document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=9536>Question 9536</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ann's age this year is a multiple of 7. Next year her age will be a multiple of 4. Her age is between 10 and 60. Hoe old is Ann </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #5210 by </B><A HREF=/tutors/aboutme.mpl?userid=mathmaven53><B>mathmaven53(29)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathmaven53><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=5210\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let A be her age this year then A = 7k for some positive integer k\r<BR>\n" );
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document.write( " A+1  is her age next year and A+1 = 4l for some positive integer l\r<BR>\n" );
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document.write( " 1 = A+1 -A\r<BR>\n" );
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document.write( "   = 4l - 7k\r<BR>\n" );
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document.write( " We have to solve 4l - 7k = 1 in positive integers\r<BR>\n" );
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document.write( " We write equivalently 4l -8k + k = 1\r<BR>\n" );
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document.write( "          4l - 8k = 1 -k\r<BR>\n" );
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document.write( "   Let 1-k = 4r for some integer r\r<BR>\n" );
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document.write( " Then k  = 1 -4r\r<BR>\n" );
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document.write( " Substitute for k and solve for l in 4l - 7k = 1\r<BR>\n" );
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document.write( " We get l = 2-7r\r<BR>\n" );
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document.write( " A = 7k<BR>\n" );
document.write( "    = 7 -28r\r<BR>\n" );
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document.write( " 10 < A < 60\r<BR>\n" );
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document.write( " By substituting for A and solving for r we get\r<BR>\n" );
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document.write( " -53/28 < r < -3/28\r<BR>\n" );
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document.write( "  The only integer that satisfies this is r=-1\r<BR>\n" );
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document.write( " Then A = 7-28r \r<BR>\n" );
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document.write( "        = 35\r<BR>\n" );
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document.write( " Ann is 35 this year which is a multiple of 7<BR>\n" );
document.write( "next year she is 36 which is a multiple of 4\r<BR>\n" );
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document.write( " and 35 is between 10 and 60<BR>\n" );
document.write( " </SPAN>\n" );
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