The Dishes Problem

 Due to all the influences on me, it was hard not to consider the problem in a non-algebraic method. Thus, I had to solve the question algebraically to find the number of guests that generates 65 dishes... is 60. After doing it algebraically, I modelled and graphed the number of dishes created, given the number of guests attending. Here, I had to make some assumptions to proceed.

My algebraic work as well as working out how an x number of guests affect the number of dishes.

Suppose 5 guests showed up, and following the logic the cook provided, I assumed the following. 3 dish of rice was used as 2 guests used a dish of rice. Then, with 5, 3 dishes are needed, so the 1 remaining guest has a rice dish. Then, 2 dishes of broth had to be used. Once again, this is so the remaining 2 guests who still need to get a dish get one. Similarly, 2 meat dishes are used, so the 1 remaining guest gets something. Thus, we took all the dishes' mathematical ceilings to ensure all the guests got adequate food. With this assumption, one will realize that there are 2 correct answers to this question. 59 and 60 guests are valid, except one will have leftovers. Since the question did not mention leftovers, it is safe to assume both are correct. Instead of using pure algebra, graphing the question has yielded some interesting results, as I realized after seeing 59 guests with 65 dishes is also a valid solution.

Number of dishes needed given the number of guests.

My assumptions came with the idea of the image as I thought what would happen when this many guests showed up. As a host, I would rather have leftovers than a hungry guest because I failed to make enough food to satisfy everyone. Thus, providing imagery to the question can also get students to think outside the box, assuming it is allowed. At the same time, if we restrict students from thinking creatively by adding a handful of restrictions, what is the point of giving the students an image if the stated rules shackle them?

It is suitable to bring up the history of math as it demonstrates to students how/ancient some of the mathematical techniques taught in class are. With a question posed back in the 4th century CE, the student can realize how some of the topic being learned was once used to solve a problem. Similarly, math techniques did not only originate in 1 culture, and I like to believe that people with diverse experiences with different cultures can be a better citizens filled with love and not hate.