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 #128573 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=128573\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i believe i stumbled into the answer.<BR>\n" );
document.write( "your equation of 66t = 33u was good.<BR>\n" );
document.write( "that means that u = 2t<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you should have made your second equation equal to 7/4<BR>\n" );
document.write( "that would be:<BR>\n" );
document.write( "(10t+u+16)/(10u+t-5) = 7/4<BR>\n" );
document.write( "then you could have solved as follows:<BR>\n" );
document.write( "cross multiply:<BR>\n" );
document.write( "7*(10u+t-5) = 4*(10t+u+16)<BR>\n" );
document.write( "working this through:<BR>\n" );
document.write( "70u + 7t - 35 = 40t + 4u + 64<BR>\n" );
document.write( "move things around to get the u and the t on the left side and the constants on the right side.<BR>\n" );
document.write( "66u - 33t = 35 + 64<BR>\n" );
document.write( "66u - 33t = 99<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "substitute 2t for u to get<BR>\n" );
document.write( "132t - 33t = 99<BR>\n" );
document.write( "99t = 99<BR>\n" );
document.write( "t = 1<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since u = 2t, your answers are:<BR>\n" );
document.write( "t = 1<BR>\n" );
document.write( "u = 2<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "to prove:<BR>\n" );
document.write( "12/21 = 4/7 if you divide numerator and denominator by 3<BR>\n" );
document.write( "12 + 16 / 21 - 5 = 28/16 = 7/4 if you divide numerator and denominator by 4<BR>\n" );
document.write( "-----<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );