Let A, B and C be three positive integers such that the sum of A and the mean of B and C is 5. In addition, the sum of B and the mean of A and C is 7. Then the sum of A and B is
Explanation:
Given,
a+b+c2=5
⇒ 2a + b + c = 10 …(1)
Also, b+a+c2=7
⇒ 2b + a + c = 14 …(2)
Solving (1) and (2) we get,
b – a = 4
⇒ b = a + 4
Substituting this in the (1)
⇒ 2a + a + 4 + c = 10
⇒ 3a + c = 6
Given all three as positive integers, only possible value for a is 1. (c cannot be 0)
So, when a = 1, c = 3 and b = 5
∴ a + b = 6.
Hence, option (c).
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