Q104: Everyone in a group of 100 either likes only turkey on their sandwich , only cheese on their sandwich , or both. For every person who likes only both turkey and cheese on their sandwich, there are 3 people who like only cheese. If 40 people like only turkey on their sandwich, how many like to have both turkey and cheese?

A: 10
B: 15
C: 20
D: 30
E: 60

Author's answer: B

In the explanation section at the back of the textbook, it made the following claim:

3B = C, i.e: (B=both turkey/cheese, C=cheese) for every person who likes cheese only on their sandwich, there are 3 people who likes both turkey and cheese.

This assertion is the complete opposite of what's stated in the question. Am I wrong?
Should it be B = 3C? (For every person who likes only both turkey and cheese on their sandwich, there are 3 people who like only cheese)

I believe the answer is correct as written.

Think of it this way.

For every person who likes both turkey and cheese on their sandwich, there are 3 people who like only cheese.

Let's say there are 10 people who like both turkey and cheese on their sandwich.
This means there are 30 people who like only cheese.

Thus, B=10 and C=30, and C=3B.

Sometimes, these are easier to see with numbers involved.

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