Suppose line k has equation x = 3. Compare the areas of ABCD and A′′B′′C′′D′′ after a reflection over line k and then a translations following the rule (x, y)-> (x+1, y+2). Justify your answer.

The average age is 7.1 years.

This problem is an example of when we need to take a weighted average. We simply can't just find the average of 5 and 8, because there are different children of each each.

To start, lets multiply the total number of children by their individual ages.

6 x 5 = 30 years
14 x 8 = 112 years

There are 142 years among the 20 years, so divide 142 by 20. This gives us an average age of 7.1 years.