document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1021147>Question 1021147</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Eight girls arrived at Lucy's party. During the party, Lucy passed around a jar of candies. The first girl took a candy, the second girl took 3 candies, the third girl took 5 candies and so on. After the last took her candies, the jar was empty. Before the party started, Lucy ate 5 candies from the jar and gave a friend 3. How many candies were in the jar at first? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #636908 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=636908\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 8 girls at the party.\r<BR>\n" );
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document.write( "first girl took 1<BR>\n" );
document.write( "second girl took 3<BR>\n" );
document.write( "third girl took 5<BR>\n" );
document.write( "each succeeding girl took 2 more than the previous girl took.\r<BR>\n" );
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document.write( "before the party started, lucy ate 5 and gave a friend 3.<BR>\n" );
document.write( "there were 8 missing from the jar when the party started.\r<BR>\n" );
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document.write( "if the first girl took 1 and each succeeding girl took 2 more than that, then you have an arithmetic sequence where An = A1 + (n-1)*2.\r<BR>\n" );
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document.write( "if n = 8, and A1 = 1, then you have A8 = 1 + 7*2 = 1 + 14 = 15.\r<BR>\n" );
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document.write( "the eighth girl took 15 candies out of the jar.\r<BR>\n" );
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document.write( "the sum of an arithmetic series is Sn = n/2 * (A1 + An)\r<BR>\n" );
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document.write( "when n = 8, you get S8 = 8/2 * (A1 + A8)\r<BR>\n" );
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document.write( "since A1 = 1 and A8 = 15, you get S8 = 8/2 * (1 + 15) which results in S8 = 8/2 * 16.\r<BR>\n" );
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document.write( "S8 is equal to 8/2 * 16 which is equal to 8 * 8 which is equal to 64.\r<BR>\n" );
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document.write( "the 8 girls took out a total of 64 candies.\r<BR>\n" );
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document.write( "add the 8 that lucy ate and her friend took, and you get 72 candies were originally in the jar.\r<BR>\n" );
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document.write( "to confirm:\r<BR>\n" );
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document.write( "start with 72.<BR>\n" );
document.write( "subtract 5 that lucy ate and 3 that her friend ate to get 64.<BR>\n" );
document.write( "first girl took 1 which left 63.<BR>\n" );
document.write( "second girl took 3 which let 60.<BR>\n" );
document.write( "third girl took 5 which left 55.<BR>\n" );
document.write( "fourth girl took 7 which left 48.<BR>\n" );
document.write( "fifth girl took 9 which left 39.<BR>\n" );
document.write( "sixth girl took 11 which left 28.<BR>\n" );
document.write( "seventh girl took 13 which left 15<BR>\n" );
document.write( "eight girl took 15 which left 0.\r<BR>\n" );
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document.write( "your solution is that 72 candies were originally in the jar.<BR>\n" );
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