Chinese Restaurant Party

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?

Show/Hide Solution

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

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

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