document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=632031>Question 632031</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The average weight of 3 men A,B and C is 85kg. Another man D joins the group the average weight becomes 81kg. If another man E whose weight is 4kg more than that of D,replace A the average weight of B,C,D and E becomes 78kg. What is the weight of A? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #397985 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=397985\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a is equal to 85 kg.<BR>\n" );
document.write( "here's how it works.<BR>\n" );
document.write( "(a+b+c)/3 = 85<BR>\n" );
document.write( "this means that a+b+c = 3*85 = 255<BR>\n" );
document.write( "d joins the group and the average weight is now 81 kg.<BR>\n" );
document.write( "this means that (a+b+c+d)/4 = 81 which means that a+b+c+d = 4*81 = 324<BR>\n" );
document.write( "this means that d has to weight 324 - 255 = 69 kg.<BR>\n" );
document.write( "since e weighs 4 kg more than d, this means that e weighs 73 kg.<BR>\n" );
document.write( "when e replaces a, the average weight becomes 78 kg.<BR>\n" );
document.write( "this means the (b+c+d+e)/4 = 78<BR>\n" );
document.write( "this means that b+c+d+e = 78*4 = 312 kg.<BR>\n" );
document.write( "we have:<BR>\n" );
document.write( "a+b+c+d = 324 kg<BR>\n" );
document.write( "b+c+d+e = 312 kg<BR>\n" );
document.write( "the difference is 12 kg.<BR>\n" );
document.write( "the difference from the first equation to the second equation is equal to -12.<BR>\n" );
document.write( "this means that the second equation is 12 kg less than the first equation.<BR>\n" );
document.write( "in order to get there, we subtracted a and added e.<BR>\n" );
document.write( "this means that e-a = -12<BR>\n" );
document.write( "we know that e is equal to 73 kg, so the equation becomes:<BR>\n" );
document.write( "73-a = -12<BR>\n" );
document.write( "if we add a to both sides of this equation and add 12 to both sides of this equation we get:<BR>\n" );
document.write( "73+12 = a<BR>\n" );
document.write( "combine like terms to get 85 = a<BR>\n" );
document.write( "commute this result to get:<BR>\n" );
document.write( "a = 85 kg.<BR>\n" );
document.write( "we started off with a+b+c = 3*85<BR>\n" );
document.write( "since a is equal to 85, this equation becomes:<BR>\n" );
document.write( "85+b+c = 3*85 = 255<BR>\n" );
document.write( "we added d to get:<BR>\n" );
document.write( "85+b+c+d = 4*81 = 324<BR>\n" );
document.write( "we found out that d was equal to 324-255 = 69 kg<BR>\n" );
document.write( "we found out that e was equal to 69+4 = 73 kg<BR>\n" );
document.write( "with d equal to 69 kg, our equation became:<BR>\n" );
document.write( "85+b+c+69 = 324<BR>\n" );
document.write( "we got rid of a and added e so our equation became:<BR>\n" );
document.write( "b+c+69+73 = 312<BR>\n" );
document.write( "what happened was we lost 85 kg and gained 73 kg.<BR>\n" );
document.write( "324 - 85 + 73 = 312<BR>\n" );
document.write( "the fact that a is equal to 85 kg makes this correct.<BR>\n" );
document.write( "the key to solving this problem is that the average times the number of elements is equal to the total.<BR>\n" );
document.write( "(a+b+c)/3 = 85 which is the average<BR>\n" );
document.write( "the average of 85 * 3 = 255 which is the total.<BR>\n" );
document.write( "that concept makes the problem doable.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );