document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=663902>Question 663902</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At the 2006 Winter Olympics in Italy, the top medal winner was Germany, which won a total of 29 medals. Germany won 1 more silver medal than gold and 5 more gold medals than bronze. Find the number of each type of medal won. How do I solve this? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #413044 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=413044\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> germany won 29 medals.<BR>\n" );
document.write( "germany won 1 more silver medal than gold and 5 more gold than bronze.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "let g = number of gold medals.<BR>\n" );
document.write( "let s = number of silver medals.<BR>\n" );
document.write( "let b = number of bronze medals.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the total number of medals won is 29 so you get:<BR>\n" );
document.write( "g + s + b = 29<BR>\n" );
document.write( "number of gold medals plus number of silver medals plus number of bronze medals = 29.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "now look at the relationships between the quantities of each type of medal.<BR>\n" );
document.write( "germany won 1 more silver than gold.<BR>\n" );
document.write( "this means that s = g + 1 which translates to the number of silver medals is equal to the number of gold medals plus 1.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "germany won 5 more gold medals than bronze.<BR>\n" );
document.write( "this means that g = b + 5 which translates to the number of gold medals is equal to the number of bronze medals plus 5.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you have 3 equation so far.<BR>\n" );
document.write( "they are:<BR>\n" );
document.write( "g + s + b = 29<BR>\n" );
document.write( "s = g + 1<BR>\n" );
document.write( "g = b + 5\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since s = g + 1, you can substitute for s in the original equation.<BR>\n" );
document.write( "since g = b + 5, you can substitute for g in the original equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "substitute for s first and then substitute for g.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when you substitute for s, g + s + b = 29 becomes g + (g + 1) + b = 29<BR>\n" );
document.write( "simplify to get 2g + b + 1 = 29\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "now substitute for g to get:<BR>\n" );
document.write( "2g + b + 1 = 29 becomes 2 * (b + 5) + b + 1 = 29<BR>\n" );
document.write( "simplify to get 3b + 11 = 29<BR>\n" );
document.write( "subtract 11 from both sides of the equation to get 3b = 18<BR>\n" );
document.write( "divide both sides of the equation by 3 to get b = 6\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "from the equation g = b + 5, substitute for b to get g = 6 + 5 which becomes g = 11 after combining like terms.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in the equation s = g + 1, substitute for g to get s = 11 + 1 which becomes s = 12 after combining like terms.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "b = 6<BR>\n" );
document.write( "g = 11<BR>\n" );
document.write( "s = 12\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "plug these values into the equation of g + s + b = 29 to see if the equation holds true.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you get 11 + 12 + 6 = 29 which becomes 29 = 29 which is true so you did good.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );