document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1171699>Question 1171699</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If 2 is subtracted from a numerator of a fraction and 3 is added to the denominator, it reduces to 1/4. If 5 is added to the numerator and 2 is subtracted from the denominator, it reduces to 3. Find 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 #796603 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=796603\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "n = original numerator<BR>\n" );
document.write( "d = original denominator<BR>\n" );
document.write( "n and d are whole numbers. To make things simple, we'll assume they are positive as well.\r<BR>\n" );
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document.write( "Let's focus on the part where it says \"If 2 is subtracted from a numerator of a fraction and 3 is added to the denominator, it reduces to 1/4\"\r<BR>\n" );
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document.write( "2 is subtracted from n getting n-2<BR>\n" );
document.write( "3 is added to d getting d+3\r<BR>\n" );
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document.write( "The fraction n/d turns into (n-2)/(d+3). <BR>\n" );
document.write( "We're told this new fraction reduces to 1/4. <BR>\n" );
document.write( "We can say (n-2)/(d+3) = 1/4\r<BR>\n" );
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document.write( "Cross multiply and solve for d.<BR>\n" );
document.write( "(n-2)/(d+3) = 1/4<BR>\n" );
document.write( "4(n-2) = 1(d+3)<BR>\n" );
document.write( "4n-8 = d+3<BR>\n" );
document.write( "d+3 = 4n-8<BR>\n" );
document.write( "d = 4n-8-3<BR>\n" );
document.write( "d = 4n-11<BR>\n" );
document.write( "This will be useful later.\r<BR>\n" );
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document.write( "Next we'll focus on the part that says \"If 5 is added to the numerator and 2 is subtracted from the denominator, it reduces to 3\".\r<BR>\n" );
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document.write( "Go back to the original numerator and original denominator (n and d). Add 5 to the original numerator getting n+5. Subtract 2 from the original denominator to get d-2. The fraction (n+5)/(d-2) reduces to 3 meaning we can say:\r<BR>\n" );
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document.write( "(n+5)/(d-2) = 3<BR>\n" );
document.write( "(n+5)/(4n-11-2) = 3 .... plug in d = 4n-11<BR>\n" );
document.write( "(n+5)/(4n-13) = 3<BR>\n" );
document.write( "n+5 = 3(4n-13)<BR>\n" );
document.write( "n+5 = 12n-39<BR>\n" );
document.write( "5+39 = 12n-n<BR>\n" );
document.write( "44 = 11n<BR>\n" );
document.write( "11n = 44<BR>\n" );
document.write( "n = 44/11<BR>\n" );
document.write( "n = 4 is the original numerator\r<BR>\n" );
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document.write( "That value of n is plugged in like so<BR>\n" );
document.write( "d = 4n-11<BR>\n" );
document.write( "d = 4*4-11<BR>\n" );
document.write( "d = 16-11<BR>\n" );
document.write( "d = 5 is the original denominator\r<BR>\n" );
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document.write( "The original fraction is n/d = 4/5.\r<BR>\n" );
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document.write( "Let's check our answers.\r<BR>\n" );
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document.write( "If n = 4 and d = 5, then,<BR>\n" );
document.write( "(n-2)/(d+3) = (4-2)/(5+3)<BR>\n" );
document.write( "(n-2)/(d+3) = 2/8<BR>\n" );
document.write( "(n-2)/(d+3) = (1*2)/(4*2)<BR>\n" );
document.write( "(n-2)/(d+3) = 1/4<BR>\n" );
document.write( "This confirms the first part where it reads \"If 2 is subtracted from a numerator of a fraction and 3 is added to the denominator, it reduces to 1/4\"\r<BR>\n" );
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document.write( "Let's check the other part:<BR>\n" );
document.write( "(n+5)/(d-2) = (4+5)/(5-2)<BR>\n" );
document.write( "(n+5)/(d-2) = 9/3<BR>\n" );
document.write( "(n+5)/(d-2) = 3<BR>\n" );
document.write( "That part is confirmed as well.\r<BR>\n" );
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document.write( "Both parts of the instructions are confirmed.\r<BR>\n" );
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document.write( "Answer: 4/5<BR>\n" );
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