document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=261549>Question 261549</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The two digits in the numerator of a fraction are reversed in its denominator.  If 1 is subtracted from both the numerator and the denominator, the value of the resulting fraction is 1/2.  The fraction whose numerator is the difference and whose denominator is the sum of the units and tens digits equals 2/5.  Find the original fraction. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #192913 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=192913\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x = the 10's digit of the numerator<BR>\n" );
document.write( "Let y = the units digit <BR>\n" );
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document.write( "The two digits in the numerator of a fraction are reversed in its denominator. If 1 is subtracted from both the numerator and the denominator, the value of the resulting fraction is 1/2.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810x%2By+-+1%29%2F%2810y%2Bx+-+1%29 ALIGN=MIDDLE  ALT=\"%2810x%2By+-+1%29%2F%2810y%2Bx+-+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cross multiply<BR>\n" );
document.write( "2(10x+y-1) = 10y+x-1)<BR>\n" );
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document.write( "20x + 2y - 2 = 10y + x -1<BR>\n" );
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document.write( "20x - x = 10y - 2y - 1 + 2<BR>\n" );
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document.write( "19x = 8y + 1<BR>\n" );
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document.write( " The fraction whose numerator is the difference and whose denominator is the sum of the units and tens digits equals 2/5.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-x%29%2F%28y%2Bx%29 ALIGN=MIDDLE  ALT=\"%28y-x%29%2F%28y%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F5 ALIGN=MIDDLE  ALT=\"2%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cross multiply<BR>\n" );
document.write( "5(y - x) = 2(y + x)<BR>\n" );
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document.write( "5y - 5x = 2y + 2x<BR>\n" );
document.write( "5y - 2y = 2x + 5x<BR>\n" );
document.write( "3y = 7x<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F3 ALIGN=MIDDLE  ALT=\"7%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >x <BR>\n" );
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document.write( "Find the original fraction.<BR>\n" );
document.write( "Replace y in the 1st equation; 19x = 8y + 1, with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F3 ALIGN=MIDDLE  ALT=\"7%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >x <BR>\n" );
document.write( "19x * 8(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F3 ALIGN=MIDDLE  ALT=\"7%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >x) + 1 <BR>\n" );
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document.write( "19x - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=56%2F3 ALIGN=MIDDLE  ALT=\"56%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + 1<BR>\n" );
document.write( "mult by 3<BR>\n" );
document.write( "3(19x) = 56x + 3(1)<BR>\n" );
document.write( "57x - 56x = 3<BR>\n" );
document.write( "x = 3, is the numerator 10's digit<BR>\n" );
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document.write( "Find y:<BR>\n" );
document.write( "y = 3(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F3 ALIGN=MIDDLE  ALT=\"7%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "y = 7, is the numerator units digit<BR>\n" );
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document.write( "The original fraction: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=37%2F73 ALIGN=MIDDLE  ALT=\"37%2F73\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Check by subtracting 1 from the numerator and denominator<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36%2F72 ALIGN=MIDDLE  ALT=\"36%2F72\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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