For how many triples of positive integers $(x,y,z)$, there exists a positive integer $n$ such that $\dfrac{x}{n} = \dfrac{y}{n+1} = \dfrac{z}{n+2}$ where $x+y+z=90$?

$ 
\textbf{(A)}\ 4
\qquad\textbf{(B)}\ 5
\qquad\textbf{(C)}\ 6
\qquad\textbf{(D)}\ 7
\qquad\textbf{(E)}\ 9
$