The logic behind the rule of three on this calculation First,
to understand my question, checkout this one:
Calculating percentages for taxes
Second, 
consider that I'm a layman in math.
So, after trying to understand the logic used to get the final result. I was wondering:
Why multiply $20,000 by 100 and then divide by 83? I know this is the rule of three, but, I can't understand the "internals"  of this approach. It isn't intuitive as think in this way:
Say 100% of one value, is the same of divide this value by 100. In other words: I have 100 separeted parts of this integer.
It's intuitive think about the taxes like this:
$$X - 17\% = \$20.000$$
So: 
$$\$20.000 = 83\%$$
For me, the most easy and compreensive way to solve this is:
$$\$20.000 / 83 = 240.96$$
It's the same as think, if 100% is 100 parts of one integer, 83% of that integer is the same of divide this integer by 83.
And finally to get the result:
$$\$20.000 + 17 * 240.96$$
My final question is:
How can I think intuitively like this using the Rule of Three?
In other words, why multiply 20.000 by 100 and then divide by 83 is a shorcut to get the result? 

I think that the form to see this more easy,is to see it as proportionally; is say:
$$\frac{X}{100}=\frac{20000}{83}$$ (Are equals as they have the same proportion)
Thus only, you must solve the equation for $X$.
Then $$X= \frac{(20000)(100)}{83}$$ Passing to multiply to 100, remember this is solved in cross multiplying .
Arturo had been clear in the other post.
