document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1182520>Question 1182520</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Four teams play in a soccer tournament. Each team plays one game against each of the other three teams. Teams earn 3 points for a win, 1 point for a draw and 0 points for a loss. After all the games have been played, one team has 6 points, two teams have 4 points and one team has 3 points. How many games ended in a draw? </SPAN>\n" );
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document.write( "With four teams each playing each other team once, there were C(4,2)=6 games played.<br><BR>\n" );
document.write( "For each game in which one team won, a total of 3+0=3 points were awarded; for each game that ended in a draw, a total of 1+1=2 points were awarded.<br><BR>\n" );
document.write( "The total points awarded were 6+4+4+3 = 17.<br><BR>\n" );
document.write( "Informally, 6 integers each either 2 or 3 with a sum of 17 means five 3's and one 2, meaning one game ended in a draw.<br><BR>\n" );
document.write( "ANSWER: 1 game ended in a draw.<br><BR>\n" );
document.write( "Formally....<br><BR>\n" );
document.write( "Let x be the number of games that ended in a draw<BR>\n" );
document.write( "Let y be the number of games in which one team won<br><BR>\n" );
document.write( "[1] x+y=6<BR>\n" );
document.write( "[2] 2x+3y=17<br><BR>\n" );
document.write( "[3] 3x+3y=18 [1], times 3<br><BR>\n" );
document.write( "[4] x=1 [3] minus [2]<br><BR>\n" );
document.write( "ANSWER: The number of games that ended in a draw was x=1.<br><BR>\n" );
document.write( " </SPAN>\n" );
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