The average weight of A, B, and C is 45 kg. If the average weight of A and B is 40 kg, and the average weight of B and C is 43 kg, determine the weight of B.

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Accepted Answer

Let the weights of A, B, and C be denoted as $$ A $$, $$ B $$, and $$ C $$, respectively.

1. **Total weight of A, B, and C:**  
   $$
   A + B + C = 45 	imes 3 = 135 \, 	ext{kg} \quad 	ext{(Equation 1)}.
   $$

2. **Total weight of A and B:**  
   $$
   A + B = 40 	imes 2 = 80 \, 	ext{kg} \quad 	ext{(Equation 2)}.
   $$

3. **Total weight of B and C:**  
   $$
   B + C = 43 	imes 2 = 86 \, 	ext{kg} \quad 	ext{(Equation 3)}.
   $$

4. **Add Equations 2 and 3:**  
   $$
   (A + B) + (B + C) = 80 + 86 = 166 \, 	ext{kg}.
   $$  
   This simplifies to:  
   $$
   A + 2B + C = 166 \, 	ext{kg} \quad 	ext{(Equation 4)}.
   $$

5. **Subtract Equation 1 from Equation 4:**  
   $$
   (A + 2B + C) - (A + B + C) = 166 - 135.
   $$  
   Simplify to find $$ B $$:  
   $$
   B = 31 \, 	ext{kg}.
   $$

**Verification:**  
- From Equation 2: $$ A = 80 - B = 80 - 31 = 49 \, 	ext{kg} $$.  
- From Equation 3: $$ C = 86 - B = 86 - 31 = 55 \, 	ext{kg} $$.  
- Total weight: $$ 49 + 31 + 55 = 135 \, 	ext{kg} $$ (matches Equation 1).

Thus, the weight of B is **31 kg**.

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