Math Gold Medalist

Lor

2023 AMC 10A

Problem 16

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?

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

Directed Graph

Translating Word Problems Into Equations

If there are n players then ans=nC2

r=2l

n=r+l=3l

wl=(1+40%)wr

w=wl+wr=nC2=(12/5)wr

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   Solution