Without having the tool of algebra, it is more difficult to solve the problem for sure. However, it allows me to think more critically rather than just define a variable and write an equation and find the unknow. I actually had so much fun in the process of figuring out how to find the number of guests. I broke down the number of total dishes 65 into two prime numbers first. Then I tested 13 was too big for a sum of 65. It only left 5 to be tested. Finally I got the number of dishes offered under each category and find the least common multiple of 15,20, and 30 which is 60, the number of the guests.

Later on I realized that my method was not the best way to find the solution. All I need to find is the least common multiple of 2,3 4, and multiply it with one of the prime factors of 65.  However, I was more involved in thinking the relations among all the elements and how do they interact with each other. Although solving this problem with the absent of the algebra is not straightforward, it does serve as a critical thinking practice. I believe this kind of mathematical exercise is valid and meaningful in classroom teaching.