SOLUTION: In a school of 698 students, 172 played basketball, 545 played soccer and 35 played both. How many students played neither one of these games?

Question 1199592: In a school of 698 students, 172 played basketball, 545 played soccer and 35 played both. How many students played neither one of these games?
Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!

B = set of people who play basketball
S = set of people who play soccer

n(B) = number who play basketball
n(B) = 172
n(S) = 545
n(B and S) = 35

n(B or S) = n(B) + n(S) - n(B and S)
n(B or S) = 172+545-35
n(B or S) = 682

n(neither B nor S) = n(Total) - n(B or S)
n(neither B nor S) = 698 - 682
n(neither B nor S) = 16

Answer: 16

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