document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1143081>Question 1143081</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 100 students enter a competition. The average score for the entire group is 63. The average score for male students is 60 and average score for female students is 70. Question: What is the difference in number of male and female students? </SPAN>\n" );
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document.write( "Here is a very non-traditional, non-algebraic method for solving this problem.<br><BR>\n" );
document.write( "Note that this is essentially a mixture problem -- you are mixing scores with an average of 60% with scores with an average of 70% and getting an overall average of 63%.<br><BR>\n" );
document.write( "To solve a mixture problem like this, you can consider the three percentages on a number line; where the average lies between the two percentages exactly determines the numbers of students with each average.<br><BR>\n" );
document.write( "Here is all that is needed to solve the problem with this method:<br><BR>\n" );
document.write( "63% is 3/10 of the way on the number line from 60% to 70%; that means 3/10 of the students are in the higher average group.<br><BR>\n" );
document.write( "That's it!  One line with rather simple calculations.<br><BR>\n" );
document.write( "With 100 students, that means 30 students are in the 70% average group, so the other 70 are in the 60% average group.<br><BR>\n" );
document.write( "ANSWER: 30 female students and 70 male students; a difference of 40. </SPAN>\n" );
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