Can someone give me homework help?

Question

In a class of 26 students, a survey determind what vegetables the students like. The top three vegetables were spinach, broccoli, and carrots. The survey revealed that 16 students like spinach, two like only carrots and spinach, eight like only spinach, four like all three vegetables, two like only broccoli but eight included broccoli among their choices, and five like only corrots or only broccoli but not both. Determine how many students like carrots, how many like broccoli or spinach and how many like broccoli or carrots but not spinach. Explain why the sum of the students making these three choices is not 26.
Please help me! If you just want to leave a message tellin me to did it myself dont even bother..it's my sister that needs help and im supposed to be her older smart sister!

Answer 1

I think the best way to do this problem is to draw a Venn Diagram. Here's a good example: http://tieguy.org/events/2004/gnomesummit/marketing-notes/venn-diagram.png

You'd label one circle broccoli, one spinach, and one carrots. Where two circles overlap (like where the broccoli circle overlaps the spinach circle) is where you put the students who like two different vegetables. In the middle, where all the circles overlap you can put the students who like broccoli, spinach, and carrots.

So first off, you know that 16 students like spinach. You have to hold on to that one for a while, because you don't have enough information about those 16 students.

2 students like only carrots and spinach, so put a 2 where carrots and spinach overlap. 8 like only spinach, so put an 8 in the spinach only part of the spinach circle. 4 students like all three vegetables, so put a 4 in the middle.

Then it says 2 like only broccoli, so you put 2 in the broccoli circle. You can't do anything yet with the 8 that included broccoli in their choices, so hold on to them until later.

5 like only carrots or only broccoli. Well, you already know 2 like only broccoli, so that means 3 like only carrots. Put a 3 in the carrots only part of the circle.

So then you go back to the 16 who like spinach. So far you've got 8 who like only spinach, 2 who like spinach and carrots, and 4 who like all three. 8 + 2 + 4 = 14, so there's 2 left over. Now you know that 2 like broccoli and spinach.

And this is where you look at the 8 who included broccoli among their choices. You know 2 like only broccoli and 4 like all three. You just figured out that 2 like broccoli and spinach. So 2 + 4 + 2 = 8. And you're done! Well, with that part.

You can see from your diagram that 9 students like carrots, 18 like broccoli or spinach, and 5 like broccoli or carrots, but not spinach.

The sum of the students making these three choices isn't 26 because you've counted some students twice (for example where it asks how many like carrots, and how many like broccoli or carrots).

Holy crap that was long! Well, good luck.

Answer 2

Let S be students who like spinach, B those who like broccoli, and C who like carrots.

Out of 26, this is what you know for sure of all the possible combos:
2 C/S
8 S
4 B/C/S
2 B
? C
? B/S
? B/C

Since 16 like spinach, and 14 are accounted for, 2 must be in the only possible remaining category: 2 B/S. You also know 8 like broccoli, and now all 8 are accounted for. So there are 0 in the last category: 0 B/C. You now have:

2 C/S
8 S
4 B/C/S
2 B
? C
2 B/S
0 B/C

Since there are 26 total students, the category C must be all those remaining: 8 C.

So how many like carrots? 8 C + 4 B/C/S + 2 C/S + 0 B/C = 14.
How many like broccoli *or* spinach? Everyone except the 8 C, so 18.
How many like broccoli or carrots but not spinach? 8 C + 0 B/C + 8C = 16.
The reason the sum of these three choices is not 26 is because the choices are not mutually exclusive. People in choice 1 are repeated in choice 3, for instance.

Answer 3

16 students like carrots, 3 like spinach, and 7 like both spinach and broccoli (2006 Pre Calculus Champ)

Answer 4

I was gonna try to help but just reading it gave me a headache. I really hope somebody can help you. Sorry.

Answer 5

yeah i don't blame you for looking for help, i would have been confused too...umm...go with the first guy's answer i guess because i have no clue