I really don't understand this question! (Combinations Question)

Question

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

1. 75 read newspapers daily.
2. 35 read books at least once a week.
3. 45 read magazines regularly.
4. 25 read both newspapers and books.
5. 15 read both books and magazines.
6. 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.

I had already made the diagram but I didn't know how to get the number between magazines and newspapers, can someone please explain and show the steps to getting the answer? I'm very confused!! Thanks.

I had already sketched the Venn diagram, but I didn't understand how to find the number between magazines and newspapers.

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

Answer 1

You have a total of 100

100 = 75+45 +35 minus the areas of overlap

100= 155 - 15-5 -10-X (where X = what you have as "?")

X = 125-100 = 25

X = 25 = the number who read magazines and newspapers

(Unless, there are some who don't read any of the 3 news items. then 0<X<30, and you can't solve it further. But if everyone reads at least one of the 3, then the overlap between magazine and newspaper readers is exactly 25)

Your Venn diagram is correct except for two numbers in the areas where you have those who read only newspapers and only magazines. You can't fill those in until you solve for the overlap between them, X. Having solved it as X=25, then you can fill in the only newspaper readers as 25 (75-25-10-5= 25) and the only magazine readers as 5 (45-10-5-25= 5))