A group of 42 children all play tennis or football, or both sports

Question: A group of 42 children all play tennis or football, or both sports. The same number play tennis as play just football. Twice as many play both tennis and football as play just tennis. How many of the children play football?

Answer: Assumption: Each child play at least one game

Children Play Tennis = T
Children Play FootBall = F
Children Play Both = B

Just FootBall = F – B
Just Tennis = T – B

The same number play tennis as play just football
=> F – B = T

Twice as many play both tennis and football as play just tennis
2B = T – B

=> T = 3B
F – B = 3B
=> F = 4B

Total = T + F – B = 42
=> 3B + 4B – B = 42
=> 6B = 42
=> B = 7

T = 3B = 21
F = 4B = 28

FootBall = 28
Tennis = 21
Both = 7

Just Football = 21
Just Tennis = 14

28 children play football

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