2020 AMC 12B Problem 5

Teams A and B are playing in a basketball league where each game results in a win for one team and a loss for the other team. Team A has won \tfrac{2}{3} of its games and team B has won \tfrac{5}{8} of its games. Also, team B has won 7 more games and lost 7 more games than team A. How many games has team A played?

\textbf{(A) } 21 \qquad \textbf{(B) } 27 \qquad \textbf{(C) } 42 \qquad \textbf{(D) } 48 \qquad \textbf{(E) } 63

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