document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1011506>Question 1011506</A>: <I><SPAN STYLE=\"word-break: break-all;\"> May you please help me with this question? two consecutive integers are represented by n and n+2 the sum of the reciprocals of the integers is 29/420. find the integers. \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #627179 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=627179\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2B2 ALIGN=MIDDLE  ALT=\"n%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > the sum of the reciprocals of the integers is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=29%2F420 ALIGN=MIDDLE  ALT=\"29%2F420\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "for integer <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > reciprocal is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fn ALIGN=MIDDLE  ALT=\"1%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "for integer <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2B2 ALIGN=MIDDLE  ALT=\"n%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  reciprocal is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28n%2B2%29 ALIGN=MIDDLE  ALT=\"1%2F%28n%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if the sum of the reciprocals  is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=29%2F420 ALIGN=MIDDLE  ALT=\"29%2F420\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fn%2B1%2F%28n%2B2%29=29%2F420 ALIGN=MIDDLE  ALT=\"1%2Fn%2B1%2F%28n%2B2%29=29%2F420\"   DISABLED_style= \"max-width:90%; height:auto;\" >........solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%28n%2B2%29%2F%28n%28n%2B2%29%29%2B%281%2An%29%2F%28n%28n%2B2%29%29=29%2F420 ALIGN=MIDDLE  ALT=\"1%28n%2B2%29%2F%28n%28n%2B2%29%29%2B%281%2An%29%2F%28n%28n%2B2%29%29=29%2F420\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2B2%2Bn%29%2F%28n%28n%2B2%29%29=29%2F420 ALIGN=MIDDLE  ALT=\"%28n%2B2%2Bn%29%2F%28n%28n%2B2%29%29=29%2F420\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282n%2B2%29%2F%28n%5E2%2B2n%29=29%2F420 ALIGN=MIDDLE  ALT=\"%282n%2B2%29%2F%28n%5E2%2B2n%29=29%2F420\"   DISABLED_style= \"max-width:90%; height:auto;\" >...cross multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=420%282n%2B2%29=29%28n%5E2%2B2n%29 ALIGN=MIDDLE  ALT=\"420%282n%2B2%29=29%28n%5E2%2B2n%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=840n%2B840=29n%5E2%2B58n ALIGN=MIDDLE  ALT=\"840n%2B840=29n%5E2%2B58n\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=29n%5E2%2B58n-840n-840 ALIGN=MIDDLE  ALT=\"0=29n%5E2%2B58n-840n-840\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=29n%5E2-782n-840=0 ALIGN=MIDDLE  ALT=\"29n%5E2-782n-840=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >...factor\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=29n%5E2-812n%2B30n-840=0 ALIGN=MIDDLE  ALT=\"29n%5E2-812n%2B30n-840=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2829n%5E2-812n%29%2B%2830n-840%29=0 ALIGN=MIDDLE  ALT=\"%2829n%5E2-812n%29%2B%2830n-840%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=29n%28n-28%29%2B30%28n-28%29=0 ALIGN=MIDDLE  ALT=\"29n%28n-28%29%2B30%28n-28%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n-28%29+%2829+n%2B30%29+=+0 ALIGN=MIDDLE  ALT=\"%28n-28%29+%2829+n%2B30%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions:\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n-28%29++=+0 ALIGN=MIDDLE  ALT=\"%28n-28%29++=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=28 ALIGN=MIDDLE  ALT=\"n=28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2829+n%2B30%29+=+0 ALIGN=MIDDLE  ALT=\"+%2829+n%2B30%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=-30%2F29 ALIGN=MIDDLE  ALT=\"n=-30%2F29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> since we need an integer, disregard this solution\r<BR>\n" );
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document.write( "so, your integers are: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=28 ALIGN=MIDDLE  ALT=\"n=28\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2B2=30 ALIGN=MIDDLE  ALT=\"n%2B2=30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " their reciprocals are: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F28 ALIGN=MIDDLE  ALT=\"1%2F28\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F30 ALIGN=MIDDLE  ALT=\"1%2F30\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "check their sum: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F28%2B1%2F30 ALIGN=MIDDLE  ALT=\"1%2F28%2B1%2F30\"   DISABLED_style= \"max-width:90%; height:auto;\" > ....since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=LCM+%2828%2C30%29=420 ALIGN=MIDDLE  ALT=\"LCM+%2828%2C30%29=420\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2F420%2B14%2F420=29%2F420 ALIGN=MIDDLE  ALT=\"15%2F420%2B14%2F420=29%2F420\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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