document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=151171>Question 151171</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the reciprocals of two consecutive integers is 11/30. Find these integers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #111108 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=111108\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The sum of the reciprocals of two consecutive integers is 11/30. Find these integers.<BR>\n" );
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document.write( "Two consecutive integers: x, (x+1)<BR>\n" );
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document.write( "Sum of reciprocals = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%2F30 ALIGN=MIDDLE  ALT=\"11%2F30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx ALIGN=MIDDLE  ALT=\"1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28%28x%2B1%29%29 ALIGN=MIDDLE  ALT=\"1%2F%28%28x%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%2F30 ALIGN=MIDDLE  ALT=\"11%2F30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiply equation by 30x(x+1) and you have:<BR>\n" );
document.write( "30(x+1) + 30x = 11x(x+1)<BR>\n" );
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document.write( "30x + 30 + 30x = 11x^2 + 11x<BR>\n" );
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document.write( "60x + 30 = 11x^2 + 11x<BR>\n" );
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document.write( "0 = 11x^2 + 11x - 60x - 30<BR>\n" );
document.write( "a quadratic equation<BR>\n" );
document.write( "11x^2 - 49x - 30 = 0<BR>\n" );
document.write( "Factors to:<BR>\n" );
document.write( "(11x + 6)((x - 5) = 0<BR>\n" );
document.write( "The integer solution:<BR>\n" );
document.write( "x = 5<BR>\n" );
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document.write( "The two numbers = 5,6<BR>\n" );
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document.write( "Check solution in original equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F5 ALIGN=MIDDLE  ALT=\"1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%2F30 ALIGN=MIDDLE  ALT=\"11%2F30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F30 ALIGN=MIDDLE  ALT=\"6%2F30\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F30 ALIGN=MIDDLE  ALT=\"5%2F30\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%2F30 ALIGN=MIDDLE  ALT=\"11%2F30\"   DISABLED_style= \"max-width:90%; height:auto;\" >   </SPAN>\n" );
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