Group A's average weight is 162 pounds .Group B's average weight is 156 pounds.There are twice as many people in group B AS IN group A.What is the over all average weight ?
Suppose there are x people in A and 2x people in B.
Now figure the total weight and divide by the total population.
To find the overall average weight, we need to consider the weights of both Group A and Group B.
Let's assume there are "x" people in Group A.
Given that the average weight of Group A is 162 pounds, the total weight of Group A would be 162 * x.
Since Group B has twice as many people as Group A, it would have 2 * x people.
The average weight of Group B is given as 156 pounds, so the total weight of Group B would be 156 * (2 * x) = 312 * x pounds.
To find the overall average weight, we need to add the total weights of Group A and Group B and divide by the total number of people.
The overall weight would be (162 * x) + (312 * x), and the total number of people would be x + 2x = 3x.
So, the overall average weight would be ((162 * x) + (312 * x)) / (3x).
Simplifying this expression, we get (474 * x) / (3x) = 474 / 3 = 158 pounds.
Therefore, the overall average weight is 158 pounds.
To find the overall average weight, we need to consider the number of people in each group and their average weights.
Let's assume the number of people in group A is "x". Since there are twice as many people in group B as in group A, the number of people in group B is 2x.
Now, let's calculate the total weight in each group:
Total weight in group A = Average weight * Number of people in group A
Total weight in group A = 162 pounds * x
Total weight in group B = Average weight * Number of people in group B
Total weight in group B = 156 pounds * 2x
To find the overall average weight, we need to calculate the total weight by adding the weights from both groups and divide it by the total number of people:
Overall average weight = (Total weight in group A + Total weight in group B) / (Number of people in group A + Number of people in group B)
Substituting the values, we have:
Overall average weight = ((162 pounds * x) + (156 pounds * 2x)) / (x + 2x)
Simplifying further:
Overall average weight = (162x + 312x) / 3x
Overall average weight = (474x) / 3x
Overall average weight = 474 / 3
Overall average weight = 158 pounds
Therefore, the overall average weight is 158 pounds.