High School

The average weight of A, B, C, and D is 60 kg. The average weight of A, B, C, D, and E is 57 kg. The weight of F is 5 kg more than that of E. The average weight of B, C, D, E, and F is 61 kg. Find the weight of A.

Answer :

Final answer:

The weight of person a is 285 kg.

Explanation:

Let's solve this problem step by step:

From the given information, we know that the average weight of a, b, c, and d is 60 kg.

We are also given that the average weight of a, b, c, d, and e is 57 kg.

Since the average weight of b, c, d, e, and f is 61 kg, we can subtract the average weight of a, b, c, and d (60 kg) from the average weight of b, c, d, e, and f (61 kg). This will give us the weight of f:

f = (average weight of b, c, d, e, and f) - (average weight of a, b, c, and d)

f = 61 kg - 60 kg

f = 1 kg

Since the weight of f is 5 kg more than that of e, we can subtract 5 kg from the weight of f to find the weight of e:

e = f - 5 kg

e = 1 kg - 5 kg

e = -4 kg

Finally, since the average weight of a, b, c, d, e, and f is 57 kg, we can substitute the weights we found for e and f into the equation and solve for a:

Average weight of a, b, c, d, e, and f = [(weight of a) + (weight of b) + (weight of c) + (weight of d) + (weight of e) + (weight of f)] / 6

57 kg = [(weight of a) + 60 kg + 0 kg + 0 kg + (-4 kg) + 1 kg] / 6

57 kg = (weight of a + 57 kg) / 6

Now solve for the weight of a:

57 kg * 6 = weight of a + 57 kg

342 kg - 57 kg = weight of a

285 kg = weight of a

Therefore, the weight of a is 285 kg.

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