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 Question from SM: How many guests were present at an Italian dinner if every 2 guests shared a bowl of salad, every 3 guests shared a bowl of pasta, and every four guests shared a bowl of meatballs, and there were 65 bowls used altogether?

Hi again Maria,

The number of guests must be divisible by 2, 3 and 4.

Write back if you need more assistance.

Penny.

Maria wrote back: I do need more assistance. Do I divide 64 bowls by 4 (making 16), and then add 2 or 3 to that 16?

The smallest number that is divisible by 2, 3, and 4 is 12, so the number of guests must be a multiple of 12. Is 12 guests the correct answer? if so then

Bowls
Every 2 guests shared a bowl of salad 6
Every 3 guests shared a bowl of pasta 4
Every 4 guests shared a bowl of meatballs 3
Total 13

and only 13 bowls would be required so this is not the correct number of guests.

The next smallest multiple of 12 is 24 so is 24 guests the correct answer? What about 36?

Penny

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