Maths problem: how to do, thanks?

The current weight of beans is 32 g.
The current weight of rice is 50 - 32 = 18 g.

Suppose Fanny's claim is correct.
Then she adds 5k (in g) and 2k (in g) of rice and beans, respectively, to the mixture, where k is a positive constant.

The new weight of beans is (32 + 2k) g.
The new weight of rice is (18 + 5k) g.

Consider (18 + 5k):(32 + 2k) = 7:9.
9(18 + 5k) = 7(32 + 2k)
162 + 45k = 224 + 14k
31k = 62
k = 2

Because the value of k can be solved as a positive constant, Fanny's claim is correct and agreed.

Note:
If k cannot be solved, or k is solved to be a non-positive number, then the claim is not agreed.

Suppose Fanny adds 5x g rice & 2x g beans so that wt. of rice:beans=7:9

(18+5x):(32+2x) = 7:9

18+5x 　 7
--------- = ---
32+2x  　9
7(32+2x) = 9(18+5x)
224+14x = 162+45x
224-162 = 45x-14x
62 = 31x
∴ x = 2

Yes, I agree that she can add 5(2)=10 g rice & 2(2)=4 g beans
so that wt. of rice:wt. of beans = 7:9