The average age of our group of n people was 37 yrs at the end of the previous month.

This month 3 new members enrolled (aged 33, 38, and 40 yrs) and one member (aged m yrs) left.

Now the average age of our group became lower by 18 months.

Given that both m and n are square numbers, find their values.

At the end of the previous month the total age of the group is 37n.
This month (before the change in memberships) the average age is 37+1/12 and the total age is (445/12)n since everyone got a month older.
After adding and subtracting members the total age increases by 111-m and there are n+2 members so the new average is
[(445/12)n+111-m]/(n+2)

Since they are 18 months lower (than which?  I've assumed than last month)
[(445/12)n+111-m]/(n+2) = 37-1.5 = 71/2
409.5n+40=m
Which doesn't seem to have any values where both are squares. n=55^2, m=1113^2 is close but that person who left is over a million years old.

Posted by Jer on 2013-04-29 14:04:46