Expert: Paul Klarreich - 9/21/2007

Question
Paul,

I have a poor understanding of this subject.

I have 1 kg of wholewheat flour the protein content of which is 11.9%.

I also have vital wheat gluten flour and its protein content is 70%.

I want to add the gluten to the wholewheat flour to make its
protein content to 15% - up from 11.9%. The protein rich mixture is used for bread baking, if you wonder. How much of the gluten to add?

Answer
Questioner:   Thomas
Category:  Advanced Math
Private:  No
 
Subject:  Flour Mixture Percent issue
Question:  Paul,

I have a poor understanding of this subject.
I have 1 kg of wholewheat flour the protein content of which is 11.9%.
I also have vital wheat gluten flour and its protein content is 70%.

I want to add the gluten to the wholewheat flour to make its
protein content to 15% - up from 11.9%. The protein rich mixture is used for bread

baking, if you wonder.

>> Yes, I was worrying about that.

How much of the gluten to add?

................................
Hi, Thomas,

I suggest that you organize this in table format, so you identify what the values stand for:

=======================================================
WARNING: USE COURIER FONT TO VIEW THIS
===================================================


Type of      Protein     Number     Protein
Ingredient   concent.    of kg      amount
------------+----------+----------+-----------+
           |          |          |           |
           |          |          |           |
------------+----------+----------+-----------+
           |          |          |           |
           |          |          |           |
------------+----------+----------+-----------+
           |          |          |           |
           |          |          |           |
------------+----------+----------+-----------+

Enter the names of the substances:

Type of      Protein     Number     Protein
Ingredient   concent.  * of kg   =  amount
------------+----------+----------+-----------+
Whole wht   |          |          |           |
Flour       |          |          |           |
------------+----------+----------+-----------+
Vital wht   |          |          |           |
Flour       |          |          |           |
------------+----------+----------+-----------+
Final       |          |          |           |
mixture     |          |          |           |
------------+----------+----------+-----------+

Enter the protein concentration of each ingredient.  Remember that the mixture is to have 15%, and that all percent concentrations are to be written as decimal fractions.


Type of      Protein     Number     Protein
Ingredient   concent.  * of kg   =  amount
------------+----------+----------+-----------+
Whole wht   | 0.119    |          |           |
Flour       |          |          |           |
------------+----------+----------+-----------+
Vital wht   | 0.7      |          |           |
Flour       |          |          |           |
------------+----------+----------+-----------+
Final       | 0.15     |          |           |
mixture     |          |          |           |
------------+----------+----------+-----------+

Now enter these facts:
There is 1 kg of the whole wheat.
We have to find the number of kg of the 'vital'.
The total of those is the weight of the final mixture.



Type of      Protein     Number     Protein
Ingredient   concent.  * of kg   =  amount
------------+----------+----------+-----------+
Whole wht   | 0.119    |   1      |           |
Flour       |          |          |           |
------------+----------+----------+-----------+
Vital wht   | 0.7      |   x      |           |
Flour       |          |          |           |
------------+----------+----------+-----------+
Final       | 0.15     | x + 1    |           |
mixture     |          |          |           |
------------+----------+----------+-----------+

Now use the fact that:

Concentration * number of kg = protein amount
And multiply across in each line.


Type of      Protein     Number     Protein
Ingredient   concent.  * of kg   =  amount
------------+----------+----------+-----------+
Whole wht   | 0.119    |   1      | 0.119     |
Flour       |          |          |           |
------------+----------+----------+-----------+
Vital wht   | 0.7      |   x      | 0.7x      |
Flour       |          |          |           |
------------+----------+----------+-----------+
Final       | 0.15     | x + 1    | 0.15(x+1) |
mixture     |          |          |           |
------------+----------+----------+-----------+

Now we use one last fact:  The protein in the final mixture is the sum of the protein amounts in the ingredients:

0.7x + 0.119 = 0.15(x + 1)

That's your equation.  Clear the fractions by multiplying every term by 1000:

700x + 119 = 150(x + 1)

700x + 119 = 150x + 150

550x + 119 =      + 150

550x       =         31
    31
x = --- kg.
   550