document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=507830>Question 507830</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Story Problem: One number is 2 more than 5 times the other.  Their product is 24.\r<BR>\n" );
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document.write( "These are the formulas that I came up with for this story problem, but after substitution method I get the polynomial and get stumped on how to solve them.\r<BR>\n" );
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document.write( "xy=24<BR>\n" );
document.write( "x=2+5y\r<BR>\n" );
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document.write( "(2+5y)y=24    5y^2 +2y=24   where do I go from here?     </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #340738 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=340738\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x * y = 24<BR>\n" );
document.write( "so<BR>\n" );
document.write( "x = 24/y<BR>\n" );
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document.write( "x = 5y + 2<BR>\n" );
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document.write( "x=x<BR>\n" );
document.write( "so<BR>\n" );
document.write( "24/y = 5y + 2<BR>\n" );
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document.write( "cross multiply<BR>\n" );
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document.write( "24 = y(5y + 2)<BR>\n" );
document.write( "24 = 5y^2 + 2y<BR>\n" );
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document.write( "5y^2 +2y - 24 = 0<BR>\n" );
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document.write( "factor<BR>\n" );
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document.write( "(5y +12)(y - 2) = 0<BR>\n" );
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document.write( "check the factoring with FOIL<BR>\n" );
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document.write( "5y^2 -10y +12y -24.<BR>\n" );
document.write( "OK<BR>\n" );
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document.write( "So, y = -12/5 or 2<BR>\n" );
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document.write( "substitute to find x<BR>\n" );
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document.write( "x*y = 24<BR>\n" );
document.write( "x*2 = 24<BR>\n" );
document.write( "x = 12<BR>\n" );
document.write( "OK<BR>\n" );
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document.write( "x*y = 24<BR>\n" );
document.write( "x*-12/5 = 24<BR>\n" );
document.write( "x = -10<BR>\n" );
document.write( "OK<BR>\n" );
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document.write( "x = -10 when y = -12/5<BR>\n" );
document.write( "x = 12 when y = 2<BR>\n" );
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document.write( "Also check the other equation.<BR>\n" );
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document.write( "One number is 2 more than 5 times the other.<BR>\n" );
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document.write( "y = -12/5<BR>\n" );
document.write( "x = 5y -2<BR>\n" );
document.write( "x = 5*(-12/5) + 2<BR>\n" );
document.write( "x = -12 + 2 <BR>\n" );
document.write( "x = -10<BR>\n" );
document.write( "OK<BR>\n" );
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document.write( "y = 2<BR>\n" );
document.write( "x = 5y +2<BR>\n" );
document.write( "x = 10 + 2<BR>\n" );
document.write( "x = 12<BR>\n" );
document.write( "OK<BR>\n" );
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document.write( "So, we have two answers as shown above.<BR>\n" );
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document.write( "x = -10 when y = -12/5<BR>\n" );
document.write( "x = 12 when y = 2<BR>\n" );
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document.write( "These could be shown as ordered pairs:  (-10,-12/5), (12,2)<BR>\n" );
document.write( "which suggests a graph.<BR>\n" );
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document.write( "x*y = 24<BR>\n" );
document.write( "y = 24/x  (red line in the following graph)<BR>\n" );
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document.write( "x = 5y + 2<BR>\n" );
document.write( "5y = x -2<BR>\n" );
document.write( "y = (1/5)x - 2/5  (blue line in the following graph)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28500%2C500%2C-20%2C20%2C-20%2C20%2C24%2Fx%2C+1%2F5%2Ax+-+2%2F5%29 ALIGN=MIDDLE  ALT=\"graph%28500%2C500%2C-20%2C20%2C-20%2C20%2C24%2Fx%2C+1%2F5%2Ax+-+2%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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