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972 patients ordered food for lunch. They could choose roast chicken, mac and cheese, vegetable chilli or cottage pie. Half chose the roast chicken, 1/3 chose the mac and cheese and 1/12 chose the cottage pie. How many opted for a vegetarian option? A) 81 B) 324 C) 405 D) 486 E) 567

Question

972 patients ordered food for lunch. They could choose roast chicken, mac and cheese, vegetable chilli or cottage pie. Half chose the roast chicken, 1/3 chose the mac and cheese and 1/12 chose the cottage pie.
How many opted for a vegetarian option?

A) 81
B) 324
C) 405
D) 486
E) 567

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Solution

To solve this problem, we first need to find out how many patients chose each of the non-vegetarian options (roast chicken, mac and cheese, and cottage pie), then subtract these numbers from the total number of patients to find out how many chose the vegetarian option (vegetable chilli).

  1. Half of the patients chose roast chicken. So, 972 / 2 = 486 patients chose roast chicken.
  2. One third of the patients chose mac and cheese. So, 972 / 3 = 324 patients chose mac and cheese.
  3. One twelfth of the patients chose cottage pie. So, 972 / 12 = 81 patients chose cottage pie.

Now, add up the number of patients who chose each of these three options: 486 (roast chicken) + 324 (mac and cheese) + 81 (cottage pie) = 891 patients.

Finally, subtract this number from the total number of patients to find out how many chose the vegetarian option: 972 (total patients) - 891 (non-vegetarian) = 81 patients.

So, 81 patients opted for a vegetarian option. The answer is A) 81.

This problem has been solved

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