<p>The average (arithmetic mean) age of the people in a certain group was 16 years before one of the members left the group and was replaced by someone who is 12 years older than the person who left. If the average age of the group is now 18, how many people are in the group?</p>
<p>Find the old and new sum of the ages:</p>
<p>old sum = 16n</p>
<p>new sum = 18n</p>
<p>old sum + 12 = new sum.</p>
<p>16n + 12 = 18n</p>
<p>n = 6</p>
<p>Here is an equivalent and perhaps more elegant approach:</p>
<p>12/n = new average - old average</p>
<p>12/n = 18 -16</p>
<p>n = 6</p>