document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=153060>Question 153060</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Tickets to a local movie were sold at $6 for adults and $4.50 for students. If 63 tickets were sold for a total of $358.50, how many adult tickets were sold? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #112517 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=112517\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x=# of adults and y=# of students\r<BR>\n" );
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document.write( "Since the \"63 tickets were sold\", this means that the first equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=63 ALIGN=MIDDLE  ALT=\"x%2By=63\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Also, because the tickets \"were sold at $6 for adults and $4.50 for students\" and they collected a \"total of $358.50\", this means that the second equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2B4.5y+=+358.5 ALIGN=MIDDLE  ALT=\"6x%2B4.5y+=+358.5\"   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=60x%2B45y+=+3585 ALIGN=MIDDLE  ALT=\"60x%2B45y+=+3585\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply every term in the second equation by 10 to move the decimal point one spot to the right\r<BR>\n" );
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document.write( "So we have the 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=63%2C60x%2B45y=3585%29 ALIGN=MIDDLE  ALT=\"system%28x%2By=63%2C60x%2B45y=3585%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.\r<BR>\n" );
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document.write( "So let's isolate y in 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=63 ALIGN=MIDDLE  ALT=\"x%2By=63\"   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=y=63-x ALIGN=MIDDLE  ALT=\"y=63-x\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x%2B63 ALIGN=MIDDLE  ALT=\"y=-x%2B63\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the equation\r<BR>\n" );
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document.write( "---------------------\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x%2B63 ALIGN=MIDDLE  ALT=\"y=-x%2B63\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can now replace each <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the second equation with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2B63 ALIGN=MIDDLE  ALT=\"-x%2B63\"   DISABLED_style= \"max-width:90%; height:auto;\" > to solve for <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=60x%2B45highlight%28%28-x%2B63%29%29=3585 ALIGN=MIDDLE  ALT=\"60x%2B45highlight%28%28-x%2B63%29%29=3585\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x%2B63 ALIGN=MIDDLE  ALT=\"y=-x%2B63\"   DISABLED_style= \"max-width:90%; height:auto;\" > into the first equation. In other words, replace each <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2B63 ALIGN=MIDDLE  ALT=\"-x%2B63\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Notice we've eliminated the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > variables. So we now have a simple equation with one unknown.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60x%2B%2845%29%28-1%29x%2B%2845%29%2863%29=3585 ALIGN=MIDDLE  ALT=\"60x%2B%2845%29%28-1%29x%2B%2845%29%2863%29=3585\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45 ALIGN=MIDDLE  ALT=\"45\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2B63 ALIGN=MIDDLE  ALT=\"-x%2B63\"   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=60x-45x%2B2835=3585 ALIGN=MIDDLE  ALT=\"60x-45x%2B2835=3585\"   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=15x%2B2835=3585 ALIGN=MIDDLE  ALT=\"15x%2B2835=3585\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the left side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15x=3585-2835 ALIGN=MIDDLE  ALT=\"15x=3585-2835\"   DISABLED_style= \"max-width:90%; height:auto;\" >Subtract 2835 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15x=750 ALIGN=MIDDLE  ALT=\"15x=750\"   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=%28750%29%2F%2815%29 ALIGN=MIDDLE  ALT=\"x=%28750%29%2F%2815%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 15 to isolate x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=50 ALIGN=MIDDLE  ALT=\"x=50\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "-----------------First Answer------------------------------\r<BR>\n" );
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document.write( "So the first part of our answer is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=50 ALIGN=MIDDLE  ALT=\"x=50\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=50 ALIGN=MIDDLE  ALT=\"x=50\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can plug it into the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x%2B63 ALIGN=MIDDLE  ALT=\"y=-x%2B63\"   DISABLED_style= \"max-width:90%; height:auto;\" > (remember we previously solved for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the first equation).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x%2B63 ALIGN=MIDDLE  ALT=\"y=-x%2B63\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the equation where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > was previously isolated.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%2850%29%2B63 ALIGN=MIDDLE  ALT=\"y=-%2850%29%2B63\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=50 ALIGN=MIDDLE  ALT=\"x=50\"   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=-50%2B63 ALIGN=MIDDLE  ALT=\"y=-50%2B63\"   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=y=13 ALIGN=MIDDLE  ALT=\"y=13\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms \r<BR>\n" );
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document.write( "-----------------Second Answer------------------------------\r<BR>\n" );
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document.write( "So the second part of our answer is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=13 ALIGN=MIDDLE  ALT=\"y=13\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "-----------------Summary------------------------------\r<BR>\n" );
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document.write( "So our answers are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=50 ALIGN=MIDDLE  ALT=\"x=50\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=13 ALIGN=MIDDLE  ALT=\"y=13\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So there were 50 adults and 13 students<BR>\n" );
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