document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1074078>Question 1074078</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If (3-x), 6, (7-5x) are consecutive terms of a geometric progression with constant ratio r>0 find x and constant ratio </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #688884 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=688884\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We can write two equations for the common ratio:<BR>\n" );
document.write( "r = 6/(3-x)  [1]<BR>\n" );
document.write( "r = (7-5x)/6 [2]<BR>\n" );
document.write( "We have two equations in two unknowns. Let's solve for x first.<BR>\n" );
document.write( "6/(3-x) = (7-5x)/6 -> 36 = 21 - 22x + 5x^2 -> 5x^2 - 22x - 15 = 0<BR>\n" );
document.write( "This can be factored as (5x+3)(x-5) = 0.  The two solutions are x = -3/5, x = 5.<BR>\n" );
document.write( "But, x=5 gives r<0, so we choose the 1st solution, x = -3/5.<BR>\n" );
document.write( "Substitute in [1] to get the value for r:<BR>\n" );
document.write( "r = 6/(3--3/5) = 6/(18/5) = 5/3.<BR>\n" );
document.write( "Ans: r = 5/3, x = -3/5<BR>\n" );
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