Question

Pleasee fast help me pleaseeeeeeeeee

In a class, one third of the students like badminton, three-fourth of the students like football, 5 out of 6 of
the students like volleyball, 60 like football and volleyball, 65 like volleyball and badminton,
17 like badminton and football, 20% of the students like all three games and 8 students don't like any
game. Draw a Venn-diagram and find the total number of students in the class.
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Answer 1

The answer is below

Explanation:

Let B represent those that like badminton, F represent those that like football and V represent those that like volleyball. Let x represent the total number of people.

n(B) = (1/3)x, n(F) = (3/4)x, n(V) = (5/6)x

n(B∩F∩V) = 20% of x = 0.2x

n(B∩F) = 17, hence n(B∩F∩V') = 17 - 0.2x

n(V∩F) = 60, hence n(B'∩F∩V) = 60 - 0.2x

n(B∩V) = 65, hence n(B∩F'∩V) = 65 - 0.2x

n(B∪F∪V)' = 8

n(B∩F'∩V') = (1/3)x - 0.2x - (17 - 0.2x) - (65 - 0.2x) = 0.533x - 82

n(B'∩F∩V') = (3/4)x - 0.2x - (17 - 0.2x) - (60 - 0.2x) = 0.95x - 77

n(B'∩F'∩V) = (5/6)x - 0.2x - (60 - 0.2x) - (65 - 0.2x) = 1.033x - 125

Therefore:

x = n(B∩F'∩V') + n(B'∩F∩V') + n(B'∩F'∩V) + n(B∩F∩V) + n(B∩F∩V') + n(B'∩F∩V) + n(B∩F'∩V) + n(B∪F∪V)'

x = (0.533x - 82) + (0.95x - 77) + (1.033x - 125) + (0.2x) + (17 - 0.2x) + (60 - 0.2x) + (65 - 0.2x) + 8

x = 2.1166x - 134

1.1166x = 134

x = 120

Therefore there was 120 students