The Dishes Problem

We know that  every 2 used a dish of rice
                        every 3 used a dish of broth and
                       every 4 had a dish of meat between them.
There were 65 dishes in all.  How many guests were there?


I suspect there are many ways to solve this problem.  Here is one way:

If the number of guests is x, then 

x/3 + x/4 + x/2 = 65

Multiply by 12 (common denominator)

4x + 3x + 6x = 780

x = 60


So there were 60 guests in total.