document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=215999>Question 215999</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Tom is half as old as Ellen was three years ago.  <BR>\n" );
document.write( "In 10 years, Ellen will be one-and-one-half times as old as Tom.\r<BR>\n" );
document.write( "\n" );
document.write( "Would you please show me the formula to use?  And the answer?  \r<BR>\n" );
document.write( "\n" );
document.write( "Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #163158 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=163158\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Tom is half as old as Ellen was three years ago.  <BR>\n" );
document.write( "In 10 years, Ellen will be one-and-one-half times as old as Tom.\r<BR>\n" );
document.write( "\n" );
document.write( "Would you please show me the formula to use?  And the answer?  \r<BR>\n" );
document.write( "\n" );
document.write( "I probably need more info but here is the problem set-up.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 1.  Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > be Tom's current age and let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > be Ellen's age\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 2.  Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3 ALIGN=MIDDLE  ALT=\"x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > be Tom's age three years ago and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-3 ALIGN=MIDDLE  ALT=\"y-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > be Ellen's age three years ago\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 3.  Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-3=2%28x-3%29 ALIGN=MIDDLE  ALT=\"y-3=2%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > be Ellen's age three years ago since Tom is half of Ellen's age three years ago.  Simply this equation as follows\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-3=2%28x-3%29 ALIGN=MIDDLE  ALT=\"y-3=2%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-3=2x-6 ALIGN=MIDDLE  ALT=\"y-3=2x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Add 6-y to both sides of the equation to isolate x and y terms on one side and numbers on the right side\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-3%2B6-y=2x-6%2B6-y ALIGN=MIDDLE  ALT=\"y-3%2B6-y=2x-6%2B6-y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=2x-y ALIGN=MIDDLE  ALT=\"3=2x-y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-y=3 ALIGN=MIDDLE  ALT=\"2x-y=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 4.  Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B10=3%28x%2B10%29%2F2 ALIGN=MIDDLE  ALT=\"y%2B10=3%28x%2B10%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > be Ellen's age in ten years since Ellen will be one and one half times as old as Tom where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5=3%2F2 ALIGN=MIDDLE  ALT=\"1.5=3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x+10 is Tom's age in ten years, and y+10 is Ellen's age in ten years.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Multiply by 2 to both sides of the equation to get rid of denominator\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28y%2B10%29=2%2A3%28x%2B10%29%2F2 ALIGN=MIDDLE  ALT=\"2%28y%2B10%29=2%2A3%28x%2B10%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y%2B20=3x%2B30 ALIGN=MIDDLE  ALT=\"2y%2B20=3x%2B30\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Subtract 3x-20 to both sides of the equation\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y%2B20-3x-20=3x%2B30-3x-20 ALIGN=MIDDLE  ALT=\"2y%2B20-3x-20=3x%2B30-3x-20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%2B2y=10 ALIGN=MIDDLE  ALT=\"-3x%2B2y=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 5.  Now we have a linear system of equations from Steps 3 and 4 and is shown below:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-y=3 ALIGN=MIDDLE  ALT=\"2x-y=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%2B2y=10 ALIGN=MIDDLE  ALT=\"-3x%2B2y=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 6.  Now solve the linear system of equations in Step 5 using substitution.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=linear_substitution.solver>SOLVE linear system by SUBSTITUTION</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Solve:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++2%5Cx+%2B+-1%5Cy+=+3%2C%0D%0A++++-3%5Cx+%2B+2%5Cy+=+10+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++2%5Cx+%2B+-1%5Cy+=+3%2C%0D%0A++++-3%5Cx+%2B+2%5Cy+=+10+%29%0D%0A++\"   DISABLED_style= \"max-width:90%; height:auto;\" >We'll use substitution. After moving -1*y to the right, we get:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax+=+3+-+-1%2Ay ALIGN=MIDDLE  ALT=\"2%2Ax+=+3+-+-1%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3%2F2+-+-1%2Ay%2F2 ALIGN=MIDDLE  ALT=\"x+=+3%2F2+-+-1%2Ay%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Substitute that<BR>\n" );
document.write( "  into another equation:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2A%283%2F2+-+-1%2Ay%2F2%29+%2B+2%5Cy+=+10 ALIGN=MIDDLE  ALT=\"-3%2A%283%2F2+-+-1%2Ay%2F2%29+%2B+2%5Cy+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify: So, we know that y=29. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3%2F2+-+-1%2Ay%2F2 ALIGN=MIDDLE  ALT=\"x+=+3%2F2+-+-1%2Ay%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x=16.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+x=16%2C+y=29+%29 ALIGN=MIDDLE  ALT=\"system%28+x=16%2C+y=29+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  </TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So x=16 and y=29.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Check the ages three ago\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3=16-3=13 ALIGN=MIDDLE  ALT=\"x-3=16-3=13\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-3=29-3=26 ALIGN=MIDDLE  ALT=\"y-3=29-3=26\"   DISABLED_style= \"max-width:90%; height:auto;\" > where Ellen is twice the age of Tom three years ago...so this is a true statement.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Check the ages ten years from now.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B10=16%2B10=26 ALIGN=MIDDLE  ALT=\"x%2B10=16%2B10=26\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B10=29%2B10=39 ALIGN=MIDDLE  ALT=\"y%2B10=29%2B10=39\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=39=3%2A26%2F2=39 ALIGN=MIDDLE  ALT=\"39=3%2A26%2F2=39\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is another true statement.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 7.  So Tom is 16 years old and Ellen is 29 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 \r<BR>\n" );
document.write( "\n" );
document.write( "http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit \r<BR>\n" );
document.write( "\n" );
document.write( "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\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );