The Dishes Problem

Every 2 guests used a dish of rice.

Every 3 guests used a dish of broth.

Every 4 guests used a dish of meat.

Let r, b, and m be the number of dishes of rice, broth, and meat, respectively.

r + b + m = 65

Every 2 guests used a dish of rice, so 2r represents the total number of guests.

Every 3 guests used a dish of broth, so 3b represents the total number of guests.

Every 4 guests used a dish of meat, so 4m represents the total number of guests.

So, 2r = 3b =4m = g represents the total number of guests

g/2 + g/3 + g/4 = 65

g(1/2 + 1/3 + 1/4) = 65

g(13/12) = 65 

g = 65(12/13) = 60 which gives the total number of guests is 60.

This puzzle can be solved without algebra by carefully considering the relationships between the guests and the dishes. However, using algebra helps formalize and generalize the solution process.

Offering examples, puzzles, and histories of mathematics from diverse cultures can significantly impact students. It not only promotes inclusivity but also helps students see the universality of mathematical thinking across cultures.

The word problem and the story context can make a significant difference in the enjoyment of solving a problem. A well-crafted story can engage students, make the problem more relatable, and enhance the overall learning experience.

Comments

  1. Qiaochu (Joy)September 28, 2023 at 9:26 PM

    Hi Shawn, thank you for sharing your way of solving this problem! Could you please double-check and ensure you've addressed the questions as requested in the class blog? If you have any questions or need clarification, feel free to reach out. Thank you!

    ReplyDelete
  2. Susan GerofskyJanuary 1, 2024 at 2:13 PM

    Thanks for the revisions -- all fine now.

    ReplyDelete

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