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 children play football (answers 7,14,21,28,35)

Answer 1

Answer: 35 children

Explanation:

Let the number of children who play only football be f , the number of children who play only

tennis be t and the number of children who play both sports be b.

Since there are 42 children, f + t + b = 42.

Also, since the number of children who play tennis is equal to the number of children who play

only football, t + b = f . Therefore f + f = 42. So f = 21 and t + b = 21.

Finally, twice as many play both tennis and football as play just tennis. Therefore b = 2t.

Substituting for b, gives t + 2t = 21. Hence t = 7.

Therefore the number of children who play football is 42 − t = 42 − 7 = 35.

Answer 2

Answer: Football = 35 children

Explanation:

I created a Venn diagram and labeled it as follows:

Tennis only = x

Both Tennis & Football = y

Football only = x + y

Total children = x + y + x + y

42 = 2x + 2y

We are also given that y = 2x (twice as many play both tennis & football as just play tennis)

Now we have two equations and can use substitution to solve for x & y:

42 = 2x + 2y

y = 2x

42 = (y) + 2y

42 = 3y

14 = y

Now let's find x:

y = 2x

14 = 2x

7 = x

We are asked to find how many children play football.

Football = x + y

Both Tennis & Football = y

Total Football = x + 2y

= 7 + 2(14)

= 7 + 28

= 35