Answer
Please see the work below.
Work Step by Step
We know that if the gravitational force had to depend on the sum of the masses of two objects then there would be an attractive force between a body of mass $m$ and a body of mass zero; that is, a non-existent body would be attracted by the mass, which is not possible. Instead, the gravitational force depends on the product, rather than the sum, of the masses, as well as their distance, which is what we observe in the real world.
