Question

At Prairieview Middle School, 100 students participate in at least one of three after-school clubs: soccer club, art club, and gaming club; 9 students participate in all three clubs; 20 students are in both soccer club and art club; 35 students are in art club and gaming club; and 29 students are in soccer club and gaming club. In total, 50 students are in soccer club, and 53 students are in art club. How many of the 100 students are in the gaming club only?

Answer 1

Answer:

17

Step-by-step explanation:

Number of students in soccer club, n(S) = 50

Number of students in Art club, n(A) = 53

Number of students in Gaming club, n(G)

n($S \cup A\cup G$) = 100

n($S \cap A\cap G$) = 9

n($S \cap A$) = 20

n($A \cap G$) = 35

n($G \cap S$) = 29

Formula:

n ( A ∪ B ∪ C ) =  n(A) + n(B) + n(C) – n ( A ∩ B ) – n(B ∩ C) – n (A ∩ C) + n( A ∩ B ∩ C )

Putting the values:

100 = 50 + 53 + n(G) - 20 - 35 - 29 + 9

100 = 112 + n(G) - 84

n(G) = 72

Number of students in gaming club only = n(G) - n($G \cap S$) - n($A \cap G$) + n($S \cap A\cap G$)

= 72 - 35 - 29 + 9

= 17