Chinese Dishes Problem

Without using any algebra, how can we find how many guests are there if there are 65 dishes, and that every rice dish is shared by 2 people, every soup dish is shared by 3 people, and every meat dish is shared by 4 people?

Surely there are many methods to do this, but the one I chose mainly involves fractions (and cross-multiplication).

If we know that...

• 1 dish of rice is shared by 2 people, then each person eats 1/2 dish of rice.
• 1 dish of soup is shared by 3 people, then each person eats 1/3 dish of soup.
• 1 dish of meat is shared by 4 people, then each person eats 1/4 dish of meat.

Then, to put all together...

We we know that each person eats 1/2 + 1/3 + 1/4 = 13/12 dish of rice AND soup AND meat. (We can also consider this summation by looking at that "each person" as a unit of measurement.)

Since each person eats 13/12 dishes of rice AND soup AND meat, and we know that there are 65 dishes of food (rice AND soup AND meat), we can use unit conversion to find how many persons are there.

The final answer is...

65 dishes / (13/12) dishes/person =  60 persons.

The culture context, in my opinion, is quite universal for a problem/puzzle like this one because food is universal across all cultures. For instance, this similar problem can be used for any large feast in any culture, such as a potluck, a wedding or a birthday celebration if any dishes are shared. However, not all events have shared dishes, so the way people think about this could be different. Regardless, I can imagine any restaurant owners who is feasting a large number of guests can undergo this kind of problem in their lives, either to maximize profits or to serve guests with an economical (appropriate) amount of food so no food can go to waste.