At a large party in a Chinese restaurant (Wok Around the Clock), every three guests used a bowl of rice among them, every four guests used a bowl of soup among them, and every pair of guests used a bowl of fish between them. There were 65 bowls of these three things altogether. How many guests were at the party?

If

*G*is the number of guests, then there were*G*/3 bowls of rice,

*G*/4 bowls of soup, and

*G*/2 bowls of fish.

*G*/3 + *G*/4 + *G*/2 = 4*G*/12 + 3*G*/12 + 6*G*/12 = 13*G*/12 = 65 → 13*G* = 780 → *G* = 60.

(Check: 20 rice + 15 soup + 30 fish = 65 bowls.)