document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=996754>Question 996754</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ompong is three years younger than VongFong. Six years ago, Ompong's age was two-thirds of VongFong's age. What are their present ages? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #615167 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=615167\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = ompong's age today.<BR>\n" );
document.write( "y = vongfong's age today.\r<BR>\n" );
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document.write( "ompong  is 3 years younger than vongfong.\r<BR>\n" );
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document.write( "x = y - 3\r<BR>\n" );
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document.write( "six years ago, ompong's age was 2/3 of vongfong's age.\r<BR>\n" );
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document.write( "x - 6 = 2/3 * (y - 6).\r<BR>\n" );
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document.write( "what are their present ages?\r<BR>\n" );
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document.write( "you have two equations to solve simultaneously.\r<BR>\n" );
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document.write( "they are x = y - 3 (first equation) and x - 6 = 2/3 * (y - 6) (second equation).\r<BR>\n" );
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document.write( "simplify the second equation to get:\r<BR>\n" );
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document.write( "x-6 = 2/3(y-6) becomes x-6 = 2/3 * y - 2/3 * 6\r<BR>\n" );
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document.write( "simplify further to get x-6 = 2/3 * y - 4.\r<BR>\n" );
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document.write( "the first equation tells you that x = y - 3.\r<BR>\n" );
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document.write( "you can replace x with y - 3 in the second equation because they are equivalent.\r<BR>\n" );
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document.write( "replace x in the second equation with (y - 3) to get:\r<BR>\n" );
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document.write( "(y - 3) - 6 = 2/3 * y - 4.\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "y - 9 = 2/3 * y - 4\r<BR>\n" );
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document.write( "add 9 to both sides of this equation to get:\r<BR>\n" );
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document.write( "y = 2/3 * y + 5\r<BR>\n" );
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document.write( "subtract 2/3 * y from both sides of this equation to get:\r<BR>\n" );
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document.write( "1/3 * y = 5\r<BR>\n" );
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document.write( "multiply both sides of this equation by 3 to get:\r<BR>\n" );
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document.write( "y = 15\r<BR>\n" );
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document.write( "if y = 15, then x must be equal to 12 because x = y - 3.\r<BR>\n" );
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document.write( "you have x = 12 and y = 15.\r<BR>\n" );
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document.write( "that's their ages today.\r<BR>\n" );
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document.write( "ompong is 12.<BR>\n" );
document.write( "vongfong is 15.\r<BR>\n" );
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document.write( "six years ago ompong was 6 and vongfong was 9.\r<BR>\n" );
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document.write( "6 is equal to 2/3 * 9.\r<BR>\n" );
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document.write( "solution looks good.\r<BR>\n" );
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document.write( "present ages of ompong and vongfong are 12 and 15.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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