Expert: Jack Cheng - 4/7/2007

Question
In a survey of 60 people, it was found that
8 read only News    (N)
12 read only Dawn  (D)
10 read only Times  (T)
3 read all three newspapers
11 read both News and Times
8 did not read any newspaper
(i) If the number of people who read news and dawn is one more than who read Times and Dawn, write and solve the pair of simultaneous equations in a and b.
(ii) How many people read News?  

Answer
Hi Shani,

I found that drawing a Venn diagram is very helpful in solving problems like this:

The only numbers that you don't have is those who read D and N and those who read D and T. You can find out that the sum of these two number is 8 (60-8-12-10-3-11-8). You are also told that DN - 1 = DT. So:

DN + DT = 8
DN - DT = 1

Solving the equations (just add the two together to get DN, and use that for DT), you get DN = 4.5 and DT = 3.5.

Those who read News is 8 + 11 + 3 + 4.5 = 26.5.

I hope this helps.

~ Jack