document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=675206>Question 675206</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At the arcade, Ryan Sara and Tom played video racing games, pinball and air hockey. Ryan spent $6 for 6 racing games, 2 pinball games, and 1 game of air hockey. Tim spent $12.25 for 2 racing games, 7 pinball games and 4 games of air hockey. How much did each of the games cost?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #419637 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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/cgi-bin/show-face.mpl?user=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=419637\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are 3 unknowns in this problem, but only<BR>\n" );
document.write( "2 equations. That usually means some extra figuring<BR>\n" );
document.write( "or guesswork.<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r+ ALIGN=MIDDLE  ALT=\"+r+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the cost of a racing game<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p+ ALIGN=MIDDLE  ALT=\"+p+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the cost of a pinball game<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+ ALIGN=MIDDLE  ALT=\"+a+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the cost of air hockey<BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6r+%2B+2p+%2B+a+=+6+ ALIGN=MIDDLE  ALT=\"+6r+%2B+2p+%2B+a+=+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2r+%2B+7p+%2B+4a+=+12.25+ ALIGN=MIDDLE  ALT=\"+2r+%2B+7p+%2B+4a+=+12.25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "Note from (1), that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r+%3C=+1+ ALIGN=MIDDLE  ALT=\"+r+%3C=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p+%3C=+3+ ALIGN=MIDDLE  ALT=\"+p+%3C=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+%3C=+6+ ALIGN=MIDDLE  ALT=\"+a+%3C=+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------<BR>\n" );
document.write( "and, from (2)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r+%3C=+6.12+ ALIGN=MIDDLE  ALT=\"+r+%3C=+6.12+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p+%3C=+1.75+ ALIGN=MIDDLE  ALT=\"+p+%3C=+1.75+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+%3C=+3.06+ ALIGN=MIDDLE  ALT=\"+a+%3C=+3.06+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "From these 2, I get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r+%3C=+1+ ALIGN=MIDDLE  ALT=\"+r+%3C=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p+%3C=+1.75+ ALIGN=MIDDLE  ALT=\"+p+%3C=+1.75+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+%3C=+3.06+ ALIGN=MIDDLE  ALT=\"+a+%3C=+3.06+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "I'll take some guesses<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r+=+.75+ ALIGN=MIDDLE  ALT=\"+r+=+.75+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p+=+1+ ALIGN=MIDDLE  ALT=\"+p+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+%2B+2.5+ ALIGN=MIDDLE  ALT=\"+a+%2B+2.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now to test them:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6r+%2B+2p+%2B+a+=+6+ ALIGN=MIDDLE  ALT=\"+6r+%2B+2p+%2B+a+=+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6%2A.75+%2B+2%2A1+%2B+2.5+=+6+ ALIGN=MIDDLE  ALT=\"+6%2A.75+%2B+2%2A1+%2B+2.5+=+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r+ ALIGN=MIDDLE  ALT=\"+r+\"   DISABLED_style= \"max-width:90%; height:auto;\" > looks too big. I'll say<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r+=+.35+ ALIGN=MIDDLE  ALT=\"+r+=+.35+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6%2A.35+%2B+2%2A1+%2B+2.5+=+6+ ALIGN=MIDDLE  ALT=\"+6%2A.35+%2B+2%2A1+%2B+2.5+=+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2.1+%2B+2+%2B+2.5+%3E+6+ ALIGN=MIDDLE  ALT=\"+2.1+%2B+2+%2B+2.5+%3E+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I'll say <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+1.75+ ALIGN=MIDDLE  ALT=\"+a+=+1.75+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6%2A.35+%2B+2%2A1+%2B+1.75+=+6+ ALIGN=MIDDLE  ALT=\"+6%2A.35+%2B+2%2A1+%2B+1.75+=+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is the only way to solve if you<BR>\n" );
document.write( "have more unknowns that equations.<BR>\n" );
document.write( "If you keep playing with it, you'll<BR>\n" );
document.write( "get closer to the answer.<BR>\n" );
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document.write( " </SPAN>\n" );
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