Question 73999: In the 2000-2001 baseball season, the Seattle Mariners tied a league record set by the 1906Chicago Cubs for most wins in a season. The Mainers won 24 more than twice as many games as they lost. They played 162 regular season games. How many wins and losses did the mariners have?
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Let the number of games that the Mariners won be represented by W and the number of games that
they lost be represented by L. The total of their wins and losses equals the 162 games that they
played. In equation form you can write:
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W + L = 162
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The tricky part to this problem is to translate "won 24 more than twice as many games as they lost"
into a math equation. If you think "wins minus 24" then that must be 2 times the number of
games they lost. In equation form this translation can be written:
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W - 24 = 2*L
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Let's solve our first equation for L by subtracting W from both sides to get:
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L = 162 - W
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Then substitute this value (the right side) for L in our second equation to get:
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W - 24 = 2*(162 - W)
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Multiplying out the right side results in:
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W - 24 = 324 - 2W
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Eliminate the - 2W on the right side by adding 2W to both sides to get:
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3W - 24 = 324
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Eliminate the -24 on the left side by adding 24 to both sides:
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3W = 348
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Finally, find the number of wins the Mariners had by dividing both sides by 3 and you
have W = 348/3 = 116
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This says the Mariners won 116 of their 162 games. Therefore, they lost 162 - 116 = 46 games.
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Notice that if we doubled their 46 games and added 24 more games the total would be 92 + 24 = 116, the
number of games they won. That works!
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Now lets go back to when we solved the first equation for L and put it into the second. We could
also have solved the first equation for W to get W = 162 - L and substituted the right side
of that for W in the second equation. It would have worked out the same except that we would
have found that L = 46 games and then would have to solve for W by subtracting 46 from 162.
So you could have done it either way.
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Hope this helps you to understand the problem better.
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