document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1159096>Question 1159096</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When Ralph asked his math teacher how old she was, she answered: \"Ten years ago, my age was equal to the square of my daughter's age. In 14 years, I will be twice as old as my daughter.\"What is the age of math Teacher </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #782081 by </B><A HREF=/tutors/aboutme.mpl?userid=VFBundy><B>VFBundy(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=VFBundy><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=VFBundy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=782081\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Teacher's age = x<BR>\n" );
document.write( "Daughter's age = y<BR>\n" );
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document.write( "x - 10 = (y - 10)²<BR>\n" );
document.write( "x + 14 = 2(y + 14)<BR>\n" );
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document.write( "x - 10 = y² - 20y + 100<BR>\n" );
document.write( "x + 14 = 2y + 28<BR>\n" );
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document.write( "x = y² - 20y + 110<BR>\n" );
document.write( "x = 2y + 14<BR>\n" );
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document.write( "y² - 20y + 110 = 2y + 14<BR>\n" );
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document.write( "y² - 22y + 96 = 0<BR>\n" );
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document.write( "y = 6; y = 16<BR>\n" );
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document.write( "So the daughter's age (y) can be either 6 or 16.  Plug y = 6 into:<BR>\n" );
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document.write( "x - 10 = (y - 10)²<BR>\n" );
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document.write( "x - 10 = (6 - 10)²<BR>\n" );
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document.write( "x - 10 = (-4)²<BR>\n" );
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document.write( "x - 10 = 16<BR>\n" );
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document.write( "x = 26<BR>\n" );
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document.write( "So, we know that one solution is that the teacher is 26 and her daughter is 6.<BR>\n" );
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document.write( "Plug y = 16 into:<BR>\n" );
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document.write( "x - 10 = (y - 10)²<BR>\n" );
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document.write( "x - 10 = (16 - 10)²<BR>\n" );
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document.write( "x - 10 = (6)²<BR>\n" );
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document.write( "x - 10 = 36<BR>\n" );
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document.write( "x = 46<BR>\n" );
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document.write( "Another solution is that the teacher is 46 and her daughter is 16.  This is probably the answer they are looking for.  <BR>\n" );
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document.write( "Each solution DOES technically work, but when the teacher is 26 and her daughter is 6, the statement \"Ten years ago, my age was equal to the square of my daughter's age,\" would involve subtracting 10 years from the daughter's age of 6 and making her be -4 years old.  The math still works, but would you ever consider someone who was 6 years old to be -4 years old 10 years ago?<BR>\n" );
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document.write( "Anyway...the safe answer is that the teacher is 46. </SPAN>\n" );
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