document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=173693>Question 173693</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395977223/algebrahomeworkh>Algebra Structure and Method Book 1</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I would appreciate your help on the following problem:  The two digits in the numerator of a fraction whose value is 4/7 are reversed in its demoninator.  The reciprocal of the fraction is the value obtained when 16 is added to the original numerator and 5 is subtracted from the original demonimator.  Find the original fraction.  I have 10t+u/10u+t=4/7; 10u+t/10t+u=10t+u+16/10u+t-5.<BR>\n" );
document.write( "7(10t+u)=4(10u+t), 70t+7u=40u+4t, 66t=33u, t=3/6u.  I'm not sure where to go from there.  Thank you so much for any help you can give me.  I appreciate it so much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #128572 by </B><A HREF=/tutors/aboutme.mpl?userid=Mathtut><B>Mathtut(3670)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Mathtut><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=128572\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> lets call the numbers a and b  <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ab%2Fba=4%2F7 ALIGN=MIDDLE  ALT=\"ab%2Fba=4%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "but remember ab can also be written as 10a+b and ba can be written as 10b+a<BR>\n" );
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document.write( "so<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810a%2Bb%29%2F%2810b%2Ba%29=4%2F7 ALIGN=MIDDLE  ALT=\"%2810a%2Bb%29%2F%2810b%2Ba%29=4%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "now cross multiply<BR>\n" );
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document.write( "4(10b+a)=7(10a+b)<BR>\n" );
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document.write( "40b+4a=70a+7b<BR>\n" );
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document.write( "66a-33b=0:.......eq 1---->or revised eq 1 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a=b%2F2%29 ALIGN=MIDDLE  ALT=\"highlight%28a=b%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "we also know that <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810a%2Bb%2B16%29%2F%2810b%2Ba-5%29=7%2F4 ALIGN=MIDDLE  ALT=\"%2810a%2Bb%2B16%29%2F%2810b%2Ba-5%29=7%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >(the reciprocal of 4/7)<BR>\n" );
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document.write( "so lets cross multiply again<BR>\n" );
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document.write( "4(10a+b+16)=7(10b+a-5)<BR>\n" );
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document.write( "40a+4b+64=70b+7a-35<BR>\n" );
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document.write( "-33a+66b=99.......eq 2<BR>\n" );
document.write( "66a-33b=0........eq 1<BR>\n" );
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document.write( "multiply eq 1 by 2 and add the equations together<BR>\n" );
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document.write( "a's are eliminated and we are left with 99b=198<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28b=2%29 ALIGN=MIDDLE  ALT=\"highlight%28b=2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":since we know that a=b/2 from revised eq 1<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a=2%2F2=1%29 ALIGN=MIDDLE  ALT=\"highlight%28a=2%2F2=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "so the original fraction is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2812%2F21%29 ALIGN=MIDDLE  ALT=\"highlight%2812%2F21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >...which reduces to 4/7<BR>\n" );
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document.write( "incidently other number that would have worked had it not been for the 2nd equation would be<BR>\n" );
document.write( "24/42<BR>\n" );
document.write( "36/63<BR>\n" );
document.write( "48/84<BR>\n" );
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document.write( "which all reduce to 4/7   </SPAN>\n" );
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