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?

Question

Social Studies

Trujillo

28 June, 07:01

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?

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Answers (1)

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Sundance · Answer 1

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.