In a group of 70 people 37 like coffee

Asked by admin @ 12/08/2021 in Math viewed by 348 People

In a group of 70 people, 37 like coffee, 52 like tea and each person likes at least one of the drinks. how many people like both coffee and tea

Answered by admin @ 12/08/2021

19 people both like coffee and tea. Let me explain.

Let’s use the letter “C” for the set op people who like coffee, and let’s use T for the set of people who like tea.

People who like coffee: n(C) = 37

People who like tea: n(T) = 52

Number of people who like at least coffee or tea = n(C U T) = 70

Number of people who like both coffee and tea = n(C , T) = ?

We know that:

n(C U T) = n(C) + n(T) - n(C , T)

70 = 37 + 52 - n(C , T)

70 = 89 - n(C , T)

n(C , T) = 89 - 70

n(C , T) = 19

Therefore 19 like both coffee and tea

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