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patriot [66]
2 years ago
6

a group of 42 children all play tennis or football or both sports, the same number play tennis as play just football, twice as m

any play both tennis and football as play just tennis, how many children play football (answers 7,14,21,28,35)
Mathematics
1 answer:
lara31 [8.8K]2 years ago
5 0

Answer:  Football = 35 children

<u>Step-by-step explanation:</u>

I created a Venn diagram and labeled it as follows:

Tennis only = x

Both Tennis & Football = y

<u>Football only </u>= <u>x + y     </u>

Total children = x + y + x + y

                42 = 2x + 2y

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

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        

<u>Both Tennis & Football</u> =<u>    y     </u>

             Total Football =  x + 2y

                                    = 7 + 2(14)

                                    = 7 + 28

                                   = 35

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