123 persons in a cafe, and pigeons and boxes

Question

$123$ persons are in a cafe. The sum of their ages is $3813$. Is it always possible to find $100$ among them so that their total age is greater or equal to $3100$?

Looks like Dirichlet-Principle type of problem, but I cant' see the solution.

Answer 1

is it possible to find 23 people so their age is less than or equal to 713? Suppose the group of the 23 youngest people has age greater than 713. Then the total age of the group is greater than $\frac{123\cdot 713}{23}=3813$ a contradiction.

Answer 2

Hint: what is the average age?

Answer 3

The worst case is that everyone is the same age, in which case picking the oldest 100 would give you only $\frac{100}{123}3813$ years in total. Does this suffice?