document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1046468>Question 1046468</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello,\r<BR>\n" );
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document.write( "I need help with the following math problem:\r<BR>\n" );
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document.write( "How many pairs of integers (b,c) satisfy the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28b%2B7%29%2F%28b%2B4%29=c%2F9+ ALIGN=MIDDLE  ALT=\"+%28b%2B7%29%2F%28b%2B4%29=c%2F9+\"   DISABLED_style= \"max-width:90%; height:auto;\" >?\r<BR>\n" );
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document.write( "Thank you,<BR>\n" );
document.write( "Nicole </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #661911 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=661911\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "The equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b%2B7%29%2F%28b%2B4%29=c%2F9 ALIGN=MIDDLE  ALT=\"%28b%2B7%29%2F%28b%2B4%29=c%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B3%2F%28b%2B4%29+=+c%2F9 ALIGN=MIDDLE  ALT=\"1%2B3%2F%28b%2B4%29+=+c%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "-> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F%28b%2B4%29+=+c%2F9+-+1 ALIGN=MIDDLE  ALT=\"3%2F%28b%2B4%29+=+c%2F9+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, after transposing 1 to the right side;<BR>\n" );
document.write( "-> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F%28b%2B4%29+=+%28c-9%29%2F9 ALIGN=MIDDLE  ALT=\"3%2F%28b%2B4%29+=+%28c-9%29%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >, after combining terms,<BR>\n" );
document.write( "-> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27+=+%28b%2B4%29%28c-9%29 ALIGN=MIDDLE  ALT=\"27+=+%28b%2B4%29%28c-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, after cross multiplying.<BR>\n" );
document.write( "Since both <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2B4 ALIGN=MIDDLE  ALT=\"b%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+-+9 ALIGN=MIDDLE  ALT=\"c+-+9\"   DISABLED_style= \"max-width:90%; height:auto;\" > are supposed to be integers, there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=eight ALIGN=MIDDLE  ALT=\"eight\"   DISABLED_style= \"max-width:90%; height:auto;\" > possibilities:\r<BR>\n" );
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document.write( "1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2B4+=+1 ALIGN=MIDDLE  ALT=\"b%2B4+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c-9+=+27 ALIGN=MIDDLE  ALT=\"c-9+=+27\"   DISABLED_style= \"max-width:90%; height:auto;\" > -> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28b+=+-3%29 ALIGN=MIDDLE  ALT=\"highlight%28b+=+-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28c=36%29 ALIGN=MIDDLE  ALT=\"highlight%28c=36%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b%2B4+=+3 ALIGN=MIDDLE  ALT=\"+b%2B4+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c-9+=+9 ALIGN=MIDDLE  ALT=\"c-9+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" > -> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28b+=+-1%29 ALIGN=MIDDLE  ALT=\"highlight%28b+=+-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28c=18%29 ALIGN=MIDDLE  ALT=\"highlight%28c=18%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2B4+=+9 ALIGN=MIDDLE  ALT=\"b%2B4+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c-9+=+3 ALIGN=MIDDLE  ALT=\"c-9+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >  -> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28b+=+5%29 ALIGN=MIDDLE  ALT=\"highlight%28b+=+5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28c=12%29 ALIGN=MIDDLE  ALT=\"highlight%28c=12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "4) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2B4+=+27 ALIGN=MIDDLE  ALT=\"b%2B4+=+27\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c-9+=+1 ALIGN=MIDDLE  ALT=\"c-9+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > -> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28b+=+23%29 ALIGN=MIDDLE  ALT=\"highlight%28b+=+23%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28c=10%29 ALIGN=MIDDLE  ALT=\"highlight%28c=10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "5) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2B4+=+-1 ALIGN=MIDDLE  ALT=\"b%2B4+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c-9+=+-27 ALIGN=MIDDLE  ALT=\"c-9+=+-27\"   DISABLED_style= \"max-width:90%; height:auto;\" > -> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28b+=+-5%29 ALIGN=MIDDLE  ALT=\"highlight%28b+=+-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28c=-18%29 ALIGN=MIDDLE  ALT=\"highlight%28c=-18%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "6) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2B4+=+-3 ALIGN=MIDDLE  ALT=\"b%2B4+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c-9+=+-9 ALIGN=MIDDLE  ALT=\"c-9+=+-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > -> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28b+=+-7%29 ALIGN=MIDDLE  ALT=\"highlight%28b+=+-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28c=0%29 ALIGN=MIDDLE  ALT=\"highlight%28c=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "7) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2B4+=+-9 ALIGN=MIDDLE  ALT=\"b%2B4+=+-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c-9+=+-3 ALIGN=MIDDLE  ALT=\"c-9+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > -> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28b+=+-13%29 ALIGN=MIDDLE  ALT=\"highlight%28b+=+-13%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28c=6%29 ALIGN=MIDDLE  ALT=\"highlight%28c=6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "8) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2B4+=+-27 ALIGN=MIDDLE  ALT=\"b%2B4+=+-27\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c-9+=+-1 ALIGN=MIDDLE  ALT=\"c-9+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > -><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28b+=+-31%29 ALIGN=MIDDLE  ALT=\"highlight%28b+=+-31%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28c=8%29 ALIGN=MIDDLE  ALT=\"highlight%28c=8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Therefore there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" > pairs of integers that will satisfy the original equation.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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