You searched for: “apportion
apportion, proportion
apportion (uh POR shuhn; uh POHR shuhn) (verb)
To divide and to assign according to a plan; to allot: The officials will have to apportion the proceeds from the auction to the families.
proportion (pruh POR shuhn, pruh POHR shuhn) (noun)
A relationship between things or parts of things with respect to comparative magnitude, quantity, or degree: Some of the money goes to cover expenses, but a large proportion is donated to charity.

At the conclusion of the country fair, the organizers had to determine how to apportion the proceeds, ensuring that a generous proportion was designated for the local charities.