document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=846903>Question 846903</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find two integers whose product is 78 such that one of the integers is five less than three times the other integer. \r<BR>\n" );
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document.write( "smaller number: <BR>\n" );
document.write( "larger number:\r<BR>\n" );
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document.write( "I got: y=-6 and y=13/3 from the factors (3y-13) and (y+6). \r<BR>\n" );
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document.write( "Thank you for your help!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #509960 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=509960\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the integers = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+ ALIGN=MIDDLE  ALT=\"+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+ ALIGN=MIDDLE  ALT=\"+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "given:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%2Ax+=+78+ ALIGN=MIDDLE  ALT=\"+y%2Ax+=+78+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+3x+-+5+ ALIGN=MIDDLE  ALT=\"+y+=+3x+-+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "Substitute (2) into (1)<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+3x+-+5+%29%2Ax+=+78+ ALIGN=MIDDLE  ALT=\"+%28+3x+-+5+%29%2Ax+=+78+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x%5E2+-+5x+=+78+ ALIGN=MIDDLE  ALT=\"+3x%5E2+-+5x+=+78+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x%5E2+-+5x+-+78+=+0+ ALIGN=MIDDLE  ALT=\"+3x%5E2+-+5x+-+78+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use quadratic formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"+x+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+3+ ALIGN=MIDDLE  ALT=\"+a+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+-5+ ALIGN=MIDDLE  ALT=\"+b+=+-5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+-78+ ALIGN=MIDDLE  ALT=\"+c+=+-78+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28+-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2+-+4%2A3%2A%28-78%29+%29%29+%2F+%282%2A3%29+ ALIGN=MIDDLE  ALT=\"+x+=+%28+-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2+-+4%2A3%2A%28-78%29+%29%29+%2F+%282%2A3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28+5+%2B-+sqrt%28+25+%2B+936+%29%29+%2F+6+ ALIGN=MIDDLE  ALT=\"+x+=+%28+5+%2B-+sqrt%28+25+%2B+936+%29%29+%2F+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28+5+%2B+sqrt%28+961+%29%29+%2F+6+ ALIGN=MIDDLE  ALT=\"+x+=+%28+5+%2B+sqrt%28+961+%29%29+%2F+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28+5+%2B+31+%29+%2F+6+ ALIGN=MIDDLE  ALT=\"+x+=+%28+5+%2B+31+%29+%2F+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+36%2F6+ ALIGN=MIDDLE  ALT=\"+x+=+36%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+6+ ALIGN=MIDDLE  ALT=\"+x+=+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+3x+-+5+ ALIGN=MIDDLE  ALT=\"+y+=+3x+-+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+3%2A6+-+5+ ALIGN=MIDDLE  ALT=\"+y+=+3%2A6+-+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+18+-+5+ ALIGN=MIDDLE  ALT=\"+y+=+18+-+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <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;\" ><BR>\n" );
document.write( "The integers are 6 and 13<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%2Ax+=+78+ ALIGN=MIDDLE  ALT=\"+y%2Ax+=+78+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+13%2A6+=+78+ ALIGN=MIDDLE  ALT=\"+13%2A6+=+78+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+78+=+78+ ALIGN=MIDDLE  ALT=\"+78+=+78+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );