I am working on an application that integrates with a payment service that charges a fee to use. I'm trying to come up with a formula, so I'll ask my question in a different format so that I don't have to get into unnecessary details.
Let's say there is a 'gatekeeper' whose job is to transfer money from person $A$ to person $B$. The gatekeeper will take $30$% of any money that he transfers from person $A$ to person $B$.
I want to transfer some amount of money (call it $X$) to person $B$. Knowing that the gatekeeper will take $30$% of any money that he transfers to person $B$, is there a formula that I can use involving $X$ and the $30$% to determine how much money I need to give the gatekeeper to ensure that person $B$ receives $X$ dollars?
I thought the formula would be simple, but I can't figure i tout.
If I understand your question correctly:
Let $x$ be the amount to be transferred. Then, let $y$ be the amount that person $B$ requires. Then, assuming that the gatekeeper keeps 30% of $x$, then
$$ 0.70x = y.$$
For example, if person $B$ requires \$299, then you must give the gatekeeper $427.14.