Cannot solve this or find answer anywhere!

Feb 2016
I'm starting a construction agency. When a contractor bills a customer, I will bill him 10% of his invoice as my commission for finding him the work. The contractor will want to add on my commission, so that after he's paid my bill, he will be left with what he would have originally charged. However, if (for example) he was to charge £1000 for his work, and he added 10% (to cover my commission and not be out of pocket) his bill would be £1100. But when I then charge him my 10% fee (£110), he's left with £990, so is £10 out of pocket. So what formula will he need to use, so that he ends up with his 'planned' invoice total after my commission. Is there a formula that will work for this, regardless of the invoice (i.e. always end up with the original number after the 10% deduction)? Thanks!
Feb 2014
United States
Let b = amount billed

Let c = commission

Let n = net to contractor

$b - c = n\ and\ c = 0.1b \implies b - 0.1b = n \implies 0.9b = n \implies b = \dfrac{n}{0.9}.$

So if the contractor wants to net 1000

the amount to bill is $\dfrac{1000.00}{0.9} \approx 1111.11\ and$

The commission $=111.11\ and$

The net to the contractor $= 1111.11 - 111.11 = 1000.00.$

As a practical matter, I'd base the commission on what the contractor gets, not what is billed. Explaining this process will not be easy, and the contractor is not going to get business by inflating his bill for no obvious benefit to him or to the client.
Feb 2016
Thanks Jeff, this is exactly what o was after!

With regards to the extra on the contractors bill, I'd like to think that we can justify the extra expense by offering a superior service than the norm!

I appreciate your time and knowledge!