Combinations Question, A survey of 100 people who volunteered information about their reading habits showed that...

Question

1. A survey of 100 people who volunteered information about their reading habits showed that,
2. 75 read newspapers daily.
3. 35 read books at least once a week.
4. 45 read magazines regularly.
5. 25 read both newspapers and books.
6. 15 read both books and magazines.
7. 10 read newspapers, books, and magazines.

a) Construct a Venn diagram to determine the maximum number of people in the survey who read both newspapers and magazines.

b) Explain why you cannot determine exactly how many of the people surveyed read both newspapers and magazines.

Answer 1

draw 3 overlapping circles

they all 3 overlap in the middle with 10 who read all 3 reading materials

Let x = the number who read both newspapers & magazines

0>x>10, maximum value of x is 30

75-25= 50 x< 50

45-15 = 30 x<30

x is less than or = to 30

x>0, 0<x<30

x could be any integer between 0 and 30

there are 100 people

100 = 75+45+35 - overlaps = 155-10-15-5-x = 125-x

125-x = 100

x = exactly 25

The only reason x might be another number between 0 and 30 is if there are some people who didn't read any books, magazines or newspapers.