AMC 12 2023a Problem 13

In a table tennis tournament every participant played every other participant exactly once. Although there were twice as many right-handed players as left-handed players, the number of games won by left-handed players was $40\%$ more than the number of games won by right-handed players. (There were no ties and no ambidextrous players.) What is the total number of games played?

$\textbf{(A) }15 \textbf{(B) }36 \textbf{(C) }45 \textbf{(D) }48 \textbf{(E) }66$