document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=938059>Question 938059</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Marianne is 4 years older than Anna and 2 years older than Khate. 4 years ago, thrice Marianne's age devided by Anna's age was # years less than Khate's age. Find their present ages?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #571549 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=571549\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> m = Maria's present age<BR>\n" );
document.write( "a = Ann's present age<BR>\n" );
document.write( "k = Kate's present age<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write an equation for each statement<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Marianne is 4 years older than Anna and 2 years older than Khate.<BR>\n" );
document.write( "m = a + 4<BR>\n" );
document.write( "or<BR>\n" );
document.write( "a = (m-4)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "m = k + 2<BR>\n" );
document.write( "or<BR>\n" );
document.write( "k = (m-2)<BR>\n" );
document.write( ";<BR>\n" );
document.write( " 4 years ago, thrice Marianne's age divided by Anna's age was 3 years less than Khate's age.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%28m-4%29%29%2F%28a-4%29 ALIGN=MIDDLE  ALT=\"%283%28m-4%29%29%2F%28a-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = (k-4) - 3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283m-12%29%29%2F%28a-4%29 ALIGN=MIDDLE  ALT=\"%28%283m-12%29%29%2F%28a-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = k - 7<BR>\n" );
document.write( "replace a with (m-4) and k with (m-2)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283m-12%29%29%2F%28%28m-4%29-4%29 ALIGN=MIDDLE  ALT=\"%28%283m-12%29%29%2F%28%28m-4%29-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = (m-2) - 7<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283m-12%29%29%2F%28%28m-8%29%29 ALIGN=MIDDLE  ALT=\"%28%283m-12%29%29%2F%28%28m-8%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = m - 9<BR>\n" );
document.write( "3m - 12 = (m-8)(m-9)<BR>\n" );
document.write( "3m - 12 = m^2 - 17m + 72<BR>\n" );
document.write( "Combine like terms on the right<BR>\n" );
document.write( "0 = m^2 - 17m - 3m + 72 + 12<BR>\n" );
document.write( "A quadratic equation<BR>\n" );
document.write( "m^2 - 20m + 84 = 0<BR>\n" );
document.write( "Factors to<BR>\n" );
document.write( "(m-6)(m-14) = 0<BR>\n" );
document.write( "Two solutions<BR>\n" );
document.write( "m =  6, not a reasonable answer<BR>\n" );
document.write( "m = 14 yrs is Maria's age<BR>\n" );
document.write( "then<BR>\n" );
document.write( "a = 14 - 4 = 10 yrs is Ann's age<BR>\n" );
document.write( "and<BR>\n" );
document.write( "k = 14 - 2 = 12 yrs is Kate's age\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );