document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=913235>Question 913235</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A boy has 231 marbles. he arranges them in rows so that each row contains on e marble less than the preceding. the last row consist of one marble only, which forms the vertex of a triangle. how many marbles are there in the base of the triangle? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #554362 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=554362\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A boy has 231 marbles. he arranges them in rows so that each row contains on e marble less than the preceding. the last row consist of one marble only, which forms the vertex of a triangle. how many marbles are there in the base of the triangle?\r<BR>\n" );
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document.write( "The arrangement is in Arithmetic progression\r<BR>\n" );
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document.write( "a= 1<BR>\n" );
document.write( "d=1<BR>\n" );
document.write( "total marbles = 231\r<BR>\n" );
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document.write( "Sn = 231\r<BR>\n" );
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document.write( "Sn = n/2(2a+(n-1)d)\r<BR>\n" );
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document.write( "231= n/2(2+(n-1)1)\r<BR>\n" );
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document.write( "231*2 = n(n+1)\r<BR>\n" );
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document.write( "n^2+n=462\r<BR>\n" );
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document.write( "n^2+n-462=0\r<BR>\n" );
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document.write( "n^2+22n-21n-462=0\r<BR>\n" );
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document.write( "n(n+22)-21(n+22)=0<BR>\n" );
document.write( "(n-21)(n+22)=0\r<BR>\n" );
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document.write( "n= 21 OR -22<BR>\n" );
document.write( "ignore negative\r<BR>\n" );
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document.write( "n= 21 number of rows\r<BR>\n" );
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document.write( "tn = a+(n-1)d\r<BR>\n" );
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document.write( "t21 = 1+(21-1)1\r<BR>\n" );
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document.write( "t20 = 21  \r<BR>\n" );
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document.write( "21 marbles on the base line </SPAN>\n" );
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