The Average Weight of A, B, and C

Finding the average weight of the individuals A, B, and C through algebraic equations not only enhances our logical and analytical skills but also demonstrates the practical application of mathematical concepts. This tutorial delves into a detailed method to determine the exact weight of individual B given the provided average weights. By breaking down the problem into smaller components, we can systematically derive the desired quantity.

Understanding the Problem Statement

Given the average weights of different combinations of A, B, and C, we are to find the weight of B. The provided information encompasses the following averages and total weights: The average weight of A, B, and C 45 kg. The average weight of A and B 40 kg. The average weight of B and C 43 kg. From these details, we deduce the following total weights for each combination: Total weight of A, B, and C 45 kg * 3 135 kg. Total weight of A and B 40 kg * 2 80 kg. Total weight of B and C 43 kg * 2 86 kg.

Deriving the Solution Step-by-Step

To solve for the weight of B, we denote the weights of A, B, and C as (a), (b), and (c) respectively. We proceed by formulating and solving a system of equations based on the given information. The total weight equation from the average weight of A, B, and C:

[frac{a b c}{3} 45] Thus, we have:

[a b c 135 quad text{(Equation 1)}]

The total weight equation from the average weight of A and B:

[frac{a b}{2} 40] Thus, we have:

[a b 80 quad text{(Equation 2)}]

The total weight equation from the average weight of B and C:

[frac{b c}{2} 43] Thus, we have:

[b c 86 quad text{(Equation 3)}] With these three equations, we can now solve for the individual weights as follows: Solving for C: From Equation 2, we express (a) in terms of (b):

[a 80 - b]

To solve for (c), we substitute (a) in Equation 1:

[(80 - b) b c 135] This simplifies to:

[80 c 135] Therefore, we find:

[c 135 - 80 55 quad text{(Equation 4)}]

Solving for B: Substitute (c) from Equation 4 into Equation 3:

[b 55 86] This simplifies to:

[b 86 - 55 31]

Thus, the weight of B is: 31 kg.

Conclusion

Through a well-structured approach involving algebraic equations and substitution, we have successfully determined the weight of B in the given scenario. By following these steps, one can easily apply similar problem-solving techniques to other analogous questions in mathematics or real-world applications involving averages and weights.

Final Answer

The weight of B is 31 kg.

Additional Reference

For additional clarity, here are the individual weights derived from our solution: Weight of A: (80 - 31 49) kg. Weight of C: 55 kg. By meticulously breaking down the problem, we have demonstrated the value of algebraic equations in finding precise solutions to real-world questions. This method not only enhances problem-solving skills but also provides a robust foundation for handling more complex mathematical scenarios.