The Dishes Problem
"How many guests are there?" said the official.
"I don't know.", said the cook, "but every 2 used a dish of rice, every 3 used a dish of broth, and every 4 used a dish of meat between them". There were 65 dishes in all. How many guests were there?
The first thing I thought of was lowest common multiples(LCM). So the LCM between 2,3, and 4 is 12. That means if we had a group of 12 people, there would be a set number of dishes. So if we had 12 people, there would need to be 6 rice dishes, 4 broth, and 3 meat.
12 People => 6 Rice + 4 Broth + 3 Meat = 13 Dishes
So for 12 people we have 13 dishes in total. Now we just think how many groups of 13 dishes are in 65 dishes, which is 5 groups. So we need to count 5 groups of 12 people, which is 60 people.
I think it's interesting to pose these puzzles from different cultures because it's neat to see how different cultures utilize math. But despite these different cultures, the basis of math is still the same, they just may be using a different method to solve a similar puzzle.
I think a background of story definitely makes a difference. It's just interesting to have a story! Sure you could just pose this problem using only equations and numbers but it wouldn't be as engaging. By doing it this way students can see how we can apply math to solve real puzzles/problems.
"I don't know.", said the cook, "but every 2 used a dish of rice, every 3 used a dish of broth, and every 4 used a dish of meat between them". There were 65 dishes in all. How many guests were there?
The first thing I thought of was lowest common multiples(LCM). So the LCM between 2,3, and 4 is 12. That means if we had a group of 12 people, there would be a set number of dishes. So if we had 12 people, there would need to be 6 rice dishes, 4 broth, and 3 meat.
12 People => 6 Rice + 4 Broth + 3 Meat = 13 Dishes
So for 12 people we have 13 dishes in total. Now we just think how many groups of 13 dishes are in 65 dishes, which is 5 groups. So we need to count 5 groups of 12 people, which is 60 people.
I think it's interesting to pose these puzzles from different cultures because it's neat to see how different cultures utilize math. But despite these different cultures, the basis of math is still the same, they just may be using a different method to solve a similar puzzle.
I think a background of story definitely makes a difference. It's just interesting to have a story! Sure you could just pose this problem using only equations and numbers but it wouldn't be as engaging. By doing it this way students can see how we can apply math to solve real puzzles/problems.
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