100 people are attending a newspaper conference. 45 of them are writers and more than 38 are editors. Of the people at the conference, x are both writers and editors and 2x are neither. What is the largest possible number of people who are both writers and editors?

There will be 16 people who are both writer and editor

Explanation:

We have given there are total of 100 people

So total = 100

There are 45 writers so, Writers = 45;

It is given that there are more than 38 editors so, Editors > 38

Both = x;

Neither = 2x

We know that

Total = Writers + Editors - Both + Neither

100 = 45 + Editors - x + 2x

x = 55 - Editors

We want to maximize x, thus we should minimize Editors minimum possible value of Editors is 39, thus:

x = Both = 55 - 39 = 16.