document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=32173>Question 32173</A>: <I><SPAN STYLE=\"word-break: break-all;\">            <BR>\n" );
document.write( "Let f(x)=2kx +9, where k is a real number.  If f(3):f(6)=1:3, determine the value of f(9)-f(3). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #18710 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=18710\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Need to determine \"k\".<BR>\n" );
document.write( "f(3)=2k(3)+9=6k+9<BR>\n" );
document.write( "f(6)=2k(6)+9=12k+9<BR>\n" );
document.write( "Then, because f(3):f(6)=1:3, you have the following:<BR>\n" );
document.write( "f(3)/f(6)=(6k+9)/(12k+9)=1/3<BR>\n" );
document.write( "18k+27=12k+9<BR>\n" );
document.write( "6k=-18<BR>\n" );
document.write( "k=-3<BR>\n" );
document.write( "Now that we have k we know f(x)=-6x+9<BR>\n" );
document.write( "So, f(9)=-54+9=-45<BR>\n" );
document.write( "And, f(3)=-18+9=-9<BR>\n" );
document.write( "So, f(9)-f(3)=-36<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );