Chinese plate-guest problem (without using algebra!)

If every two people share a dish of rice, then every person eats 1/2 a dish of rice.
If every three people share a dish of broth, then every person eats 1/3 a dish of broth.
If every four people share a dish of meat, then every person eats 1/4 a dish of meat.
Therefore, a single person eats the equivalent of 1/2 + 1/3 + 1/4 = 13/12 dishes of food.
Since there were 65 dishes in all, we can determine how many guests there were by dividing 65 with 13/12, which is the amount that each guest ate.
65/(13/12) = 60.  Hence, there are 60 guests.
This method only works if all the dishes of food were consumed entirely (that is, there were a perfect number of guests needed to consume all the food).
I think that cultural context certainly makes the question more understandable, and easier to relate to.  This problem presupposes an understanding that all the guests share the food equally, that they eat from common bowls, and that just enough food was put out to feed everyone.  In a western banquet, one would certainly not eat all the food, and just eat selections of the menu.  Underlying assumptions might sometimes be based on cultural context.