"At a party, 65 bowls were used to serve hot food: soup, rice and chicken. Each
bowl of rice served two guests, each bowl of soup served three guests, and each
bowl of chicken served four guests. How many guests were present at the dinner?
Assume that all guests ate the full meal: soup, rice and chicken, and that all the food
in the bowls was consumed."
Do you set this problem up like 2x+3x+4x = 65?
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The least common denominator for your question is 12. Rice serves 2, Soup Serves 3, Chicken Serves 4. Least common denominator for 2,3, and 4 is 12. So for every 12 guests you would use 6 bowls of rice, 4 bowls of soup, and 3 bowls of chicken giving you total bowls of 13. So 12 guests = 13 bowls. Divide 65 total bowls by 13 bowls = 5. So to cover 65 bowls you would serve 60 guests which is 5 sets of 12.