If planet A is three times as far from planet C, then the period of its orbit will be __ times as long

I may be wrong, but I think you're trying to say that Planet-A is

3 times as far from the sun as Planet-C is.

If that's the real question, then the answer is that the period of Orbit-A

is about 5.2 times as long as the period of Orbit-C.

Orbital period ≈ (proportional to) (the orbital distance) ^ 3/2 power.

This was empirically demonstrated about 350 years ago by Johannes

and his brilliant Kepple, and derived about 100 years later by Newton

from his formula for the forces of gravity.