Mathematical Formula for Business Partners Questions

### Question Description

I’m working on a algebra project and need an explanation and answer to help me learn.

I have the following fact scenario. A group of 3 business partners each own 1/3 of a small company. Owner A has brought in a large client and solely wants them working on their files. Owner A desires to adjust the level of compensation for this one client since they brought the client in and is doing all the upfront work on this one client. The other partners will assist with the post job work.

Owner A wants 2/3 of the gross profit/revenue on this client’s files. Due to the complexities in bookkeeping and the fact that Owner A will receive a 1/3 of the Net profit from being an owner of the company, the 3 have agreed to do a referral fee to Owner A upfront, and remaining balance will go to the company, which Owner A will eventually receive 1/3. Essentially I am having trouble coming up with a formula that is consistent as the revenue per file changes that always gives Owner A 2/3 of the Gross Revenue. Ultimately this formula will need to be put into excel to confirm based upon the files assigned to Owner A.

GP= Gross Profit

NP = Net Profit after Referral Fee = GP – X * GP

X = Percentage of Referral Fee

For instance, I have explored

.6666GP = X * GP + .3333 * NP

.6666 GP = XGP +.3333(GP-XGP)

2GP = XGP + GP – XGP

However, that is where I am lost as 2GP cannot equal 1GP.

Any assistance would be greatly appreciated.

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