To most comfortably arrive at my solution for this problem, I used algebra. I let x represent the number of guests. Since we know the number guests that are fed with each food, we can write a single equation with one unknown.
1/2x + 1/3x + 1/4x = 65
Here is my rough work with algebra. It has been a long time since I did long division by hand, so I refreshed these long-forgotten skills.
I then attempted to solve the puzzle without algebra. I've drawn out my solution with groups of people and the corresponding dishes that they may share. I figured out that the lowest guest count that groups the guests into 2, 3, and 4 is 12. As the diagram on the right shows, these 12 guests will use 13 dishes and 65 dishes requires 5 groups of 12 guests.
For better or for worse, I've arrived at the same solution.
Good solutions -- but you did not reflect on the cultural aspects of this problem from a teacher's point of view, and that was part of the assignment!
ReplyDeleteHi Susan, here is my refection on the cultural aspects.
ReplyDeleteWe are fortunate to teach in Canada where students and their families come from all around the world. It is important for students to see themselves in that which we teach. Though textbooks may strive to do so, there are limitations on the depths and breadth of the content, as we touched on in a later reading. Puzzles are a great way to incorporate mathematical thinking from different cultures and historical periods. This promotes an inclusive learning environment and students learn more about other cultures through developing their mathematical thinking in new ways.