document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=73999>Question 73999</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #53006 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=53006\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the number of games that the Mariners won be represented by W and the number of games that <BR>\n" );
document.write( "they lost be represented by L.  The total of their wins and losses equals the 162 games that they<BR>\n" );
document.write( "played. In equation form you can write:<BR>\n" );
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document.write( "W + L = 162<BR>\n" );
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document.write( "The tricky part to this problem is to translate \"won 24 more than twice as many games as they lost\"<BR>\n" );
document.write( "into a math equation.  If you think \"wins minus 24\" then that must be 2 times the number of <BR>\n" );
document.write( "games they lost. In equation form this translation can be written:<BR>\n" );
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document.write( "W - 24 = 2*L<BR>\n" );
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document.write( "Let's solve our first equation for L by subtracting W from both sides to get:<BR>\n" );
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document.write( "L = 162 - W<BR>\n" );
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document.write( "Then substitute this value (the right side) for L in our second equation to get:<BR>\n" );
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document.write( "W - 24 = 2*(162 - W)<BR>\n" );
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document.write( "Multiplying out the right side results in:<BR>\n" );
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document.write( "W - 24 = 324 - 2W<BR>\n" );
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document.write( "Eliminate the - 2W on the right side by adding 2W to both sides to get:<BR>\n" );
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document.write( "3W - 24 = 324 <BR>\n" );
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document.write( "Eliminate the -24 on the left side by adding 24 to both sides:<BR>\n" );
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document.write( "3W = 348<BR>\n" );
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document.write( "Finally, find the number of wins the Mariners had by dividing both sides by 3 and you<BR>\n" );
document.write( "have W = 348/3 = 116<BR>\n" );
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document.write( "This says the Mariners won 116 of their 162 games.  Therefore, they lost 162 - 116 = 46 games.<BR>\n" );
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document.write( "Notice that if we doubled their 46 games and added 24 more games the total would be 92 + 24 = 116, the<BR>\n" );
document.write( "number of games they won. That works!<BR>\n" );
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document.write( "Now lets go back to when we solved the first equation for L and put it into the second.  We could<BR>\n" );
document.write( "also have solved the first equation for W to get W = 162 - L and substituted the right side<BR>\n" );
document.write( "of that for W in the second equation.  It would have worked out the same except that we would<BR>\n" );
document.write( "have found that L = 46 games and then would have to solve for W by subtracting 46 from 162.<BR>\n" );
document.write( "So you could have done it either way.<BR>\n" );
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document.write( "Hope this helps you to understand the problem better.<BR>\n" );
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