SOLUTION: I hope I picked the right topic... Here is the word problem, out of my book: In the 2005 regular baseball season, the Chicago White sox won 27 fewer than twice as many games as

Question 156697This question is from textbook Beginning and Intermediate Algebra
: I hope I picked the right topic...
Here is the word problem, out of my book:
In the 2005 regular baseball season, the Chicago White sox won 27 fewer than twice as many games as they lost. They played 162 regular-season games. How many wins and losses did the team have?
I have been trying to figure this problem out with my friend for the last two days. We are stuck on it. I finally thought that I figured it out today, and seeing as it has been such a burden to us, I decided to look up the figures online and found out that I was wrong! So now I know what the correct answer is, but I want to know how to reach it. Here is what I had done when I thought I finally figured it out:
2x-27=62
2x=189
x=94.5
I questioned myself when a fraction came up, but seeing as it is a half, I figured maybe they tied one game with another team??
From there, I went on to do this:
162-94.5=67.5
So I figured that 67.5 and 94.5 were my answers. When I added them together to check my math, I found that they do add up to 162. I don't know anything about baseball so I don't know if tying is even possible... I guess it isn't, since my answer is wrong.
Some help in understanding how the correct answer of 99 wins and 63 losses is reached would be wonderful.
Thank you very much. This question is from textbook Beginning and Intermediate Algebra

Found 2 solutions by nerdybill, jim_thompson5910:
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!

In the 2005 regular baseball season, the Chicago White sox won 27 fewer than twice as many games as they lost. They played 162 regular-season games. How many wins and losses did the team have?
.
Let x = games lost
which means (because they played a total of 162 games) that
162 - x = games won
.
2x-27 = 162 - x
3x-27 = 162
3x = 189
x = 63 (games lost)
.
162 - 63 = 99 (games won)

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Note: this is a system of linear equations problem since we have a system two linear equations with two variables.

Let W=# of wins and L=# of losses

Since they played a total of 162 games (and each game was either a win or a loss), this means that we have the first equation

Also, since the "White Sox won 27 fewer than twice as many games as they lost", this tells us that the second equation is

Start with the first equation

Plug in . In other words, replace "W" with

Combine like terms.

Add 27 to both sides

Divide both sides by 3 to isolate "L"

So the White Sox lost 63 games

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

Go back to the second equation

Plug in

Multiply

Subtract

So the White Sox won 99 games
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