document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=9360>Question 9360</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A two-digit number is such that the product of its digits is 12.When 36 is added to this number, the digits interchange their places.Find the number. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #5072 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=5072\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let the 2-digit number be thought of as xy. This means the number is really 10x+y, as 34 means 30+4--> 3x10 + 4\r<BR>\n" );
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document.write( "Product is xy = 12 --eqn1\r<BR>\n" );
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document.write( "straightaway, this means we have either 26 or 34. Looking at these, adding 36 to both gives 62 or 70. So the answer is 26.\r<BR>\n" );
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document.write( "Anyway, algebraically...\r<BR>\n" );
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document.write( "adding 36 to the number is 10x+y+36<BR>\n" );
document.write( "and this equals \"yx\" or rather 10y+x\r<BR>\n" );
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document.write( "so, 10x+y+36 = 10y+x<BR>\n" );
document.write( "--> 9x - 9y = -36<BR>\n" );
document.write( "--> x - y = -4\r<BR>\n" );
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document.write( "and subbing in eqn1 into this gives <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2Fy+-+y+=+-4 ALIGN=MIDDLE  ALT=\"12%2Fy+-+y+=+-4\"   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=12+-+y%5E2+=+-4y ALIGN=MIDDLE  ALT=\"12+-+y%5E2+=+-4y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2+-+4y+-+12+=+0 ALIGN=MIDDLE  ALT=\"y%5E2+-+4y+-+12+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(y+2)(y-6) = 0<BR>\n" );
document.write( "so y = -2 or y=6\r<BR>\n" );
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document.write( "ignore the -2 value...we are looking for a positive number, so y=6. Hence from eqn1, x = 2...number is 26!\r<BR>\n" );
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document.write( "jon.<BR>\n" );
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