document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=112422>Question 112422</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The product of two consecutive integers is 9 less than 9 times their sum. Find the integers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #82024 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=82024\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the smaller of the two consecutive integers is x, then the other one must be x + 1.\r<BR>\n" );
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document.write( "The product of these two integers is then:  x(x+1), and the sum of these two integers is x + (x + 1), or 2x + 1.\r<BR>\n" );
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document.write( "Now we can translate the first sentence of the problem into mathematical symbols:\r<BR>\n" );
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document.write( "The product of two consecutive integers (x(x + 1)) is (=) 9 times their sum (9(2x + 1)), less 9 (-9).  Or,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x%2B1%29=%289%282x%2B1%29%29-9 ALIGN=MIDDLE  ALT=\"x%28x%2B1%29=%289%282x%2B1%29%29-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now simplify and solve:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Bx=18x%2B9-9 ALIGN=MIDDLE  ALT=\"x%5E2%2Bx=18x%2B9-9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Bx-18x=0 ALIGN=MIDDLE  ALT=\"x%5E2%2Bx-18x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-17x=0 ALIGN=MIDDLE  ALT=\"x%5E2-17x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x-17%29=0 ALIGN=MIDDLE  ALT=\"x%28x-17%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and finally,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=17 ALIGN=MIDDLE  ALT=\"x=17\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "This means that the two consecutive integers are either 0 and 1 or 17 and 18.\r<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2A%280%2B1%29=9%2A%282%2A0%2B1%29-9 ALIGN=MIDDLE  ALT=\"0%2A%280%2B1%29=9%2A%282%2A0%2B1%29-9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=0 ALIGN=MIDDLE  ALT=\"0=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and our first answer checks.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17%2A18=9%2A%2817%2B18%29-9 ALIGN=MIDDLE  ALT=\"17%2A18=9%2A%2817%2B18%29-9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=306=9%2A%2835%29-9 ALIGN=MIDDLE  ALT=\"306=9%2A%2835%29-9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=306=315-9=306 ALIGN=MIDDLE  ALT=\"306=315-9=306\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and the second answer checks also.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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