Question

more practice with venn diagrams

1. the venn diagram below shows the number of senior boys who play football or wrestle.

venn diagram: two overlapping circles labeled football (18 in only football, 9 in both) and wrestling (12 in only wrestling), 104 outside
a. how many senior boys play football and wrestle?
b. how many senior boys play football but do not wrestle?
c. how many senior boys play football or wrestle?
d. how many senior boys wrestle?

Explanation:

Step1: Find overlap (both sports)

The overlapping section of the Venn diagram is given as 9.

Step2: Find football only

Subtract overlap from football circle: $18$

Step3: Find football or wrestle

Sum football, wrestling, overlap: $18 + 12 + 9 = 39$

Step4: Find total wrestlers

Sum wrestling only and overlap: $12 + 9 = 21$

Answer:

a. 9
b. 18
c. 39
d. 21