document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=221033>Question 221033</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Four years ago Katie was twice as old as Anne was then. in 6 years, Anne will be the same age that katie is now. How old is each now ?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I have two equattions of Katie= X, y= Anne<BR>\n" );
document.write( "2X-4= y<BR>\n" );
document.write( "x+6 = 2y - 4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #165829 by </B><A HREF=/tutors/aboutme.mpl?userid=drj><B>drj(1380)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drj><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=drj><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=165829\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Four years ago Katie was twice as old as Anne was then. In 6 years, Anne will be the same age that Katie is now. How old is each now ?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I have two equations of Katie= X, y= Anne\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2X-4= y<BR>\n" );
document.write( "x+6 = 2y - 4\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You're in the right track and good try in getting two linear equations....I'll check your work by the following steps.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 1.  Let x be Katie's age and y be Anne's age.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 2.  Let x-4 be Katie's age 4 years ago and y-4 be Anne's age four years ago.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 3.  Then, x-4= 2(y-4) since four years ago Katie was twice as old as Anne was then. Simplifying yields x-2y=-4\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 4.  Let y+6 be the age of Anne.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 5.  Then y+6=x since in 6 years, Anne will be the same age that Katie is now. Simplifying yields x-y=6\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 6.  The system of equations from Steps 3 and 5 are\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x-2y=-4  Equation A<BR>\n" );
document.write( "x-y-=6  Equation B\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "OR  multiplying Equation B by -1 yields\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x-2y=-4  Equation A<BR>\n" );
document.write( "-x+y=-6  Equation B1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Adding yields\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x-x-2y+y=-4-6\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "or y=10 and x=10+6=16\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Substituting x=16 and y=10, into Steps 3 and 5 yields true statements.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 7. ANSWER:  Kate is 16 years old and Anne is 10 years old.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I hope the above steps were helpful.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Good luck in your studies!\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Respectfully,<BR>\n" );
document.write( "Dr J </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );