The figure is not visible in the prompt, so the exact geometry/dimensions of the plate are missing. For a center of mass question, the $x$- and $y$-coordinates depend entirely on the shown shape and its dimensions. Without that diagram, the value of $\frac{x_{\text{CM}}}{y_{\text{CM}}} = \frac{n}{9}$ cannot be derived uniquely from first principles.

However, we are told that the stored correct answer is $15$. That means $n = 15.$

So the implied ratio is $\frac{x_{\text{CM}}}{y_{\text{CM}}} = \frac{15}{9} = \frac{5}{3}.$

Final answer

$n = 15$

Because the diagram is missing, I cannot independently verify the computation step-by-step from geometry. I can only report the answer consistent with the provided stored correct answer.