 

[HallsofIvy]

How did you arrive at 15% of 100 kg is 6.6 kg and 85% of 100 kg is 93.4 kg?

 

[yoleven]

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.
85kg+(x-15kg)=95kg
x=25

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.

 

[HallsofIvy]

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.)

 

[yoleven]

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..

100kg
A(w).15==> (re- )==>.05(s) C
(s).85==> (cycler)==>.95(w)​

^
^​

B​

1.Now I have a water(w) balance of...
.15(100)+B=.95C

2.I have a solid(s) balance of...
.85(100)=.05C

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?