Venn diagram applied problem 
Among a group 15% speak French, 45% are women, and 20% of the women also speak French.
Q: What percentage are women that don't speak French, what percentage only speak French and not woman?

My thoughts:
(1) Using a venn diagram
Let $A = \text{French}$ and $B = \text{Women}$
Since $B = (B \cap A^{c}) \space \cap (B \cap A)$, we have to find $B \cap \overline{B \cap A}$ right?
What is the way? Is the answer $45% - 20% = 25%? But I don't see the manipulation of formulas behind it. Like the way I was trying?
 A: To simplify our thinking, let's just say we have a 100 people. We're basically told that 15 of these people speak French and that 45 are women. We're also told that 20% of the women speak French. In other words 1/5 of the women speak French. That is, $45*\frac{1}{5}=9$ women speak French.
Let's address the first question: out of the 100 people, how many are non-French speaking women? Well we found that 9 women speak French, so 36 women don't. So out of the 100 people, 36 people are non-French speaking women. So 36%.
As for the second question, we established at the start that 15 people speak French. We also know that there are 9 French-speaking women. So we must have 15-9=6 men that speak French. So that gives us 6%. 
A: $20\%$ of the women speak French means that $20\%\cdot45\%=9\%$ of the group are women who speak French.
So women who don't speak French are $45\%-9\%=36\%$
Speak French and not women are $15\%-9\%=6\%$
A: What's wrong is that your Venn Diagram is a bit incorrect.
Since we have 20% of the women speaking French that would be $45\%\cdot 20\%=9\%$ total.
So the amount of women that don't speak French is 36%.
The amount of men that speak French is 6%.
