document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=977076>Question 977076</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the number of pairs of natural number a and b which satisfy 1/a + 2/b = 1/18 where b is an odd natural number less than 80 ?? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #598616 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=598616\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the number of pairs of natural number a and b which satisfy 1/a + 2/b = 1/18 where b is an odd natural number less than 80 ??<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fa ALIGN=MIDDLE  ALT=\"1%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Fb ALIGN=MIDDLE  ALT=\"2%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F18 ALIGN=MIDDLE  ALT=\"1%2F18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiply equation by 18ab, cancel the denominators, we have<BR>\n" );
document.write( "18b + 36a = ab<BR>\n" );
document.write( "18b - ab = -36a<BR>\n" );
document.write( "Factor out b<BR>\n" );
document.write( "b(18-a) = -36a<BR>\n" );
document.write( "b = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-%2836a%29%29%2F%28%2818-a%29%29 ALIGN=MIDDLE  ALT=\"%28-%2836a%29%29%2F%28%2818-a%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-%2836a%29%29%2F%28-1%28a-18%29%29 ALIGN=MIDDLE  ALT=\"%28-%2836a%29%29%2F%28-1%28a-18%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2836a%29%2F%28a-18%29 ALIGN=MIDDLE  ALT=\"%2836a%29%2F%28a-18%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "I don't think there are any pairs of natural numbers (meaning positive integers) that satisfy this.<BR>\n" );
document.write( "A graph of the above equation shows this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+%2836x%29%2F%28x-18%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+%2836x%29%2F%28x-18%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );