document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=152717>Question 152717</A>: <I><SPAN STYLE=\"word-break: break-all;\"> MY LAST MODULE QUESTION!!! YAYA! but i cant figues it out .... <BR>\n" );
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document.write( "q: A concert promoter set the following ticket prices: $8 for adults, $5 for students. There were 1800 tickets sold for a total of $12 750.\r<BR>\n" );
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document.write( "a. Write a system of equations in two variables to model the situation.<BR>\n" );
document.write( "b. solve the system of equations.<BR>\n" );
document.write( "c.indicate the number of adult tickets and student tickets sold.<BR>\n" );
document.write( "d. check that your answer fits the equation. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #112237 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=112237\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a)\r<BR>\n" );
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document.write( "Let x=# of adults and y=# of students\r<BR>\n" );
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document.write( "Since \"There were 1800 tickets sold\", this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=1800 ALIGN=MIDDLE  ALT=\"x%2By=1800\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Also,  because the prices were \"$8 for adults, $5 for students\" which gave them \"a total of $12 750\", this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%2B5y=12750 ALIGN=MIDDLE  ALT=\"8x%2B5y=12750\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So we have the system:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x%2By=1800%2C8x%2B5y=12750%29 ALIGN=MIDDLE  ALT=\"system%28x%2By=1800%2C8x%2B5y=12750%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b)\r<BR>\n" );
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document.write( "Start with the given system of equations:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x%2By=1800%2C8x%2B5y=12750%29 ALIGN=MIDDLE  ALT=\"system%28x%2By=1800%2C8x%2B5y=12750%29\"   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=-8%28x%2By%29=-8%281800%29 ALIGN=MIDDLE  ALT=\"-8%28x%2By%29=-8%281800%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the both sides of the first equation by -8.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8x-8y=-14400 ALIGN=MIDDLE  ALT=\"-8x-8y=-14400\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply.\r<BR>\n" );
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document.write( "So we have the new system of equations:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28-8x-8y=-14400%2C8x%2B5y=12750%29 ALIGN=MIDDLE  ALT=\"system%28-8x-8y=-14400%2C8x%2B5y=12750%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-8x-8y%29%2B%288x%2B5y%29=%28-14400%29%2B%2812750%29 ALIGN=MIDDLE  ALT=\"%28-8x-8y%29%2B%288x%2B5y%29=%28-14400%29%2B%2812750%29\"   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=%28-8x%2B8x%29%2B%28-8y%2B5y%29=-14400%2B12750 ALIGN=MIDDLE  ALT=\"%28-8x%2B8x%29%2B%28-8y%2B5y%29=-14400%2B12750\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0x%2B-3y=-1650 ALIGN=MIDDLE  ALT=\"0x%2B-3y=-1650\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms. Notice how the x terms cancel out.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3y=-1650 ALIGN=MIDDLE  ALT=\"-3y=-1650\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-1650%29%2F%28-3%29 ALIGN=MIDDLE  ALT=\"y=%28-1650%29%2F%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   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=y=550 ALIGN=MIDDLE  ALT=\"y=550\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8x-8y=-14400 ALIGN=MIDDLE  ALT=\"-8x-8y=-14400\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now go back to the first equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8x-8%28550%29=-14400 ALIGN=MIDDLE  ALT=\"-8x-8%28550%29=-14400\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=550 ALIGN=MIDDLE  ALT=\"y=550\"   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=-8x-4400=-14400 ALIGN=MIDDLE  ALT=\"-8x-4400=-14400\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8x=-14400%2B4400 ALIGN=MIDDLE  ALT=\"-8x=-14400%2B4400\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4400 ALIGN=MIDDLE  ALT=\"4400\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8x=-10000 ALIGN=MIDDLE  ALT=\"-8x=-10000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-10000%29%2F%28-8%29 ALIGN=MIDDLE  ALT=\"x=%28-10000%29%2F%28-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8 ALIGN=MIDDLE  ALT=\"-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   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=x=1250 ALIGN=MIDDLE  ALT=\"x=1250\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "So our answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1250 ALIGN=MIDDLE  ALT=\"x=1250\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=550 ALIGN=MIDDLE  ALT=\"y=550\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "-----------------------------------\r<BR>\n" );
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document.write( "c)\r<BR>\n" );
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document.write( "Since  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1250 ALIGN=MIDDLE  ALT=\"x=1250\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=550 ALIGN=MIDDLE  ALT=\"y=550\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means that there were 1,250 adults and 550 students.\r<BR>\n" );
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document.write( "d)\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "Let's check the first equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=1800 ALIGN=MIDDLE  ALT=\"x%2By=1800\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the first equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1250%2B550=1800 ALIGN=MIDDLE  ALT=\"1250%2B550=1800\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1250 ALIGN=MIDDLE  ALT=\"x=1250\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=550 ALIGN=MIDDLE  ALT=\"y=550\"   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=1800=1800 ALIGN=MIDDLE  ALT=\"1800=1800\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add. Since this equation is true, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1250 ALIGN=MIDDLE  ALT=\"x=1250\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=550 ALIGN=MIDDLE  ALT=\"y=550\"   DISABLED_style= \"max-width:90%; height:auto;\" > are solutions to the equation.\r<BR>\n" );
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document.write( "Now let's check the second equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%2B5y=12750 ALIGN=MIDDLE  ALT=\"8x%2B5y=12750\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the second equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2A%281250%29%2B5%2A%28550%29=12750 ALIGN=MIDDLE  ALT=\"8%2A%281250%29%2B5%2A%28550%29=12750\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1250 ALIGN=MIDDLE  ALT=\"x=1250\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=550 ALIGN=MIDDLE  ALT=\"y=550\"   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=10000%2B2750=12750 ALIGN=MIDDLE  ALT=\"10000%2B2750=12750\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12750=12750 ALIGN=MIDDLE  ALT=\"12750=12750\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add. Since this equation is true, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1250 ALIGN=MIDDLE  ALT=\"x=1250\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=550 ALIGN=MIDDLE  ALT=\"y=550\"   DISABLED_style= \"max-width:90%; height:auto;\" > are solutions to the equation.\r<BR>\n" );
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document.write( "Since <font size=\"4\"><b>both</b></font> equations of the system are true, this verifies our answer.<BR>\n" );
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