Question 1143081
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Here is a very non-traditional, non-algebraic method for solving this problem.<br>
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>
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>
Here is all that is needed to solve the problem with this method:<br>
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>
That's it!  One line with rather simple calculations.<br>
With 100 students, that means 30 students are in the 70% average group, so the other 70 are in the 60% average group.<br>
ANSWER: 30 female students and 70 male students; a difference of 40.