This is probably mind-numbingly easy for some of you but I have trouble figuring this one out.
Here's the situation:
A company called A sells a product to an individual called B.
C, another company who hooked up A and B looks at this transaction and takes a certain % from this
D, the one who eventually handles the payment looks at the transaction between A & B, adds what C wants to take and then takes a certain % for themselves.
What would the calculation be for the transaction so that A gets the money they asked for, C gets the % they desire, D can take a % without regard for all parties and B has to pay for the costs C and D as well.
Any starting points as to how I can figure this one out?
A wants a price $P$. C takes a certain percentage of that amount for themselves. Now "percentage" literally means "per 100". For example, if C wants $10\%$, they actually want a fraction $\dfrac{10}{100} = \dfrac 1{10}$ of the price.
Let $r$ be the ratio (percentage over 100) that C wants. The amount of money that C wants is this ratio times the price $P$. That is $rP$. Therefore, if D were not around, then B would have to pay $P$ to A and $rP$ to C. So they would have to pay out $P + rP = (1 + r)P$ in total.
But D wants their blood money too. Just as with C, the percentage D wants is actually a ratio, obtained by dividing the percentage by 100. Call that ratio $R$. But this ratio is not of $P$, but of the amount that A and C receive together, $(1+r)P$. So D wants $R(1+r)P$ for themselves.
Now B must dig deeper into their wallet and come up with not just the $(1 + r)P$ needed to pay off A and C, but also the $R(1+r)P$, or $(1+r)P + R(1+r)P = (1+R)(1+r)P$ in total.
The pattern continues like this. If E figures he can spot a sucker here, and demands an additional ratio $\rho$ of the total payment to A, C, D. Then B would be stuck paying out $(1 + \rho)(1 + R)(1 + r)P$.