Answer
160 child plates and 90 adult plates.
Work Step by Step
We first write the word problem as an equation. Next, we solve the equation using substitution. Doing this, we find:
$$ x+y=250 , 5.5x+9y=1935 \\ \frac{11}{2}\left(250-y\right)+9y=1935 \\ y=160 \\ x=250-160 \\ x=90$$