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
