document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1067722>Question 1067722</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When 15 is appended to a list of integers, the mean is increased by 2. When 1 is appended to the enlarged list, the mean of the enlarged list is decreased by 1. How many integers were in the original list? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #682832 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=682832\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n+ ALIGN=MIDDLE  ALT=\"+n+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the number of integers in the original list<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m+ ALIGN=MIDDLE  ALT=\"+m+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the mean of the original list<BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "Originally, the total, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+T+ ALIGN=MIDDLE  ALT=\"+T+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, of the integers was:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m+=+T%2Fn+ ALIGN=MIDDLE  ALT=\"+m+=+T%2Fn+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+T+=+m%2An+ ALIGN=MIDDLE  ALT=\"+T+=+m%2An+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+15+ ALIGN=MIDDLE  ALT=\"+15+\"   DISABLED_style= \"max-width:90%; height:auto;\" > to the list<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m+%2B+2+=+%28+m%2An+%2B+15+%29+%2F+%28+n+%2B+1+%29+ ALIGN=MIDDLE  ALT=\"+m+%2B+2+=+%28+m%2An+%2B+15+%29+%2F+%28+n+%2B+1+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------------------------<BR>\n" );
document.write( "Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++1+ ALIGN=MIDDLE  ALT=\"++1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > to the enlarged list<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m+%2B+2+-+1+=+%28+m%2An+%2B+15+%2B+1+%29+%2F+%28+n+%2B+2+%29+ ALIGN=MIDDLE  ALT=\"+m+%2B+2+-+1+=+%28+m%2An+%2B+15+%2B+1+%29+%2F+%28+n+%2B+2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------------------------<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+m+%2B+2+%29%2A%28+n+%2B+1+%29+=+m%2An+%2B+15+ ALIGN=MIDDLE  ALT=\"+%28+m+%2B+2+%29%2A%28+n+%2B+1+%29+=+m%2An+%2B+15+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m%2An+%2B+2n+%2B+m+%2B+2+=+m%2An+%2B+15+ ALIGN=MIDDLE  ALT=\"+m%2An+%2B+2n+%2B+m+%2B+2+=+m%2An+%2B+15+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m+%2B+2n+=+13+ ALIGN=MIDDLE  ALT=\"+m+%2B+2n+=+13+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+m+%2B+1+%29%2A%28+n+%2B+2+%29+=+m%2An+%2B+16+ ALIGN=MIDDLE  ALT=\"+%28+m+%2B+1+%29%2A%28+n+%2B+2+%29+=+m%2An+%2B+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m%2An+%2B+n+%2B+2m+%2B+2+=+m%2An+%2B+16+ ALIGN=MIDDLE  ALT=\"+m%2An+%2B+n+%2B+2m+%2B+2+=+m%2An+%2B+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2m+%2B+n+=+14+ ALIGN=MIDDLE  ALT=\"+2m+%2B+n+=+14+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "Multiply both sides of (2) by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2+ ALIGN=MIDDLE  ALT=\"+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "and subtract (1) from (2)<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4m+%2B+2n+=+28+ ALIGN=MIDDLE  ALT=\"+4m+%2B+2n+=+28+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-m+-+2m+=+-13+ ALIGN=MIDDLE  ALT=\"+-m+-+2m+=+-13+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3m+=+15+ ALIGN=MIDDLE  ALT=\"+3m+=+15+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m+=+5+ ALIGN=MIDDLE  ALT=\"+m+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m+%2B+2n+=+13+ ALIGN=MIDDLE  ALT=\"+m+%2B+2n+=+13+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5+%2B+2n+=+13+ ALIGN=MIDDLE  ALT=\"+5+%2B+2n+=+13+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2n+=+8+ ALIGN=MIDDLE  ALT=\"+2n+=+8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n+=+4+ ALIGN=MIDDLE  ALT=\"+n+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------------------------<BR>\n" );
document.write( "There were 4 integers in the original list<BR>\n" );
document.write( "-----------------------------------------<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+T+=+m%2An+ ALIGN=MIDDLE  ALT=\"+T+=+m%2An+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+T+=+5%2A4+ ALIGN=MIDDLE  ALT=\"+T+=+5%2A4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+T+=+20+ ALIGN=MIDDLE  ALT=\"+T+=+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m+%2B+2+=+%28+m%2An+%2B+15+%29+%2F+%28+n+%2B+1+%29+ ALIGN=MIDDLE  ALT=\"+m+%2B+2+=+%28+m%2An+%2B+15+%29+%2F+%28+n+%2B+1+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5+%2B+2+=+%28+20+%2B+15+%29+%2F+%28+4+%2B+1+%29+ ALIGN=MIDDLE  ALT=\"+5+%2B+2+=+%28+20+%2B+15+%29+%2F+%28+4+%2B+1+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+7+=+35%2F5+ ALIGN=MIDDLE  ALT=\"+7+=+35%2F5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+7+=+7+ ALIGN=MIDDLE  ALT=\"+7+=+7+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m+%2B+2+-+1+=+%28+m%2An+%2B+15+%2B+1+%29+%2F+%28+n+%2B+2+%29+ ALIGN=MIDDLE  ALT=\"+m+%2B+2+-+1+=+%28+m%2An+%2B+15+%2B+1+%29+%2F+%28+n+%2B+2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5+%2B+2+-+1+=+%28+20+%2B+15+%2B+1+%29+%2F+%28+4+%2B+2+%29+ ALIGN=MIDDLE  ALT=\"+5+%2B+2+-+1+=+%28+20+%2B+15+%2B+1+%29+%2F+%28+4+%2B+2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6+=+36%2F6+ ALIGN=MIDDLE  ALT=\"+6+=+36%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6+=+6+ ALIGN=MIDDLE  ALT=\"+6+=+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );