document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=39134>Question 39134</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The Marble Club has six members. Each member contributes his marbles and holds office on the basis of the number of marbles he contributes. The president has contributed 104 marbles more than the vice-president, who in turn has contributed 203 more than the treasurer. The secretary donated 1/2 the amount of the vice-president. The marble counter contributed 3 more than the sergeant at arms, and they have contributed 485 marbles together. If the total number of marbles is 3,886, how many did each contribute?\r<BR>\n" );
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document.write( "(not from a text) Please help me solve, Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #24558 by </B><A HREF=/tutors/aboutme.mpl?userid=fractalier><B>fractalier(6550)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=fractalier><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=fractalier><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=24558\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Okay, this will take a while but here goes...<BR>\n" );
document.write( "Let the variables be P, V, T, S, M, and G, for prez, vice-prez, treas, sec, marb, and sergeant.<BR>\n" );
document.write( "From the problem we have<BR>\n" );
document.write( "P = V + 104<BR>\n" );
document.write( "V = T + 203 or T = V - 203<BR>\n" );
document.write( "S = (1/2)V<BR>\n" );
document.write( "M = G + 3<BR>\n" );
document.write( "M + G = 485<BR>\n" );
document.write( "Main equation:  P + V + T + S + M + G = 3886<BR>\n" );
document.write( "Let's do M and G first.<BR>\n" );
document.write( "By substitutng, we get<BR>\n" );
document.write( "2G + 3 = 485<BR>\n" );
document.write( "2G = 482<BR>\n" );
document.write( "G = 241<BR>\n" );
document.write( "M = 244<BR>\n" );
document.write( "Now plug everything into the main equation and we get<BR>\n" );
document.write( "(V+104) + V + (V-203) + (1/2)V + 485 = 3886<BR>\n" );
document.write( "combining we get<BR>\n" );
document.write( "(7/2)V + 386 = 3886<BR>\n" );
document.write( "(7/2)V = 3500<BR>\n" );
document.write( "V = 1000<BR>\n" );
document.write( "so then<BR>\n" );
document.write( "P = 1104<BR>\n" );
document.write( "S = 500<BR>\n" );
document.write( "T = 797<BR>\n" );
document.write( "and we're done!  Whew! </SPAN>\n" );
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