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Let's say that I have a tax of 17% over my services and I want to receive $20,000.00 regardless (after paying) the tax.

So I want something like: $$X - 17\% = \$20,000.00$$

Where $X$ is the final value that I need to charge to receive $\$20,000$.

How do I calculate this?

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I think that you wrote this on wrong forum. Questions here should be on research level. –  Tomek Tarczynski Dec 16 '10 at 20:25
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@Tomek: No, they are not. You are confusing this site with Mathoverflow. Questions of all levels are welcome here. –  Aryabhata Dec 16 '10 at 20:26
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@Tomek: math.stackexchange.com is for math questions at any level. –  Isaac Dec 16 '10 at 20:27
    
Then sorry, I thought that it is research level forum just as TCS stackexchange. –  Tomek Tarczynski Dec 16 '10 at 20:43

2 Answers 2

up vote 6 down vote accepted

The Rule of Three is your friend.

You want the 83% that is left to be $\$20,000$. If $X$ is 100% of what you need to charge, then you have: $$\begin{array}{rcl} X &\longrightarrow &100\%\\\ 20,000 &\longrightarrow&83\% \end{array}$$ By the Rule of Three, to get the value of $X$ you multiply across the known diagonal and divide by the remaining quantity; so $X = \frac{(20,000)(100)}{83}\approx \$24,096.39$.

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Thanks! Very clear. –  Telephone Dec 16 '10 at 20:58

Removing 17% leaves (100-17)%=83%, so you want 83%*x=20.000. Divide both sides by 83% to get your answer.

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Thanks. Your answer was very useful. –  Telephone Dec 16 '10 at 20:57

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