SOLUTION: 80 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 34 less than 2 times the number of away team

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Question 655512: 80 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 34 less than 2 times the number of away team fans.
How many home team and away team fans attended the game?
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Let h = home fans
Let a = away fans
The problem statement results with
(1) h + a = 80 and
(2) h = 2*a - 34
Solve the system of equations (1) and (2), by substitution.
Solving (1) for h gives us
(3) h = 80 - a
Put (3) into (2) and get
(4) 80 - a = 2*a - 34 or
(5) 80 + 34 = 2*a + a or
(6) 114 = 3*a or
(7) a = 114/3 or
(8) a = 38
Using (8) in (1) we can get h
(9) h + 38 = 80 or
(10) h = 80 - 38 or
(11) h = 42
Use (2) to check our answer.
Is (42 = 2*38 - 34)?
Is (42 = 76 - 34)?
Is (42 = 42)? Yes
Answer: There were 42 home-team fans and 38 away-team fans that attended the baseball game.