document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=825543>Question 825543</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The numerator of a fraction is 1 more than the denominator. If 1 is added to the numerator, and the denominator is unchanged, the resulting fraction has a value of 3/4. 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 #497403 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=497403\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let n = the original numerator and d = the original denominator. Then the numerator with 1 added to it would be: n + 1.<br><BR>\n" );
document.write( "With two variables we need two equations to solve this problem. \"The numerator of a fraction is 1 more than the denominator.\" translates into:<BR>\n" );
document.write( "n = d + 1<BR>\n" );
document.write( "and \"If 1 is added to the numerator, and the denominator is unchanged, the resulting fraction has a value of 3/4\" translates into:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2B1%29%2Fd+=+3%2F4 ALIGN=MIDDLE  ALT=\"%28n%2B1%29%2Fd+=+3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Now we can solve. Since the first equation is already solved for n, the Substitution Method seems like it would be easiest. Substituting for n in the second equation we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28d%2B1%29%2B1%29%2Fd+=+3%2F4 ALIGN=MIDDLE  ALT=\"%28%28d%2B1%29%2B1%29%2Fd+=+3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplifying we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d%2B2%29%2Fd+=+3%2F4 ALIGN=MIDDLE  ALT=\"%28d%2B2%29%2Fd+=+3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cross-multiplying we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d%2B2%29%2A4+=+d%2A3 ALIGN=MIDDLE  ALT=\"%28d%2B2%29%2A4+=+d%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which simplifies to:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4d%2B8+=+3d ALIGN=MIDDLE  ALT=\"4d%2B8+=+3d\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtracting 4d we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8+=+-d ALIGN=MIDDLE  ALT=\"8+=+-d\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiplying (or dividing) both sides by -1 we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8+=+d ALIGN=MIDDLE  ALT=\"-8+=+d\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Now we find the value for n. Using the first equation, n = d + 1, and the value we found for d, we should get n = -7. And since n and d are the original fraction:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-7%29%2F%28-8%29 ALIGN=MIDDLE  ALT=\"%28-7%29%2F%28-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );