Question

At a baseball game, there were three times as many males as females. 5/6 of the males were boys and the rest were men. 2/3 of the females were girls and the rest were women. Given that there were 121 more boys than girls, how many adults were there at the baseball game.

Answer 1

$x-females\\\frac{2}{3}x-girls\\\frac{1}{3}x-women\\3x-males\\\frac{5}{6}\cdot3x=\frac{5}{2}x-boys\\\frac{1}{6}\cdot3x=\frac{1}{2}x-men\\\\\frac{5}{2}x-121=\frac{2}{3}x\\\\\frac{15}{6}x-\frac{4}{6}x=121\\\\\frac{11}{6}x=121\ \ \ \ \ |\cdot\frac{6}{11}\\\\x=66\\\\\frac{1}{3}\cdot66=22\\\\\frac{1}{2}\cdot66=33\\\\33+22=55\\\\There\ were\ 55\ adults$