document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1129854>Question 1129854</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Nora is twice as old as Raj and half as old as Ethan. In 22 years' time, Ethan will be twice as old as Raj. Find Nora's present age! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #746484 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=746484\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let n = nora's age today, and r = raj's age today and e = ethan's age today.\r<BR>\n" );
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document.write( "today, nora is twice as old as raj and half as old as ethan.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "n = 2 * r<BR>\n" );
document.write( "n = 1/2 * e\r<BR>\n" );
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document.write( "in 22 years, ethan will be twice as old as raj.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "e + 22 = 2 * (r + 22)<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "e + 22 = 2 * r + 44\r<BR>\n" );
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document.write( "from n = 2 * r, solve for r to get r = 1/2 * n.<BR>\n" );
document.write( "from n = 1/2 * e, solve for e to get e = 2 * n.\r<BR>\n" );
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document.write( "in e + 22 = 2 * r + 44, replace r with 1/2 * n and replace e with 2 * n to get:\r<BR>\n" );
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document.write( "2 * n + 22 = 2 * (1/2 * n) + 44<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "2 * n + 22 = n + 44<BR>\n" );
document.write( "solve for n to get:<BR>\n" );
document.write( "n = 22\r<BR>\n" );
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document.write( "your solution looks like it's n = 22.\r<BR>\n" );
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document.write( "confirm by finding r and e and then working the problem to see if it's true with those values.\r<BR>\n" );
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document.write( "r = 1/2 * n leads to r = 1/2 * 22 = 11<BR>\n" );
document.write( "e = 2 * n leads to e = 2 * 22 = 44\r<BR>\n" );
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document.write( "currently, ...\r<BR>\n" );
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document.write( "n = 22<BR>\n" );
document.write( "r = 11<BR>\n" );
document.write( "e = 44\r<BR>\n" );
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document.write( "in 22 years, ....\r<BR>\n" );
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document.write( "n = 44<BR>\n" );
document.write( "r = 33<BR>\n" );
document.write( "e = 66\r<BR>\n" );
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document.write( "in 22 years, e = 2 * r = 2 * 33 = 66, confirming the solution is correct when nora is 22 today.\r<BR>\n" );
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document.write( "you basically have equations that need to be solved simultaneously.<BR>\n" );
document.write( "i solved using substitution.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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