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The restaurant serves five different dishes, which between them can be served to a total of forty customers.One fifth of the dishes served are carbonara dishes.There are six more risotto dishes than there are bream or steak dishes, and four fewer lobster dishes than there are risotto dishes.There are the same number of carbonara dishes as there are lobster dishes.How many risotto and steak dishes are served?A10B18C6D12E8

Question

The restaurant serves five different dishes, which between them can be served to a total of forty customers.One fifth of the dishes served are carbonara dishes.There are six more risotto dishes than there are bream or steak dishes, and four fewer lobster dishes than there are risotto dishes.There are the same number of carbonara dishes as there are lobster dishes.How many risotto and steak dishes are served?A10B18C6D12E8

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Solution

Let's denote the number of each dish as follows:

C - Carbonara R - Risotto B - Bream or Steak L - Lobster

From the problem, we know that:

  1. C + R + B + L = 40 (total number of dishes)
  2. C = 1/5 * 40 = 8 (one fifth of the dishes are Carbonara)
  3. R = B + 6 (there are six more Risotto dishes than Bream or Steak)
  4. L = R - 4 (there are four fewer Lobster dishes than Risotto)
  5. C = L (there are the same number of Carbonara dishes as Lobster dishes)

Substituting 2, 3, 4, and 5 into equation 1, we get:

8 + (8 + 4) + (8 + 4 - 6) + 8 = 40 8 + 12 + 6 + 8 = 40 34 + 6 = 40 40 = 40

So, the number of Risotto dishes is 12 (R = 8 + 4) and the number of Bream or Steak dishes is 6 (B = 8 + 4 - 6). Therefore, the answer is D12.

This problem has been solved

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