Question

A survey of 100 people who volunteered information about their reading habits showed that • 75 read newspapers daily • 35 read books at least once a week • 45 read magazines regularly • 25 read both newspapers and books • 15 read both books and magazines • 10 read newspapers, books, and magazines

Construct a Venn diagram to determine

the maximum number of people in the

survey who read both newspapers and

magazines.

Answer 1

Let x be the number of people who read both newspaper and magazins, then
75 - (25 - 10 + 10 + x - 10) + 35 - (25 - 10 + 15 - 10 + 10) + 45 - (15 - 10 + 10 + x - 10) + 25 - 10 + 15 - 10 + x - 10 + 10 = 100
60 - x + 5 + 40 - x + 20 + x = 100
125 - x = 100
x = 125 - 100 = 25
x = 25

Therefore,
the maximum number of people in the survey who read both newspapers and magazines.