Let the son's age be x.

The father's age is $9x$. The mother's age is $8x$.

The sum of the father's and mother's age is 51: $9x + 8x = 51$

Simplifying: $17x = 51$

Solving for x: $x = \frac{51}{17} = 3$

Therefore, the son's age is 3 years.

Answer: D. 3 years