Question : The average weight of A, B, and C is 65 kg. If the average weight of C and B is 61.5 kg, and the average weight of A and C is 68.5 kg, then the weight of C (in kg) is:
Option 1: 65
Option 2: 60
Option 3: 68
Option 4: 67
Correct Answer: 65
Solution : Let the weights of A, B, and C as $a$, $b$, and $c$, respectively. From the problem, 1. The average weight of A, B, and C is 65 kg. $⇒\frac{a + b + c}{3} = 65$ $⇒a + b + c = 195$ 2. The average weight of B and C is 61.5 kg. $⇒\frac{b + c}{2} = 61.5$ $⇒b + c = 123$ 3. The average weight of A and C is 68.5 kg. $⇒\frac{a + c}{2} = 68.5$ $⇒a + c = 137$ Subtracting the second equation from the first, $⇒a = 72$ kg Substituting $a = 72$ kg into the third equation, $⇒c = 137 - 72 = 65$ kg Hence, the correct answer is 65.
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