Of the 4700 students at Medium Suburban College MSC 50 play

Of the 4,700 students at Medium Suburban College (MSC), 50 play collegiate soccer, 60 play collegiate lacrosse, and 96 play collegiate football. Only 5 students play both collegiate soccer and lacrosse, 8 play collegiate soccer and football, and 16 play collegiate lacrosse and football. No students play all three sports. (a) Solve the Venn diagram. HINT [See Example 4.]

x =

y =

z =

u =

v =

w =

t =

(b) Complete the following sentence:____ % of the college soccer players also play one of the other two sports at the collegiate level.

Solution

a) Only 5 students play both collegiate soccer and lacrosse, y=5

8 play collegiate soccer and football,u =8

and 16 play collegiate lacrosse and football,v = 16

50 play collegiate soccer: x= 50 -y -u = 50 -5 -8 = 37

60 play collegiate lacrosse: z = 60 -y -v = 60 -5-16 = 39

96 play collegiate football : w = 96 - u -v = 96 - 8 -16 = 72

t = 4700 - x-y-z-w-u-v-w =4700 - 177 = 4523

b) (y+u)/(x+y+u) =(37+8)/(37+8+5)*100 =45x100/50 =90 % of the college soccer players also play one of the other two sports at the collegiate level.