Answer: 8 binx games were played.
11 zonk games were played
Explanation:
Let x represent the number of binx games that was played.
Let y represent the number of zonks games that was played.
60 people attend a game night and all 60 people are playing either binx or zonks. Everyone chooses to play binx, a two player game, or zonks a four player game. This means that
2x + 4y = 60 - - - - - - - - -1
There are 3 more games of zonks being played. This means that
x = y - 3
Substituting x = y + 3 into equation 1, it becomes
2(y - 3) + 4y = 60
2y - 6 + 4y = 60
2y + 4y = 60 + 6
6y = 66
y = 66/6 = 11
x = 11 - 3 = 8