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

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) (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.

RELATED QUESTIONS
80 people attended a baseball game. Everyone there was a fan of either the home team or... (answered by AlgebraLady88)

75 people attended a baseball game. Everyone there was a fan of either the home team or... (answered by ewatrrr)

79 people attende a baseball game.everyone there was a fan of either the home team or the (answered by macston)

At a basketball game, 80% of the fans cheered for the home team. In the same crowd, 20%... (answered by Glaviolette)

at a college baseball game 4/5 of the spectators are home team fans. the rest of the... (answered by rfer,palanisamy)

For the opening home game of the baseball season, the Madd Batters minor league baseball... (answered by josmiceli)

The number of home team fans was seven more than four times the number of visiting team... (answered by greenestamps,josgarithmetic)

Refer to the Baseball 2016 data. Compute the mean number of home runs per game. To do... (answered by ikleyn,Alan3354)

Please help me solve this problem The number of home runs scored by a certain team in... (answered by math_tutor2020)