Let's say I have 65% of a company and my partner has 15% of the same company, so together we both have 80% of the company.
We want to give a new partner 7% of our company, and for that to happen, we've decided each one of us would give a fair share of our individual quotas, proportional to the amount of % each one of us has.
For example: as I have 65%, my given share would be greater to the share given by my partner (which only has 15%) so that the quota given in total by both of us to the new partner would be 7%. I imagine I would lose about 5% of my quota and my partner would lose about 2% of his. But I’m just going through my intuition.
What would be the mathematical expression for this?
Let $x$ be the quota that your partner gives.
We then have
$$\frac{65}{15}x + x = 7 \implies x = \frac{21}{16}$$
Hence, you give $$\frac{65}{15} \times \frac{21}{16} = \frac{91}{16} = \boxed{5.6875\, \%}$$
Your partner gives
$$\frac{21}{16} = \boxed{1.3125\, \%}$$