Ages in a Group

Difficulty: Hard · Topics: Discrete Mathematics, Sets, Word Problems

In a group of acquaintances nobody is exactly 20, 40 or 60 years old, and half of the group is older than 40.

The number of people younger than 20 is 21 less than the number of people younger than 60. Deniz, who is younger than 20, has as many acquaintances in the group younger than 20 as there are people in the group older than 60.

At most how many people in this group can be 45 years old?