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 #128574 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=128574\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I would appreciate your help on the following problem: <BR>\n" );
document.write( "The two digits in the numerator of a fraction whose value is 4/7 are reversed in its denominator. <BR>\n" );
document.write( "I have 10t+u/10u+t=4/7<BR>\n" );
document.write( "Rearrange:<BR>\n" );
document.write( "7(10t+u) = 4(10u+t)<BR>\n" );
document.write( "70t + 7u = 40u+4t<BR>\n" );
document.write( "66t - 33u = 0<BR>\n" );
document.write( "t = (1/2)u<BR>\n" );
document.write( "-----------------------------\r<BR>\n" );
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document.write( "The reciprocal of the fraction is the value obtained when 16 is added to the original numerator and 5 is subtracted from the original denominator. <BR>\n" );
document.write( "(10u+t)/(10t+u) = [10t+u+16]/[10u+t-5]<BR>\n" );
document.write( "Rearrange:<BR>\n" );
document.write( "(10u+t)(10u+t-5) = (10t+u)(10t+u+16)<BR>\n" );
document.write( "[(10u+t)^2 - 5(10u+t)] = [(10t+u)^2 + 16(10t+u)]\r<BR>\n" );
document.write( "\n" );
document.write( "[100u^2 + 20tu + t^2 -50u - 5t] = [100t^2 + 20tu + u^2 + 160t + 16u]\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "[99u^2 - 99t^2 -66u - 165t] = 0\r<BR>\n" );
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document.write( "----------------------------------------------<BR>\n" );
document.write( "Substitute t = (1/2)u into the last equation to solve for \"u\":\r<BR>\n" );
document.write( "\n" );
document.write( "Comment: This is a messy problem.  I'll leave the substitution to you.<BR>\n" );
document.write( "I get u = 2 so t = 1<BR>\n" );
document.write( "Number: 12\r<BR>\n" );
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document.write( "===================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );