SOLUTION: A poll of 500 people determines that 382 like ice cream and 362 like cake. How many people like both if each of them likes at least one of the two?

Question 1147242: A poll of 500 people determines that 382 like ice cream and 362 like cake. How many
people like both if each of them likes at least one of the two?
Answer by ikleyn(52878) (Show Source): You can put this solution on YOUR website!
.


As the first approximation, add the two numbers 382 and 362:


    382 + 362 = 744.    (1)


But doing so, you count twice those people of 500, who like both products.


Therefore, your sum exceeds 500, although it should be equal 500, in reality.


This exceeding amount over 500 is exactly the number of those who like both products


    382 + 362 - 500 = 244.


It is your answer: 244 people like both products.

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To see many other similar solved problems, look into the lesson
- Counting elements in sub-sets of a given finite set
in this site.

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