The average age of a group of 50 people is 45. Three members, ages 50, 60, and 72, leave the group. What is the average age of the remaining 47 people?

If we know that the average of 50 ages is 45, we also know that the sum of the 50 ages is 50 · 45 = 2250. (This is a useful bright idea.)

The three people who left have a total age of 50 + 60 + 72 = 182.

We subtract: 2250 – 182 = 2068. This is the sum of the ages of the remaining 47 folks, so we divide 2068 by 47 and we get 44 as the new average age.