2007 AMC 8 Problem 20

Before district play, the Unicorns had won 45\% of their basketball games. During district play, they won six more games and lost two, to finish the season having won half their games. How many games did the Unicorns play in all?

\textbf{(A)}\ 48 \qquad \textbf{(B)}\ 50 \qquad \textbf{(C)}\ 52 \qquad \textbf{(D)}\ 54 \qquad \textbf{(E)}\ 60

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