Question

In a survey one-forth like cake only and 20 didn't like cake at all. Also 50% children like ice cream but 12 like none of them.How many like both?

Answer 1

2

Explanation:

Let x represent the total number of people. Let C represent those that like cake and let I represent those that like ice cream. Given:

C = (1/4)x = 0.25x, I = 0.5x, (C ∪ I)' = 12, C' = 20

Therefore:

C ∩ I' = C' - (C ∪ I)' = 20 - 12 = 8

C ∩ I = C - C ∩ I' = 0.25x - 8

C' ∩ I = I - C ∩ I = 0.5x - (0.25x - 8) = 0.25x + 8

The total students = (C ∩ I) + (C' ∩ I) + (C ∩ I') + (C ∪ I)'

x = 0.25x - 8 + 0.25x + 8 + 8 + 12

x = 0.5x + 8 + 12

x = 0.5x + 20

0.5x = 20

x = 40

Students that liked both = C ∩ I = 0.25(40) - 8 = 2