Question

75 people attended a baseball game. Everyone there was a fan of either the home team or the away team. The number of home team fans was 90 less than 4 times the number of away team fans, How many home team and away team fans attended the game?

Answer 1

Home fans = 42, Away fans = 33

Explanation:

Let's set `H` as the number of home team fans and `A` as the number of away team fans.

75 people attended the game, and we know that everyone was either an `H` or an `A`, so we can say:

`H+A=75`

We're also told that the number of `H` was 90 less than four times `A`, which we can write as:

`H=4A-90`

I'm going to set the first equation equal to `H` and then set the two equations equal to each other (since they will both be solved for `H`):

`H+A=75=>H=75-A`

and so

`75-A=4A-90`

`5A=165`

`A=33`

and so we can take `H=75-A` and find `H`:

`H=75-33=42`