Survey Word Problem- How Many Students?

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sanddollars

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Sep 7, 2005
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I need some help with this math problem and I don't want the answer. I would like to give it a stab myself, problem is I don't know where to begin. Here goes.....

Several students were questioned about their favorite music groups, with the following results:

22 like Hole
25 like U2
39 like3rd Eye Blind
9 like U2 and Hole
17 like Hole and 3rd Eye Blind
20 like U2 and 3rd Eye Blind
6 like all three
4 like none of these performers

Where do I begin? :shock: TIA!
 
I think the best place to start would be a problem statement.

What is wanted? I can't tell.
 
I am sorry I left out the most important detail...it asks the question at the end...

How many students were questioned?
 
I came up with a total of 90 students. I added 22 + 25 + 39 + 4= 90 I did not account for ones that liked both or all of them. Am I headed in the right direction? Arrrrghhhh!
 
22 like Hole
25 like U2
39 like3rd Eye Blind
9 like U2 and Hole
17 like Hole and 3rd Eye Blind
20 like U2 and 3rd Eye Blind
6 like all three
4 like none of these performers
Click to expand...
Start at the bottom.

4 like none

Total of 4, so far

6 like all 3

4+6 = 10 New Total

20 like U2 and 3rd Eye Blind

We already used 6 of these from the all 3 bucket, so only 17 more.

10+17 = 27 New Total

17 like Hole and 3rd Eye Blind

We already used 6 of these from the all 3 bucket, so only 11 more.

27 + 11 = 38

9 like U2 and Hole

We already used 6 of these from the all 3 bucket, so only 3 more.

38 + 3 = 42

39 like 3rd Eye Blind

We already used 6 from the all three, 11 from hole+3rd eye, and 14 from u2+3rd eye, so only 8 more.

Can you do the other two pieces? It helps a lot to draw three intersecting corcles in a box that contains them all.
 
You also left out the fact that you posted this in another forum. Don't do that.

PKA's drawing is perfect. Learn from that.
 
I am kinda getting it but I get confused when you add 10 + 17. If 20 like both U2 and 3rd Eye Blind wouldn't you add 14 because you have already used 6 in the 3 bucket. Arrrgh!
 
You're welcome to post the same question as often as you like. But when people start seeing the same question over and over, don't be surprised if they don't answer, figuring somebody else will. (The frequent result of multi-posting is a reduction in the volume of replies.)

Eliz.
 
Thank you for your initial help tkhunny. I apologize about the dual posting. I posted consecutively and was just trying to glean help from mutiple sources in case no one was able to reply to this post.
 
stapel...

I didn't post this question more than once on this site. Actually, I posted this to another math forum. And, I was not aware people from this site perused other math forums, my bad.
 
sanddollars: Don't worry about it. Now you know. "Live and learn", right? :wink:

Eliz.
 
No worries...

Just start where you can. The 4 that like nothing are completely unrelated to all the others. The 6 that like all three are in EVERY other classification. The trick is counting folks only once. Just stare at PKA's drawing for a while. It should soak in.
 
tkhunny said:
Start at the bottom.
4 like none
Total of 4, so far
6 like all 3
4+6 = 10 New Total
20 like U2 and 3rd Eye Blind
We already used 6 of these from the all 3 bucket, so only 17 more.
10+17 = 27 New Total : NOTE#1

17 like Hole and 3rd Eye Blind
We already used 6 of these from the all 3 bucket, so only 11 more.
27 + 11 = 38
9 like U2 and Hole
We already used 6 of these from the all 3 bucket, so only 3 more.
38 + 3 = 42 : NOTE#2

39 like 3rd Eye Blind
We already used 6 from the all three, 11 from hole+3rd eye, and 14 from u2+3rd eye, so only 8 more.
Can you do the other two pieces? .
Click to expand...
In case you're getting confused, TK made his 1st 2 mistakes this year:
NOTE#1: should be 24 (14 more)
NOTE#2: should be 41 (38 really)

So, finishing it off:
38 + 8 = 46 (3rdEyeBlind; per TK)
46 + 2 = 48 (U2: 25 - 6 - 14 - 3)
48 + 2 = 50 (Hole: 22 - 6 - 11 - 3)

Just noticed this:

a = 22 like Hole
b = 25 like U2
c = 39 like3rd Eye Blind
d = 9 like U2 and Hole
e = 17 like Hole and 3rd Eye Blind
f = 20 like U2 and 3rd Eye Blind
g = 6 like all three
h = 4 like none of these performers

a+b+c - (d+e+f) + g + h = 50

Haven't "analysed" it...is it coincidence?

Also:
a+b...+h = 142
2(d+e+f) = 92
142 - 92 = 50

Question: where oh where is pka's "drawing"?
 
Wow! Now I'm confused. So, you're saying that 20 - 6 ≠ 17 AND 38 + 3 ≠ 42. Was I typing with my feet?
 
Now I'm the confused one:
20 - 6 ≠ 17 AND 38 + 3 ≠ 42 are both TRUE statements; sincere apologies :)
 
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