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.

Question

Mathematics

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3 April, 14:24

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.

+2

Answers (1)

Know the Answer?

Elyse Schroeder · 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.