document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=67915>Question 67915</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395430526/algebrahomeworkh>Algebra:Structure and Method</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the reciprocals of two consecutive even integers is 11/60. Find the integers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #48294 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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=48294\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The sum of the reciprocals of two consecutive even integers is 11/60. Find the integers.<BR>\n" );
document.write( "Let the first even integer be:x<BR>\n" );
document.write( "Then the next even integer is: x+2<BR>\n" );
document.write( "The reciprocal of x=1/x<BR>\n" );
document.write( "The reciprocal of x+2=1/(x+2)<BR>\n" );
document.write( "Sum means add:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx%2B1%2F%28x%2B2%29=11%2F60 ALIGN=MIDDLE  ALT=\"1%2Fx%2B1%2F%28x%2B2%29=11%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" >  The LCD is 60x(x+2), multiply everything by that.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60x%28x%2B2%29%2A1%2Fx%2B60x%28x%2B2%29%2A1%2F%28x%2B2%29=60x%28x%2B2%29%2A11%2F60 ALIGN=MIDDLE  ALT=\"60x%28x%2B2%29%2A1%2Fx%2B60x%28x%2B2%29%2A1%2F%28x%2B2%29=60x%28x%2B2%29%2A11%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" >  cancel any matching numerators and denominators.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%28x%2B2%29%2B60x=11x%28x%2B2%29 ALIGN=MIDDLE  ALT=\"60%28x%2B2%29%2B60x=11x%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60x%2B120%2B60x=11x%5E2%2B22x ALIGN=MIDDLE  ALT=\"60x%2B120%2B60x=11x%5E2%2B22x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120x%2B120=11x%5E2%2B22x ALIGN=MIDDLE  ALT=\"120x%2B120=11x%5E2%2B22x\"   DISABLED_style= \"max-width:90%; height:auto;\" >  set = to 0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120x-120x%2B120-120=11x%5E2%2B22x-120x-120 ALIGN=MIDDLE  ALT=\"120x-120x%2B120-120=11x%5E2%2B22x-120x-120\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=11x%5E2-98x-120 ALIGN=MIDDLE  ALT=\"0=11x%5E2-98x-120\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Factor<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=11x%5E2-110x%2B12x-120 ALIGN=MIDDLE  ALT=\"0=11x%5E2-110x%2B12x-120\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=11x%28x-10%29%2B12%28x-10%29 ALIGN=MIDDLE  ALT=\"0=11x%28x-10%29%2B12%28x-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=%2811x%2B12%29%28x-10%29 ALIGN=MIDDLE  ALT=\"0=%2811x%2B12%29%28x-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  set each parentheses =0 and solve for x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11x%2B12=0 ALIGN=MIDDLE  ALT=\"11x%2B12=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-10=0 ALIGN=MIDDLE  ALT=\"x-10=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11x%2B12-12=0-12 ALIGN=MIDDLE  ALT=\"11x%2B12-12=0-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-10%2B10=0%2B10 ALIGN=MIDDLE  ALT=\"x-10%2B10=0%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11x=-12 ALIGN=MIDDLE  ALT=\"11x=-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=10 ALIGN=MIDDLE  ALT=\"x=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11x%2F11=-12%2F11 ALIGN=MIDDLE  ALT=\"11x%2F11=-12%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=10 ALIGN=MIDDLE  ALT=\"x=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-12%2F11 ALIGN=MIDDLE  ALT=\"x=-12%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=10 ALIGN=MIDDLE  ALT=\"x=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-12/11 is not an integer so reject it.<BR>\n" );
document.write( "x=10<BR>\n" );
document.write( "Therefore the first integer is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=10%29 ALIGN=MIDDLE  ALT=\"highlight%28x=10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and the second integer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x%2B2=10%2B2=12%29 ALIGN=MIDDLE  ALT=\"highlight%28x%2B2=10%2B2=12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Sanity check:<BR>\n" );
document.write( "does the reciprocal of 10 and 12 = 11/60?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F10%2B1%2F12=11%2F60 ALIGN=MIDDLE  ALT=\"1%2F10%2B1%2F12=11%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F60%2B5%2F60=11%2F60 ALIGN=MIDDLE  ALT=\"6%2F60%2B5%2F60=11%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%2F60=11%2F60 ALIGN=MIDDLE  ALT=\"11%2F60=11%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" > We're right!!!<BR>\n" );
document.write( "Happy Calculating!!!!<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );