document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=122035>Question 122035</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Q: For a particular event, 812 tickets were sold for a total of $1912.  If students paid $2 per ticket and nonstudents paid $3 per ticket, how many student tickets were sold?<BR>\n" );
document.write( "Totally stumped!!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #89581 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=89581\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is the same as one of those coin problems where you have to figure out how many dimes and nickels you have.  You will have two equations in two variables, one of the equations shows the relationship between the numbers of the two kinds of tickets, and the other equation shows the relationship between their values.\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s ALIGN=MIDDLE  ALT=\"s\"   DISABLED_style= \"max-width:90%; height:auto;\" > be the number of student tickets and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > be the number of non-student tickets.\r<BR>\n" );
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document.write( "The first thing we know is that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+%2B+n=812 ALIGN=MIDDLE  ALT=\"s+%2B+n=812\"   DISABLED_style= \"max-width:90%; height:auto;\" > because the problem says 812 tickets were sold.\r<BR>\n" );
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document.write( "Since each student ticket costs $2, the total value of the student tickets must be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2s ALIGN=MIDDLE  ALT=\"2s\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Likewise, the total value of non-student tickets must be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3n ALIGN=MIDDLE  ALT=\"3n\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  We are also given that the total value of all the tickets is $1912, so we can write:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2s%2B3n=1912 ALIGN=MIDDLE  ALT=\"2s%2B3n=1912\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Take the first equation and solve it for one of the variables, let's solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+%2B+n=812 ALIGN=MIDDLE  ALT=\"s+%2B+n=812\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%2Bn-s=812-s ALIGN=MIDDLE  ALT=\"s%2Bn-s=812-s\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=812-s ALIGN=MIDDLE  ALT=\"n=812-s\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we have an expression for n that can be substituted into the second equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cartoon%282s%2B3%2Ared%28n%29=1912%2C2s%2B3%2Ared%28%28812-s%29%29=1912%29 ALIGN=MIDDLE  ALT=\"cartoon%282s%2B3%2Ared%28n%29=1912%2C2s%2B3%2Ared%28%28812-s%29%29=1912%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Distribute the 3 and collect like terms:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2s%2B2436-3s=1912 ALIGN=MIDDLE  ALT=\"2s%2B2436-3s=1912\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2436-s=1912 ALIGN=MIDDLE  ALT=\"2436-s=1912\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-s=1912-2436 ALIGN=MIDDLE  ALT=\"-s=1912-2436\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-s=-524 ALIGN=MIDDLE  ALT=\"-s=-524\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=524 ALIGN=MIDDLE  ALT=\"s=524\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we know that 524 student tickets were sold, which is what the question asked.\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "If 524 student tickets were sold, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=812+-+524+=+288 ALIGN=MIDDLE  ALT=\"812+-+524+=+288\"   DISABLED_style= \"max-width:90%; height:auto;\" > non-student tickets were sold.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=524%2A2%2B288%2A3=1048%2B864=1912 ALIGN=MIDDLE  ALT=\"524%2A2%2B288%2A3=1048%2B864=1912\"   DISABLED_style= \"max-width:90%; height:auto;\" > answer checks. </SPAN>\n" );
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