document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1188700>Question 1188700</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let $a$, $b$, $c$, $d$, and $e$ be positive integers. The sum of the four numbers on each of the five segments connecting \"points\" of the star is 28. What is the value of the sum $a + b + c + d + e$?<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 #819850 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=819850\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "From the description of the problem and the figure...<br><BR>\n" );
document.write( "a+1+4+c=28; a+c=23  [1]<BR>\n" );
document.write( "b+4+2+d=28; b+d=22  [2]<BR>\n" );
document.write( "c+2+5+e=28; c+e=21  [3]<BR>\n" );
document.write( "d+5+3+a=28; d+a=20  [4]<BR>\n" );
document.write( "e+3+1+b=28; e+b=24  [5]<br><BR>\n" );
document.write( "Adding [1] through [5]...<br><BR>\n" );
document.write( "2(a+b+c+d+e)=110<BR>\n" );
document.write( "a+b+c+d+e=55  [6]<br><BR>\n" );
document.write( "ANSWER: a+b+c+d+e=55<br><BR>\n" );
document.write( "Note we can determine the values of a, b, c, d, and e individually, even though the problem doesn't ask us to.<br><BR>\n" );
document.write( "Combining [1], [2], and [6] gives us e=10;<BR>\n" );
document.write( "Then using the figure gives us b=14, d=8, a=12, c=11.<br><BR>\n" );
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