In our system, we got a booking of the price 1100, the default commission percentage is 15% hence the raw price is
1100 / 1.15 = 956.52173913
Which means that the current commission amount is
1100 - 956.52173913 = 143.47826087
I need to change the commission percentage of this booking, but i only know the commission amount which is 100
How do i calculate the new commission, based on the only on commission amount?
I'm not sure I really understand the context, but I think what you're trying to do is solve the equation: \begin{equation} 1100(1 - \frac{1}{1 + p}) = 100 \end{equation} which yields $p = 0.10$.
More general. The following formula can be solved for $x$.
$P\cdot \left(1-\frac{1}{1+x}\right)=C$
with $P=$ gross price, $x$=comission rate and $C$=commission
Multipying out the brackets
$P-\frac{P}{1+x}=C$
$P-C=\frac{P}{1+x}$
Interchanging numerators and denominators
$\frac{1}{P-C}=\frac{1+x}{P}$
$\frac{P}{P-C}=1+x$
$\frac{P}{P-C}-1=x$
$\frac{P}{P-C}-\frac{P-C}{P-C}=x$
$\boxed{\frac{C}{P-C}=x}$
With $P=1100$ and $C=100$
$x=\frac{100}{1100-100}=0.1=10\%$
