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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 68 less than 3 times the number of away team fans. How many home team and away team fans attended the game?

Pls people can u help me at solving this?? :/

helen1709  Sep 5, 2014

Best Answer 

 #1
avatar+3450 
+5

Here we have to set up two equations (or a system of equations), and then solve them for the two different teams (home team, and away team).

First, we know that there is 80 people, and this is made up of home team members (h) and away team members. (a) This means:

80 = a + h

Now we need to make a sencond equation, because we cacn't solve for a and h with just this information. a and h could be pretty much anything!

We are given that the number of home team fans (h) was 68 less than 3 times the number of away team fans (a)

This means:

h = (3 times a) - 68              ---Simplifies to:

h = 3a -68

 

Alright, now we have our two equations.

Let's subtract h from both sides on the first equation, and then we can "add" this equation to the second one, and we can find a.

80 = a + h              ---This was our first equation, subtract h from btoh sides to "clear" h from the right side

-h + 80 = a             ---Now "add" this to the second equation. This is called solving by elimination.

h = 3a -68             ---Second equation

---------------

80 = 4a - 68              ---Add 68 to both sides to "clear" -68 from the right side

80 + 68 = 4a

148 = 4a                   ---Now divide 4 from both sides to "clear" the 4 from 4a on the right side

37 = a

 

This means there was 37 fans from the away team.

To find how many people from the home team were there, we put 37 in for a (because a = 37) and solve for h. Let's take the first equation and do this.

80 = a + h               ---First equation

80 = (37) + h          ---Put 37 in for a, subtracrt 37 from both sides to "clear" 37 from the right side

43 = h    

 

So there was 43 home team fans there.

 

Whew, that was a long one! My fingers need a break now. :)

NinjaDevo  Sep 5, 2014
 #1
avatar+3450 
+5
Best Answer

Here we have to set up two equations (or a system of equations), and then solve them for the two different teams (home team, and away team).

First, we know that there is 80 people, and this is made up of home team members (h) and away team members. (a) This means:

80 = a + h

Now we need to make a sencond equation, because we cacn't solve for a and h with just this information. a and h could be pretty much anything!

We are given that the number of home team fans (h) was 68 less than 3 times the number of away team fans (a)

This means:

h = (3 times a) - 68              ---Simplifies to:

h = 3a -68

 

Alright, now we have our two equations.

Let's subtract h from both sides on the first equation, and then we can "add" this equation to the second one, and we can find a.

80 = a + h              ---This was our first equation, subtract h from btoh sides to "clear" h from the right side

-h + 80 = a             ---Now "add" this to the second equation. This is called solving by elimination.

h = 3a -68             ---Second equation

---------------

80 = 4a - 68              ---Add 68 to both sides to "clear" -68 from the right side

80 + 68 = 4a

148 = 4a                   ---Now divide 4 from both sides to "clear" the 4 from 4a on the right side

37 = a

 

This means there was 37 fans from the away team.

To find how many people from the home team were there, we put 37 in for a (because a = 37) and solve for h. Let's take the first equation and do this.

80 = a + h               ---First equation

80 = (37) + h          ---Put 37 in for a, subtracrt 37 from both sides to "clear" 37 from the right side

43 = h    

 

So there was 43 home team fans there.

 

Whew, that was a long one! My fingers need a break now. :)

NinjaDevo  Sep 5, 2014

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