Question

A number of people were asked whether they liked drinks of orange, lemon or Grape flavor. The replies showed: 85 liked orange 65 liked grape 90 liked lemon 30 liked orange and grape 45 liked orange and lemon 40 liked lemon and grape 15 liked orange, lemon and grape 25 liked none of the three. Find the total number of people interviewed

Answer 1

Answer:

Let’s solve this using a venn diagram.

T = Tea

C = Coffee

n means number

n(T) = 30

n(C) = 20

Universal = 50

n(T U C)' = 6 , T union C complement (people who like to drink neither)

Let n(T Π C) i.e. T intersection C (People who like to drink both) = x

n(T) + n(C) - n(T Π C) + n(T U C)' = 50

30 + 20 - x + 6 = 50

56 - x = 50

- x = 50 - 56

-x = -6

x = 6

Therefore people who like to drink BOTH Tea and Coffee are 6.

People who drink coffee = 20

Thus, People who ONLY drink coffee = 20 - 6 = 14 people

I've attached an image with diagram below for better understanding.

Answer 2

Answer:

Step-by-step explanation:

Watch this video for complete step by step solution to this question.

Maths with Ms. Sumbel