document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1119317>Question 1119317</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A total of 290 people attended the highschool play. The admission prices were $11 for&#8203; adults, $7 for high school&#8203; students, and $2 for children not yet in high school. The ticket sales totaled $1750. The principal suggested that next year they raise prices to $15 for&#8203; adults, $8 for high school&#8203; students, and $3 for children not yet in high school. He said that if exactly the same number of people attend next&#8203; year, the ticket sales at the higher prices will total $2280. How many&#8203; adults, high school&#8203; students, and children not yet in high school attended this&#8203; year? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #734816 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=734816\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "If you don't have access to a tool that solves systems of equations for you, you are stuck with having to do a pencil-and-paper solution.<br><BR>\n" );
document.write( "For a general system of three linear equations, this can be very tedious.<br><BR>\n" );
document.write( "However, in a timed competitive exam (for example), there will usually be a way of combining the given equations to make the solution relatively easy.  So look at the coefficients in the given equations and see if you can see a way to combine them to perhaps eliminate one of the variables.<br><BR>\n" );
document.write( "The system of equations for this problem is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%2Bz+=+290 ALIGN=MIDDLE  ALT=\"x%2By%2Bz+=+290\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11x%2B7y%2B2z+=+1750 ALIGN=MIDDLE  ALT=\"11x%2B7y%2B2z+=+1750\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15x%2B8y%2B3z+=+2280 ALIGN=MIDDLE  ALT=\"15x%2B8y%2B3z+=+2280\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "In this system, I immediately see the \"z\", \"2z\" and \"3z\" in the three equations; if I add the first two equations and compare the resulting equation to the third, variable z will be eliminated.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x%2B8y%2B3z+=+2040 ALIGN=MIDDLE  ALT=\"12x%2B8y%2B3z+=+2040\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15x%2B8y%2B3z+=+2280 ALIGN=MIDDLE  ALT=\"15x%2B8y%2B3z+=+2280\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+=+240 ALIGN=MIDDLE  ALT=\"3x+=+240\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+80 ALIGN=MIDDLE  ALT=\"x+=+80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "I got a bonus this time -- I eliminated TWO variables at once, allowing me to immediately find the value of the third.<br><BR>\n" );
document.write( "Plugging the value of x into the first two of the original equations, we get<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2Bz+=+210 ALIGN=MIDDLE  ALT=\"y%2Bz+=+210\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7y%2B2z+=+870 ALIGN=MIDDLE  ALT=\"7y%2B2z+=+870\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Double the first equation and compare to the second to eliminate z:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y%2B2z+=+420 ALIGN=MIDDLE  ALT=\"2y%2B2z+=+420\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5y+=+450 ALIGN=MIDDLE  ALT=\"5y+=+450\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+90 ALIGN=MIDDLE  ALT=\"y+=+90\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90%2Bz+=+210 ALIGN=MIDDLE  ALT=\"90%2Bz+=+210\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+120 ALIGN=MIDDLE  ALT=\"z+=+120\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Answer: x = 80 (adults); y = 90 (high school students); z = 120 (younger students) </SPAN>\n" );
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