venn diagram problem

nancyhackerplace

New member
Joined
Jun 1, 2014
Messages
2
frustrated with this problem, I conducted a survey of 50 customers The customers were asked if they like orange soda, root beer, cherry soda, or none of the three all the customers who liked cherry also liked root beer. 30 customers liked root beer or orange. Half the customers did not like root beer. no customer who liked cherry liked orange. Ten of the customers liked both root beer and orange. Seven of the customers liked cherry. How many customers liked orange soda
 
What have you done, so far? Did you draw the Venn diagram? (Three overlapping circles.)

They've given you numerical values for some regions of the diagram; you need to deduce the others.

Can you upload your diagram? :cool:
 
reply

What have you done, so far? Did you draw the Venn diagram? (Three overlapping circles.)

They've given you numerical values for some regions of the diagram; you need to deduce the others.

Can you upload your diagram? :cool:


have drawn 3 interconnected circles farthest left "orange" then rootbeer to the right, cherry on the bottom then a single letter underneath to signify the don't like any sodas. I only have a definite value for likes orange and root beer of 10 then the other values are more this or that or not definitive that's where I'm stuck
 
have drawn 3 interconnected circles farthest left "orange" then rootbeer to the right, cherry on the bottom

That's good.

So, you have eight regions total, yes?

You mentioned that you have "a letter" to represent the number surveyed who don't like soda. What letter did you pick?

How did you label the other seven regions?

(We could just assign our own names at this end, but then you'd need to convert our notation to yours; it is better for you to simply explain what you've already done. That way, everybody can use the same notation.)


I only have a definite value for likes orange and root beer of 10

That's not true; other definite values are provided for other conditions.

For example, the statement, "Seven of the customers liked cherry" is definite.

Another example, the phrase "half the customers" appears. That number is definitely 25.

I also see the numbers 30 and 7 mentioned.

To determine the number of people in each of the eight regions requires some logic; we need to think about the meaning of given information in terms of those circles, the seven regions created by their overlap, and the region outside. We look for inconsistencies between what we're told and what we see in the diagram. We work through processes of deduction.

Consider this given condition: No customer who liked cherry liked orange. What does this statement tell us, in terms of the diagram? It tells us that any regions where the 'cherry' and 'orange' circles overlap cannot contain any people. Do you understand why? If you don't, then imagine giant circles drawn on the ground and each of the 50 people standing at their respective position. There are two regions where the 'cherry' and 'orange' circles overlap, yes? Well, IF any person WERE to be standing in either of those two regions, then that person would be saying that they like both cherry and orange soda because they would not be standing there if they didn't like both.

Therefore, whatever letters you assigned to represent those regions, you may now write that each equals zero.

Re-read the remaining five conditions. Think about them, in terms of the regions in your diagram (knowing that two of the inner regions are empty). You ought to be able to begin writing some equations, as you begin to realize that certain combinations of regions must contain equal numbers of people.

If you need more help, please explain where you're at or why you're stuck.

Please provide the labeling on your diagram, so that we may discuss regions and equations/relationships using the names you've chosen.

Ciao :)
 
Last edited:
Top