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Find n for a tennis tourney with n women and 2n men

Source: 1978 AHSME Problem 30

June 18, 2014
ratiomodular arithmeticAMC

Problem Statement

In a tennis tournament, nn women and 2n2n men play, and each player plays exactly one match with every other player. If there are no ties and the ratio of the number of matches won by women to the number of matches won by men is 7/57/5, then nn equals
<spanclass=′latex−bold′>(A)</span>2<spanclass=′latex−bold′>(B)</span>4<spanclass=′latex−bold′>(C)</span>6<spanclass=′latex−bold′>(D)</span>7<spanclass=′latex−bold′>(E)</span>none of these<span class='latex-bold'>(A) </span>2\qquad<span class='latex-bold'>(B) </span>4\qquad<span class='latex-bold'>(C) </span>6\qquad<span class='latex-bold'>(D) </span>7\qquad <span class='latex-bold'>(E) </span>\text{none of these}
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