venn diagram and survey

[pinktoothfairy]

Forty shoppers are surveyed. 12 like wheat bran cereal and 23 like crunchy cereal. Twice as many dislike both cereals as the amount that like both cereals. How many like both cereals and how many dislike both cereals?

 

[Deleted member 4993]

Forty shoppers are surveyed. 12 like wheat bran cereal and 23 like crunchy cereal. Twice as many dislike both cereals as the amount that like both cereals. How many like both cereals and how many dislike both cereals?

Please show us your work, indicating exactly where you are stuck - so that we know where to begin to help you.

 

[mmm4444bot]

I think that drawing a Venn diagram is useful for writing an equation in this exercise.

Have you learned about Venn diagrams?

If not, you can still reason out expressions for the subsets of people surveyed (out of the set of 40 people).

A Venn diagram clearly shows the two given overlapping sets of people surveyed (i.e., the set of 12 who like wheat and the set of 23 who like crunchy). This makes it easy -- after picking symbol x to represent the number who like BOTH cereals -- to label the three subsets: (1) those who like only wheat, 12 - x; (2) those who like only crunchy, 23 - x; (3) those who like both, x.

Of course, the exercise states how to express (in terms of x also) the number out of all 40 people surveyed who dislike both cereals.

All four of these expressions must sum to 40.

Solve for x.

MY EDITS: Fixed poor wording, corrected improper article, and clarified overlapping sets

 

[patricialec]

I also am learning the Venn diagram....this was very helpful ...thank you.