When I read this question, I immediately have an
image of people sitting in a round table. I think this is due to my background,
I am used to sitting in a round table when dinning. Also, in the Chinese culture,
it is more common to share dishes so it may be easier for Chinese students to
imagine. For other cultures where they eat and sit differently, for example in
rectangular tables, they may approach the problem differently.
I pictured in my mind 2 people sharing a rice,
3 sharing a broth, and 4 sharing a meat. I drew a diagram of this, and
continuing the drawing after the first 4 people. When I got to 12 people in a
table, all dishes were shared equally with no leftovers or anyone missing a
dish. So I see that 12 people will share 6 rice, 4 broths, and 3 meat dishes.
And that is a total of 13 dishes per table of 12 people. I know that there is a
total of 65 dishes in total so I have 65/13 = 5 tables. So there should be
5*12= 60 people in total. Without algebra, students can continue drawing the
tables of guests and they should see that they get 5 tables of 12 people and a
total of 65 dishes. Or, students can draw a bigger table, and continue the
process of drawing until they have 65 dishes, then count the number of guests,
which should be 60.
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