$x-12\%=100$, find $x$

Question

I need to pay someone after deducting $12\%$ commission. I want to pay him round amount of $10,000$ What is the formula to establish the $112\%$ figure so that once I have deducted my comm I will be left with $10,00$. I know the answer is not $11200$ because $11200 - 12\% = 9856$.

Please help me with a formula that will calculate $x - 12\%= 10,000$ or $x - 12\% = 7000$ or $x-12\% = 5000$.

Thanks so much, Maurice

Answer 1

One may observe that, in general, $$ x - a\%\:x=b $$ is just $$ \left(1-\frac{a}{100} \right)\times x=b $$ giving, if $a \neq 100$,

$$ x=\frac{b}{\left(1-a/100\right)} $$

Answer 2

see its quite simple sorry for misinterpreting first time. so here we assume total amount to be $x$ thus you want $12\%$ commision of $x$ and extra $10K$. so our equation becomes $\frac{12x}{100}+10000=x$ thus on solving you get $x=11363.63..$ now i hope i have interpreted your question correctly.

Answer 3

$88\%$ of $x$ is $10000$, then $x=\dfrac{10000}{88\%}=10000\cdot\dfrac{100}{88}=11363.63$.

Check: $88\%$ of $11363.63$ is $9999.99$.