document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=131557>Question 131557</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395937760/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Solving Linear Equations:\r<BR>\n" );
document.write( "\n" );
document.write( "You are selling tickets for a high school play. Student tickets cost $4 and general admission tickets cost $6. You sell 525 tickets and collect $2,876. How many of each type of ticket did you sell.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "First I said x = student tickets and y = general admission tickets, but then I got lost. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #96036 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=96036\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Perfectly good start:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = the NUMBER of student tickets<BR>\n" );
document.write( "y = the NUMBER of GA tickets\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "And we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=525 ALIGN=MIDDLE  ALT=\"x%2By=525\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (First equation)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since student tickets cost $4, the total amount of money collected from the sale of student tickets must be 4 times the number of student tickets, i.e., 4x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Likewise, the total money collected from general admission tickets must be 6y.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "And since those were the only two types of tickets sold, these two expressions must add up to the total amount of money collected, or:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B6y=2876 ALIGN=MIDDLE  ALT=\"4x%2B6y=2876\"   DISABLED_style= \"max-width:90%; height:auto;\" > (Second equation)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's solve this by elimination.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Multiply the first equation by -4:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x-4y=2100 ALIGN=MIDDLE  ALT=\"-4x-4y=2100\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now add this new equation term-by-term to the second equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-4x-4y%29=-2100 ALIGN=MIDDLE  ALT=\"%28-4x-4y%29=-2100\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B6y=2876 ALIGN=MIDDLE  ALT=\"4x%2B6y=2876\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0x%2B2y=776 ALIGN=MIDDLE  ALT=\"0x%2B2y=776\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y=776 ALIGN=MIDDLE  ALT=\"2y=776\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=388 ALIGN=MIDDLE  ALT=\"y=388\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "388 general admission tickets.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Go back to the original first equation and multiply by -6, then add term-by-term to the second equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6x-6y=-3150 ALIGN=MIDDLE  ALT=\"-6x-6y=-3150\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B6y=2876 ALIGN=MIDDLE  ALT=\"4x%2B6y=2876\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%2B0y=-274 ALIGN=MIDDLE  ALT=\"-2x%2B0y=-274\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x=-274 ALIGN=MIDDLE  ALT=\"-2x=-274\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=137 ALIGN=MIDDLE  ALT=\"x=137\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "137 student tickets.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Check:<BR>\n" );
document.write( "388 + 137 = 525\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "388 * 6 = 2328<BR>\n" );
document.write( "137 * 4 = 548\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2328 + 548 = 2876.  Answer checks.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );