Question

The average age of a group of 12 people is 26 years. If 8 new people are added to the group, the average of the group increases to 32 years. In years, what is the average of the 8 new people?

Answer 1

A roundabout way of solving this problem involves writing out the two averages given:

Average age of the original group of 12 people = 26 = (sum of the ages of these 12)/12

Thus, (sum of the ages of the first 12 people) = 12 * (average age 26) = 312.

Average age of the augmented (larger) group of 20 people = 32 = (sum of the ages of these 20)/20

Thus, (sum of the ages of all 20 people) = 20 * (average age 32) = 640

Subtract 312 from 640 to obtain the (sum of the ages of the additional 8 people)

Divide the result by 8 to obtain the average age of the 8 new people.


Can anyone condense this work into a simpler form?