Of the 4,700 students at Medium Suburban College (MSC), 50 play collegiate socce
ID: 3410129 • Letter: O
Question
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.
Explanation / Answer
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.
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