document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1166462>Question 1166462</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi<BR>\n" );
document.write( "The points P Q R S lie on a straight line. The ratio of the length PQ to the length of QR is 3:5. The ratio of the length of PR to QS is 5:4. What is the ratio of the length of QR to the length RS to the length of PS.\r<BR>\n" );
document.write( "\n" );
document.write( "thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #791203 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=791203\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Technically, the statement of the problem is faulty.  There are different solutions possible for different orderings of the four points.<br><BR>\n" );
document.write( "For solving the problem, I will assume the four points are in the given order.<br><BR>\n" );
document.write( "P.....Q.....R.....S<br><BR>\n" );
document.write( "(1) The ratio of PQ:QR is 3:5.  So let PQ=3x and QR=5x:<br><BR>\n" );
document.write( "P<-- 3x -->Q<-- 5x -->R.....S<br><BR>\n" );
document.write( "(2) The ratio of PR:QS is 5:4.  Currently PR is 8x.  Change the scale so that PR is a multiple of 5:<br><BR>\n" );
document.write( "P<-- 15x -->Q<-- 25x -->R.....S<br><BR>\n" );
document.write( "Now PR is 40x; the ratio 5:4 means QS is 32x.  Since QR is 25x, RS is 7x:<br><BR>\n" );
document.write( "P<-- 15x -->Q<-- 25x -->R<-- 7x -->S<br><BR>\n" );
document.write( "Now you can answer the question.  QR is 25x; RS is 7x; PS is 47x.  So<br><BR>\n" );
document.write( "QR:RS:PS = 25:7:47<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );