SOLUTION: 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: Wha

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Question 1143081: 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?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
x, females
y, males
system%28x%2By=100%2C%2870x%2B60y%29%2F100=63%29
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7x%2B6y=630
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system%287x%2B6y=630%2C6x%2B6y=600%29
E1-E2:
x=30,meaningthat y=70

Forty more female students than male students.

Answer by greenestamps(13214) About Me  (Show Source):
You can put this solution on YOUR website!


Here is a very non-traditional, non-algebraic method for solving this problem.

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%.

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.

Here is all that is needed to solve the problem with this method:

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.

That's it! One line with rather simple calculations.

With 100 students, that means 30 students are in the 70% average group, so the other 70 are in the 60% average group.

ANSWER: 30 female students and 70 male students; a difference of 40.