document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1149530>Question 1149530</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Antonette age is 3 years older than her sister. 6 years ago her sister is 4 times antonette age. How old is antonette? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #770870 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=770870\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The statement of the problem is faulty; it says now Antonette is older and 6 years ago her sister was older.<br><BR>\n" );
document.write( "I will ignore that and solve the problem as it was probably intended -- with Antonette older.<br><BR>\n" );
document.write( "Using formal algebra... which I will assume is what you are learning to do by asking this question....<br><BR>\n" );
document.write( "Let the sister's age be x<BR>\n" );
document.write( "Then Antonette's age is x+3<br><BR>\n" );
document.write( "Then 6 years ago the sister's age was x-6, and Antonette's age was (x+3)-6 = x-3.<br><BR>\n" );
document.write( "Then, since 6 years ago Antonette was 4 times as old as her sister,<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3+=+4%28x-6%29 ALIGN=MIDDLE  ALT=\"x-3+=+4%28x-6%29\"   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+=+4x-24 ALIGN=MIDDLE  ALT=\"x-3+=+4x-24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21+=+3x ALIGN=MIDDLE  ALT=\"21+=+3x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+7 ALIGN=MIDDLE  ALT=\"x+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: Antonette's age is x+3 = 10 years<br><BR>\n" );
document.write( "CHECK: 6 years ago, Antonette was 10-6 = 4 years old and her sister was 7-6 = 1 year old; Antonette was 4 times as old as her sister.<br><BR>\n" );
document.write( "Note that, if a formal algebraic solution is not required, the question can be answered quickly with a little logical reasoning and simple arithmetic.<br><BR>\n" );
document.write( "If the difference between their ages is 3 years, then when Antonette was 4 times as old as her sister, their ages had to be 4 and 1.<br><BR>\n" );
document.write( "And since that was 6 years ago, their ages now are 10 and 7.<br><BR>\n" );
document.write( "While knowing how to solve problems like this with formal algebra is important, solving them using logical reasoning is also good mental exercise.<br><BR>\n" );
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