Answer:
Please see the second image attached to this response post.
Explanation:
You have most of the numbers right. So I am going to fill in those in the correct boxes.
We could use set intersection notation but it complicates the explanation so i will just use variables for the missing boxes
For the missing boxes, I am adding variables to denote the missing numbers. The explanation is lengthy. For example, the variable x is the number of readers who read both the Buzz and the Rag less the number of readers who read all three newspapers. The other variables can be interpreted in the same way.
The variable A is the number of readers who read all three newspapers
The number of people who read both Buzz and Rag is x + A, the number who read both Buzz and Gossip is y + A, and the number who read both Rag and Gossip is z + A
So we have
x + A = 76 [a]
y + A = 125 [b]
z + A = 77 [c]
Adding up we get x + y + z + 3A = 76 + 125 + 77 = 278
or
x + y + z + 3A = 278 [1]
If we look at the four unknowns and add them up we get
x + y + z + A
However this is the number of people who are left over from the total readership of 411
Therefore x + y + z + A = 411 -(76 + 63 + 38 + 38)
==> x + y + z + A = 411 - 215
==> x + y + z + A = 196 [2]
Subtract [2] from [1] to get
2A = 278 - 196
2A = 82
A = 41
Now that we have A we can compute x, y and z from equations [a], [b] and [c] to get
x = 35
y = 84
z = 36
Assuming I have not made some silly mistakes, the answer should be as in the second image with all values filled in.
Unfortunately, I have no way of checking the answer so please let me know if all is well.
This is a great question
Good Luck