document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=887591>Question 887591</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A man is 5 times as old as his son. 2 years ago the sum of the squares of their ages was 114. Find the present age of son. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #536760 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=536760\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = man's age<BR>\n" );
document.write( "y = son's age.<BR>\n" );
document.write( "x = 5*y\r<BR>\n" );
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document.write( "2 years ago the sum of the squares of their ages was equal to 114.<BR>\n" );
document.write( "(x-2)^2 + (y-2)^2 = 114\r<BR>\n" );
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document.write( "simplify this to get:<BR>\n" );
document.write( "x^2 - 4x + 4 + y^2 - 4y + 4 = 114\r<BR>\n" );
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document.write( "since x = 5y, replace x with 5y to get:<BR>\n" );
document.write( "(5y)^2 - 4(5y) + 4 + y^2 - 4y + 4 = 114\r<BR>\n" );
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document.write( "simplify this to get:<BR>\n" );
document.write( "25y^2 - 20y + 4 + y^2 - 4y + 4 = 114\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "26y^2 - 24y + 8 = 114\r<BR>\n" );
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document.write( "subtract 114 from both sides of this equation to get:\r<BR>\n" );
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document.write( "26y^2 - 24y - 106 = 0\r<BR>\n" );
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document.write( "factor out the gcf of this equation to get:\r<BR>\n" );
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document.write( "2 * (13y^2 - 12y - 53) = 0\r<BR>\n" );
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document.write( "use the quadratic formula to factor (13y^2 - 12y - 53) to get:\r<BR>\n" );
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document.write( "y = 2.53275... or y = -1.60967...\r<BR>\n" );
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document.write( "since y can't be negative, then y has to be equal to 2.53275...\r<BR>\n" );
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document.write( "if i did this correctly, that's the age of his son presently.\r<BR>\n" );
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document.write( "that means the man is 5 * 2.53275... = 12.66377... years old.\r<BR>\n" );
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document.write( "that's not very old to be a father, but that's what the numbers show.\r<BR>\n" );
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document.write( "let's see if they're accurate in terms of the problem.\r<BR>\n" );
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document.write( "2 years ago, the sum of the squares of their ages was 114.\r<BR>\n" );
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document.write( "the man is 12.66377... years old<BR>\n" );
document.write( "2 years ago, the man was 10.66377... years old.<BR>\n" );
document.write( "square that and you get 113.71617...\r<BR>\n" );
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document.write( "the boy is 2.53275... years old.<BR>\n" );
document.write( "2 years ago, the boy was 0.53275... years old.<BR>\n" );
document.write( "square that and you get .283828...\r<BR>\n" );
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document.write( "add 113.71617... and .38382... and you get 114.\r<BR>\n" );
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document.write( "even though the ages don't look right, the formulas work out ok so i have to assume those are your answers.\r<BR>\n" );
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document.write( "the father's age is 12.66377... and the son's age is 2.53275...\r<BR>\n" );
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document.write( "you can round those number to whatever number of decimal places less than 5 that you want.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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