I'm working with a website that can be used to pay contractors on my behalf, instead of requiring them to submit to me their W9 for taxes. The website takes $2.75\%$ in processing fees.
If I'm paying someone $\$22$ per hour, and the website requires $2.75\%$, I believe that would be $\$0.60$ of each hour that would be paid to the website.
That would mean if I still wanted to pay the developer $\$22$/hr including the fees, I would effectively be paying him $\$21.40$ per hour.
My problem is with checking my math. I was trying to figure out how to take the $\$21.40$ and multiply it some value to reach the $\$22$, but I don't know how to do that.
What value times $\$21.40$ equals $\$22$?
[I also could not figure out why the dollar sign caused the post to lose its formatting so surrounded it in preformatted tags.]
If the processing fee is $2.75\%$ of the amount processed, and you want to have $\$22$ after the fee is taken out, then you have the following equation: $$x-x\times2.75\%=22,$$ where $x$ is the initial amount (i.e. before the processing fee is taken).
Read the equation as:
Factorization of the left-hand side (further referred to as LHS) gives $$x\left(1-2.75\%\right)=22$$ (multiply out to check); then notice that a percent is exactly one hundredth of the unity: $$x\left(1-2.75\frac1{100}\right)=22;$$ now rewrite the unity as $100/100$ and multiply the $2.75$ by the fraction, which in this case just moves $2.75$ into the numerator: $$x\left(\frac{100}{100}-\frac{2.75}{100}\right)=22;$$ denominators are now equal, so we can bring the numerators over one fraction bar: $$x\left(\frac{100-2.75}{100}\right)=22;$$ perform the subtraction in the numerator: $$x\frac{97.25}{100}=22;$$ divide both sides by the fraction: $$x\frac{97.25}{100}/\frac{97.25}{100}=22/\frac{97.25}{100};$$ that gets rid of the fraction on the LHS: $$x=22/\frac{97.25}{100};$$ division by a fraction is equivalent to multiplication by the same fraction but with numerator and denominator swapped: $$x=22\frac{100}{97.25};$$ multiply the integer $22$ by the fraction, which brings it into the numerator as a multiple: $$x=\frac{22\times100}{97.25};$$ perform the multiplication: $$x=\frac{2200}{97.25};$$ we arrived at the desired answer; the fraction may be further simplified, or a decimal approximation up to four decimals after the decimal point may be obtain by division on a calculator: $$x\approx22.6221;$$ round the value up (need to explain why?), which gives
$$22\text{ dollars and }63\text{ cents.}$$
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