document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=699427>Question 699427</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two numbers differ by 16. The sum of twice the larger number and three times the smaller number is equal to 72. Find the numbers </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #431396 by </B><A HREF=/tutors/aboutme.mpl?userid=neatmath><B>neatmath(302)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=neatmath><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=neatmath><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=431396\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><font face=\"Tahoma\">This is a system of equations with two variables:<br>\r<BR>\n" );
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document.write( "Let x be the larger number, let y be the smaller number.  Then:<br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-y=16 ALIGN=MIDDLE  ALT=\"x-y=16\"   DISABLED_style= \"max-width:90%; height:auto;\" > given<br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2Ax%29%2B%283%2Ay%29=72 ALIGN=MIDDLE  ALT=\"%282%2Ax%29%2B%283%2Ay%29=72\"   DISABLED_style= \"max-width:90%; height:auto;\" > given<br>\r<BR>\n" );
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document.write( "At this point you can use any method to solve for x or y.<br>\r<BR>\n" );
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document.write( "Let's use substitution, by solving the first equation for x:<br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=y%2B16 ALIGN=MIDDLE  ALT=\"x=y%2B16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "Then substitute this value for x into the second equation:<br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2A%28y%2B16%29%29%2B%283%2Ay%29=72 ALIGN=MIDDLE  ALT=\"%282%2A%28y%2B16%29%29%2B%283%2Ay%29=72\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y%2B32%2B3y=72 ALIGN=MIDDLE  ALT=\"2y%2B32%2B3y=72\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5y%2B32=72 ALIGN=MIDDLE  ALT=\"5y%2B32=72\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5y=40 ALIGN=MIDDLE  ALT=\"5y=40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=8 ALIGN=MIDDLE  ALT=\"y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "If y=8, then it is easy to see that:<br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-y=16 ALIGN=MIDDLE  ALT=\"x-y=16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-8=16 ALIGN=MIDDLE  ALT=\"x-8=16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=24 ALIGN=MIDDLE  ALT=\"x=24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "So the two numbers are 24 and 8.<br>\r<BR>\n" );
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document.write( "Check it, it works.<br>\r<BR>\n" );
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document.write( "I hope this helps!  Keep practicing!  :)<br>\r<BR>\n" );
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document.write( "Thank you and good luck with all your future studies!<br><br> </SPAN>\n" );
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