document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=628326>Question 628326</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please , i find it difficult deducing the equation in this problem\r<BR>\n" );
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document.write( "Timmy enjoys playing old-fashioned video games.  He found 3 game systems on eBay and wants to purchase a Nintendo game system, an Atari game system, and a Sega arcade game system.  The Sega system costs $600 more than the sum of the Atari and the Nintendo systems.  All together, the three game systems cost $11,000.   The Atari system costs $1100 less than the Nintendo.  Determine how much Timmy paid for each game system.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #395563 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=395563\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, assign letters to the unknown quantities you are looking for:<BR>\n" );
document.write( "Let:<BR>\n" );
document.write( "A = the cost of the Atari system.<BR>\n" );
document.write( "N = the cost of the Nintendo system.<BR>\n" );
document.write( "S = the cost of the Sega system.<BR>\n" );
document.write( "Next, write down the problem in algebraic notation using the variable (unknown) letters.<BR>\n" );
document.write( "1) A+N+S = $11,000 \"All together, the three game systems cost $11,000\"<BR>\n" );
document.write( "2) S = (A+N)+$600 \"The Sega system costs $600 more than the sum of the Atari and the Nintendo systems.\"<BR>\n" );
document.write( "3) A = N-$1100 \"The Atari system costs $1100 less than the Nintendo.\"<BR>\n" );
document.write( "Now you have a system of three equations with three unknowns (A, N, and S).<BR>\n" );
document.write( "You can use a number of methods to solve this sytem of equations, one of which is \"substitution\".  <BR>\n" );
document.write( "Start with:<BR>\n" );
document.write( "A+N+S = $11,000 now substitute the S from equation 2) to get:<BR>\n" );
document.write( "A+N+((A+N)+$600 = $11,000 Simply this.<BR>\n" );
document.write( "2A+2n+$600 = $11,000 Subtract $600 from both sides.<BR>\n" );
document.write( "2A+2N = $10,400 Now divide both sides by 2 to further simplify.<BR>\n" );
document.write( "A+N = $5200 Substitute the A from equation 3) to get:<BR>\n" );
document.write( "(N-$1100)+N = $5200 Simplify.<BR>\n" );
document.write( "2N-$1100 = $5200 Add $1100 to both sides.<BR>\n" );
document.write( "2N = $6300 Divide both sides by 2.<BR>\n" );
document.write( "N = $3150 The Nintendo system costs $3150.<BR>\n" );
document.write( "From here you should be able to work out the rest of the problem.<BR>\n" );
document.write( "If you still have trouble, re-post. </SPAN>\n" );
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