2010 AMC 12B Problem 10

The average of the numbers 1, 2, 3,\cdots, 98, 99, and x is 100x. What is x?

\textbf{(A)}\ \dfrac{49}{101} \qquad \textbf{(B)}\ \dfrac{50}{101} \qquad \textbf{(C)}\ \dfrac{1}{2} \qquad \textbf{(D)}\ \dfrac{51}{101} \qquad \textbf{(E)}\ \dfrac{50}{99}

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