Answer :
Final answer:
The average weight of A, B, C, D, E, and F, with the information given, is calculated as 40 kg. The individual weights are determined by using the provided averages and understanding that the weight of F equals B, enabling a solution through simple algebra. A) 40 kg
Explanation:
Calculating the Average Weight
To solve the problem, we start by understanding that the average weight of a group is the sum of all weights divided by the number of individuals. Given the average weights of different groups, we can calculate the combined average weight by totaling the sum of weights of each group and then dividing by the total number of individuals.
Let A, B, C, D, E, and F be the weights of the respective individuals. We are given that:
- The average weight of A, B, C is 40 kg, so (A + B + C) = 3 imes 40 = 120 kg.
- The average weight of B, D, E is 42 kg, so (B + D + E) = 3 imes 42 = 126 kg.
- The weight of F is equal to that of B.
Adding these equations gives us (A + 2B + C + D + E + F), but we know that F equals B, so we replace F with B to get (A + 2B + C + D + E + B), which simplifies to (A + B + C) + (B + D + E) + B. Hence, the total weight is 120 kg + 126 kg + B.
We can find B by subtracting the sum weights of one group (B, D, E) from the other group (A, B, C), which gives us A + C = D + E. By rearranging, we can express A + C − D − E. This difference is 120 kg − 126 kg = -6 kg. Since F equals B, we add this difference to our total weight calculation: 120 kg + 126 kg - 6 kg = 240 kg.
Finally, to find the average weight of A, B, C, D, E, and F, we divide the total weight by the number of individuals, which is 240 kg / 6 = 40 kg.
The correct answer to the question is A) 40 kg.
