document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1181704>Question 1181704</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Anna is 12 years older than her sister Sue.7 years from now Sue will be 5/9 as old as Anna.How old is Anna ? How old is She? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #811608 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=811608\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "A typical setup for solving using formal algebra....<br><BR>\n" );
document.write( "The number we are looking for is Anna's age, so<br><BR>\n" );
document.write( "let x = Anna's age now<BR>\n" );
document.write( "then x-12 = Sue's age now<br><BR>\n" );
document.write( "In 7 years, Sue's age will be 5/9 of Anna's age:<BR>\n" );
document.write( "x+7 = Anna's age 7 years from now<BR>\n" );
document.write( "(x-12)+7 = x-5 = Sue's age 7 years from now<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-5+=+%285%2F9%29%28x%2B7%29 ALIGN=MIDDLE  ALT=\"x-5+=+%285%2F9%29%28x%2B7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%28x-5%29+=+5%28x%2B7%29 ALIGN=MIDDLE  ALT=\"9%28x-5%29+=+5%28x%2B7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x-45+=+5x%2B35 ALIGN=MIDDLE  ALT=\"9x-45+=+5x%2B35\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+=+80 ALIGN=MIDDLE  ALT=\"4x+=+80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+20 ALIGN=MIDDLE  ALT=\"x+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: Anna is 20 years old.<br><BR>\n" );
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document.write( "Here is an informal solution that uses \"nicer\" numbers....<br><BR>\n" );
document.write( "In 7 years, Sue will be 5/9 of Anna's age, so let their ages then be 5x and 9x. The difference between their ages will be 9x-5x=4x.<BR>\n" );
document.write( "But the difference in their ages is 12 years.  So 4x=12; x=3.<BR>\n" );
document.write( "So in 7 years their ages will be 5x=15 and 9x=27.<BR>\n" );
document.write( "So Anna's current age is 27-7 = 20.<br><BR>\n" );
document.write( "Here is the formal algebraic solution by that path....<br><BR>\n" );
document.write( "Let 5x = Sue's age 7 years from now<BR>\n" );
document.write( "let 9x = Anna's age 7 years from now<br><BR>\n" );
document.write( "The difference in their ages then will be 4x.<br><BR>\n" );
document.write( "The difference in their ages then, as always, is 12 years:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x=12 ALIGN=MIDDLE  ALT=\"4x=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<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;\" ><br><BR>\n" );
document.write( "Anna's current age is 9x-7 = 9(3)-7 = 27-7 = 20.<br><BR>\n" );
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document.write( "The numbers you have to work with are much easier with that method than with the method shown earlier.<br><BR>\n" );
document.write( "It is a lesson in how there can be a great deal of difference in the amount of work you need to do to solve a problem because of different ways of setting up the problem.<br><BR>\n" );
document.write( "Always look for possible different ways to solve problems to find ways that are easier for you.<br><BR>\n" );
document.write( "Given the \"5/9 as old...\" in the statement of the problem, I would never set up the problem by the \"straightforward\" method that leads to having to solve an equation like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-5+=+%285%2F9%29%28x%2B7%29 ALIGN=MIDDLE  ALT=\"x-5+=+%285%2F9%29%28x%2B7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, because I know there is another path that is going to be easier.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );