Answer :
Final answer:
The overall average weight of the combined groups is calculated by adding the total weights of both groups and dividing by the total number of people. Since Group Y has twice as many people as Group X, the overall average weight can be found as 158 pounds, which is option d.
Explanation:
To find the overall average weight of the two groups combined, we need to consider the total weight of each group and the number of people in each group. Since there are twice as many people in Group Y as in Group X, we can denote the number of people in Group X as x and the number of people in Group Y as 2x.
Now, the total weight for Group X is 162 pounds per person times x people, which equals 162x pounds. The total weight for Group Y is 156 pounds per person times 2x people, which equals 312x pounds.
The overall total weight is the sum of the total weights for both groups, which is 162x + 312x = 474x pounds. The total number of people is x + 2x = 3x people. Thus, the overall average weight (W) is the total weight divided by the total number of people:
W = 474x / 3x = 158 pounds
Therefore, the overall average weight is 158 pounds, which corresponds to option d.
