document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=511287>Question 511287</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The numerator and denominator of a fraction are together equal to 100. Increase the numerator by 18 and decrease the denominator by 16 and the fraction is doubled. What is the fraction? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #342100 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=342100\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The numerator and denominator of a fraction are together equal to 100.<BR>\n" );
document.write( "n + d = 100<BR>\n" );
document.write( "d = (100-a)<BR>\n" );
document.write( ":<BR>\n" );
document.write( " Increase the numerator by 18 and decrease the denominator by 16 and the fraction is doubled.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28n%2B18%29%29%2F%28%28d-16%29%29 ALIGN=MIDDLE  ALT=\"%28%28n%2B18%29%29%2F%28%28d-16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282n%29%2Fd ALIGN=MIDDLE  ALT=\"%282n%29%2Fd\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cross multiply<BR>\n" );
document.write( "d(n+18) = 2n(d-16)<BR>\n" );
document.write( "dn + 18d = 2dn - 32n<BR>\n" );
document.write( "18d = 2dn - dn - 32n<BR>\n" );
document.write( "18d = dn - 32n<BR>\n" );
document.write( ":<BR>\n" );
document.write( "replace d with (100-n)<BR>\n" );
document.write( "18(100-n) = n(100-n) - 32n<BR>\n" );
document.write( "1800 - 18n = 100n - n^2 - 32n<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Arrange as a quadratic equation on the left<BR>\n" );
document.write( "n^2 - 18n -100n + 32n + 1800 = 0<BR>\n" );
document.write( "n^2 - 86n + 1800 = 0<BR>\n" );
document.write( ":<BR>\n" );
document.write( "You can use the quadratic formula here but it will factor to:<BR>\n" );
document.write( "(n-50){n-36) = 0<BR>\n" );
document.write( "Two solutions (remember n + d = 100)<BR>\n" );
document.write( "n = 50, then d = 50, but of course 50/50 = 1, not really considered a fraction<BR>\n" );
document.write( "and<BR>\n" );
document.write( "n = 36, then d = 64<BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36%2F64 ALIGN=MIDDLE  ALT=\"36%2F64\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the fraction we want, reduces to  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F16 ALIGN=MIDDLE  ALT=\"9%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check this in the original equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2836%2B18%29%29%2F%28%2854-16%29%29 ALIGN=MIDDLE  ALT=\"%28%2836%2B18%29%29%2F%28%2854-16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=54%2F48 ALIGN=MIDDLE  ALT=\"54%2F48\"   DISABLED_style= \"max-width:90%; height:auto;\" > reduces to: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2F16 ALIGN=MIDDLE  ALT=\"18%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" > twice the original fraction\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );