document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1127332>Question 1127332</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When John was as old as Paul is now, the sum of their ages was 51. When Paul will be as old as John is now, the sum of<BR>\n" );
document.write( "their ages will be 103. John is older than Paul by how many years? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #743731 by </B><A HREF=/tutors/aboutme.mpl?userid=FrankM><B>FrankM(1040)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=FrankM><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=FrankM><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=743731\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \"When John was as old as Paul is now\" \r<BR>\n" );
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document.write( "The key thing is to understand the set-up. <BR>\n" );
document.write( "Say John is 30, and Paul is 20, the phrase above is the difference in their ages. J-P, or 10 years ago. . And both of them 'were' J-P (or here, 10) years younger. The 30/20 was an example. \r<BR>\n" );
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document.write( "J+P-2(J-P)= 51  \r<BR>\n" );
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document.write( "Next is J-P years from now. So we add. \r<BR>\n" );
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document.write( "J+P+2(J-P)= 103\r<BR>\n" );
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document.write( "Next, simplify the first eq.\r<BR>\n" );
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document.write( "J+P-2J+2P=51\r<BR>\n" );
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document.write( "-J+3P = 51\r<BR>\n" );
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document.write( "And the second \r<BR>\n" );
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document.write( "J+P+2(J-P)= 103\r<BR>\n" );
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document.write( "3J-P = 103   (next, triple the first equation to add it)<BR>\n" );
document.write( "-3J+9P=153\r<BR>\n" );
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document.write( "8P=256\r<BR>\n" );
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document.write( "P = 32 and J = 45\r<BR>\n" );
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document.write( "13 years ago (J-P), P was 19, J was 32, these add to 51.<BR>\n" );
document.write( "In 13 years, P will be 45, J, 58, adding to 103. \r<BR>\n" );
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document.write( "You can also see that the way the question is set up, the sum of their ages changes (103-51) years, or by 52. From X years ago to X years hence, we can see that their age difference must be 52/4 or 13.  26 years pass from the point in past to point in future, times the 2 people. Once you see the 13 is true, the set-up can use 13 instead of J-P. \r<BR>\n" );
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document.write( " </SPAN>\n" );
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