Maths
posted by Gaye on .
There are 47 in a club. 18 play chess and 13 play tennis. The number who play neither is 3 times the number who play both. How many play both?

Let x = number who play both
then 3x = number who play neither.
C = set of people who play chess
T = set of people who play tennis
U = total membership of the club
By the principle of inclusionexclusion,
C∪T = C + T  C∩T
or
U  C∪T = U  (C + T  C∩T)
3x = 47  (18+13x)
2x = 16
x = 8 (number of members who play both)
3x = 24 (number of members who play neither)
Total number of players
= C∪T
= C + T  C∩T
= 18 + 13  8
= 23
Check:
U=C∪T+24
= 23+24
=47 OK