document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=144721>Question 144721</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A DOUBLE BIRTHDAY:\r<BR>\n" );
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document.write( "\"Your birthday today and also your son's! That's amazing. How old is he now?\"<BR>\n" );
document.write( "Bob smiled.  \"I'll tell you with fractions. One over his age, plus one over my age, makes one over seven.  That's one-seventh, of course.\"\r<BR>\n" );
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document.write( "So what were their respective ages? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #105457 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=105457\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The given relationship, if the son's age is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the father's age is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >, is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Fx%29%2B%281%2Fy%29=1%2F7 ALIGN=MIDDLE  ALT=\"%281%2Fx%29%2B%281%2Fy%29=1%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Solving for y we get: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=7x%2F%28x-7%29 ALIGN=MIDDLE  ALT=\"y=7x%2F%28x-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We also know that since today is their mutual birthday, their ages must be integers.\r<BR>\n" );
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document.write( "We also know that the father's age cannot be a negative number and we cannot divide by zero, therefore the son's age must be an integer greater than or equal to 8.\r<BR>\n" );
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document.write( "Let's try 8:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=7%288%29%2F%288-7%29=56 ALIGN=MIDDLE  ALT=\"y=7%288%29%2F%288-7%29=56\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  56 is an integer, so age 8 for the son, and 56 for the father is a solution.  But are there any others?\r<BR>\n" );
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document.write( "Let's try 9:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=7%289%29%2F%289-7%29=63%2F2 ALIGN=MIDDLE  ALT=\"y=7%289%29%2F%289-7%29=63%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Not an integer AND smaller than 56\r<BR>\n" );
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document.write( "Let's try 10:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=7%2810%29%2F%2810-7%29=70%2F3 ALIGN=MIDDLE  ALT=\"y=7%2810%29%2F%2810-7%29=70%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Not an integer and smaller than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=63%2F2 ALIGN=MIDDLE  ALT=\"63%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Ah hah! As the son's possible age increases, the father's possible age decreases.  This suggests an upper limit to the son's age -- after all, the father must be older than his son (discounting any weird genetic engineering or travel near the speed of light scenarios).\r<BR>\n" );
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document.write( "Let's try 14:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=7%2814%29%2F%2814-7%29=14 ALIGN=MIDDLE  ALT=\"y=7%2814%29%2F%2814-7%29=14\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  An integer, but impossible because both the father and son could not have been born on the same day.\r<BR>\n" );
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document.write( "You can check out 11, 12, and 13 as potential ages for the son.<BR>\n" );
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