Question

A survey of 60 college women gave the following results:
30 subscribed to Newsweek
21 subscribed to Cosmo
30 subscribed to Runner's World
14 subscribed to Newsweek and Cosmo
7 subscribed to Runner's World and Cosmo
2 subscribed to all three of these magazines
8 subscribed to none of these magazines
How many students subscribed to exactly one of these three magazines?

Answer 1

30+21+30-14-7-2-8=52
60-52=8 may b

Answer 2

21 subscribed to Cosmo
14 subscribed to Newsweek and Cosmo
7 subscribed to Runner's World and Cosmo
2 subscribed to all three (seems like this should be 0 based on the above three statements unless these 2 are included in the 14 and/or 7)

Sounds like a job for a three circle Venn diagram. Let me try and get back to you.

Answer 3

Explanation coming...

Answer 4

So, everything has to add up to 60 students.

There are 2 who subscribe to everything, that's the easy number to figure out.
14 subscribe to C and NW
7 subscribe to C and RW
But out of those 21, 2 subscribe to all three, so I subtracted one from each to get 13 and 6.
This left no one who subscribed to C by itself.

Answer 5

Hold on, I think there is a bit of an error.

Answer 6

Back to the beginning. I've only input the 2 who subscribe to all three magazines and the 8 who subscribe to none. There are still 50 more subscribers to account for.

The numbers in the Cosmo circle need to add up to 21, the numbers in the NW and RW circles need to add up to 30 each.

Answer 7

So, to get 21 in the Cosmo circle, subtract one from each of the NW/C and RW/C numbers and that leaves 0 who subscribe only to C.

Answer 8

You can start by inputting the remainder of 30 subscribers in the NW only and RW only circles, but now, the total adds up to more than 60. 66 to be exact, so some of the 15 NW subscribers and some of the 22 RW subscribers must subscribe to both NW and RW.

Answer 9

Since there are 6 too many subscribers, that means that there must be 6 subscribers who get both NW and RW. Subtracting 6 from each of NW and RW and inputting 6 into the shared section results in the correct number of people all together.

Answer 10

What a fun question that was.

Answer 11

wait so do I have to divide NW/C and RW/C?

Answer 12

No, sorry, I just wrote in shorthand. NW/C meant the people who subscribed to Newsweek and Cosmo.

Answer 13

My professor wrote something along these lines and I don't know how he got this...do you?

Answer 14

That is what I was working with to start, but realized I had too many to start with. The correct numbers AFAIK should be 15-x and 22-x.

The x is just the number of people who are subscribed to both NW and RW. You need to subtract that from 15 and 22 as they are still subscribed to each magazine, but they are subscribed exclusively. You are essentially moving those x people from the individual magazine subscription groups to the two-magazine subscription groups.

Answer 15

so how do I solve for x? Do i write down
15-X+X+22-X=60

Answer 16

Sorry, I had to step out for a few minutes.

You were close, but you have to include the rest of the numbers in order for them all to equal 60.

15-x+x+22-x+2+13+6+8+0=60 which, of course simplifies down quite a bit.

x = 6

Answer 17

And with the correct titles.