document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1020786>Question 1020786</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many pairs of integers (b,c) satisfy the equation (b+7)/(b+4)=c/9? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #636719 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=636719\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 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( "==> 27 = (b+4)(c-9), after cross multiplying.<BR>\n" );
document.write( "Since both b+4 and c - 9 are supposed to be integers, there are eight possibilities<BR>\n" );
document.write( "(i) b+4 = 1, c-9 = 27 ==> b = -3, c=36<BR>\n" );
document.write( "(ii) b+4 = 3, c-9 = 9 ==> b = -1, c = 18<BR>\n" );
document.write( "(iii) b+4 = 9, c-9 = 3  ==> b = 5, c = 12<BR>\n" );
document.write( "(iv) b+4 = 27, c-9 = 1 ==> b = 23, c = 10<BR>\n" );
document.write( "(v) b+4 = -1, c-9 = -27 ==> b = -5, c = -18<BR>\n" );
document.write( "(vi) b+4 = -3, c-9 = -9 ==> b = -7, c = 0<BR>\n" );
document.write( "(vii) b+4 = -9, c-9 = -3 ==> b = -13, c = 6<BR>\n" );
document.write( "(viii) b+4 = -27, c-9 = -1 ==> b = -31, c = 8\r<BR>\n" );
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document.write( "Therefore there are 8 pairs of integers that will satisfy the original equation. </SPAN>\n" );
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