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:  Football = 35 children

Step-by-step 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