2011 AMC 12B Problem 7

Let $x$ and $y$ be two-digit positive integers with mean $60$ . What is the maximum value of the ratio $\frac{x}{y}$ ?

$\textbf{(A)}\ 3 \qquad \textbf{(B)}\ \frac{33}{7} \qquad \textbf{(C)}\ \frac{39}{7} \qquad \textbf{(D)}\ 9 \qquad \textbf{(E)}\ \frac{99}{10}$

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.