document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=121044>Question 121044</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of two numbers is sixty-five, and if the larger number is divided by the smaller number, then quotient is three and the remainder is five. 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 #88791 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=88791\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's say your numbers are m and n.\r<BR>\n" );
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document.write( "The first thing we know is that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+%2B+m+=+65 ALIGN=MIDDLE  ALT=\"n+%2B+m+=+65\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Let's assume that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%3Em ALIGN=MIDDLE  ALT=\"n%3Em\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2Fm=3%2B5%2Fm ALIGN=MIDDLE  ALT=\"n%2Fm=3%2B5%2Fm\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiplying by m:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=3m+%2B+5 ALIGN=MIDDLE  ALT=\"n=3m+%2B+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n-3m=5 ALIGN=MIDDLE  ALT=\"n-3m=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we have two standard form equations in two variables, so\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+%2B+m+=+65 ALIGN=MIDDLE  ALT=\"n+%2B+m+=+65\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n-3m=5 ALIGN=MIDDLE  ALT=\"n-3m=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiply the second equation by -1:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+%2B+m+=+65 ALIGN=MIDDLE  ALT=\"n+%2B+m+=+65\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-n%2B3m=-5 ALIGN=MIDDLE  ALT=\"-n%2B3m=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now add the equations, term by term:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0n%2B4m=60 ALIGN=MIDDLE  ALT=\"0n%2B4m=60\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Divide by 4:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=15 ALIGN=MIDDLE  ALT=\"m=15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now that we know the value of m, we can calculate n by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=65-15=50 ALIGN=MIDDLE  ALT=\"n=65-15=50\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Note that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%3Em ALIGN=MIDDLE  ALT=\"n%3Em\"   DISABLED_style= \"max-width:90%; height:auto;\" > is true.\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "50 divided by 15 is 3 with a remainder of 5.  Checks. </SPAN>\n" );
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