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A cook wanted to find out how many guests she cooked for. An official told her that for every dish of rice, there were 2 people. And every three people had a dish of broth. There was 1 dish of meat for every four people. There were 65 dishes in all. The cook then figured out how many guests there were. How many guests did the cook cook for?

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60 guests

Let x be the number of guests. According to the puzzle, the equation for total number of dishes is x/2 + x/3 + x/4 = 65. Solving this, we get x=60.