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May 24th, 2014, 04:27 AM   #1
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How Many Male Students in a Class

The average score of a class which consists 40 students is 72. If the male students' average score is 74 and the female students' average score is 69, how many male students are in that class?
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May 24th, 2014, 05:26 AM   #2
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m + f = 40

(74m + 69f) / (m + f) = 72

Take over, rover!
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May 24th, 2014, 07:12 AM   #3
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Quote:
Originally Posted by Denis View Post
m + f = 40

(74m + 69f) / (m + f) = 72

Take over, rover!
74m + 69f = 72 (m + f)
74m + 69f = 72m + 72f
74m - 72m = 72f - 69f
2m = 3f

m = 2 / (2 + 3) x 40
m = 2/5 x 40
m = 16?
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May 24th, 2014, 05:45 PM   #4
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2m = 3f
2m = 3(40 - m) (from m + f = 40)
2m = 120 - 3m
5m = 120
m = 24.
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May 24th, 2014, 06:24 PM   #5
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Quote:
Originally Posted by Monox D. I-Fly View Post
2m = 3f

m = 2 / (2 + 3) x 40
m = 2/5 x 40
m = 16?
Your approach is fine here, it's just that 2m = 3f implies that m is three-fifths of 40, not two-fifths.
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May 24th, 2014, 06:50 PM   #6
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Quote:
Originally Posted by greg1313 View Post
2m = 3f
2m = 3(40 - m) (from m + f = 40)
2m = 120 - 3m
5m = 120
m = 24.
Thanks for the explanation. I thought it could only be solved using elimination. I forgot that it could be solved using substitution.

Quote:
Originally Posted by v8archie View Post
Your approach is fine here, it's just that 2m = 3f implies that m is three-fifths of 40, not two-fifths.
I thought that for every 2 males, there were 3 females.
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May 24th, 2014, 08:38 PM   #7
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No, it says that if you double the number of males you get the same number as if you treble the number of females.
$$2m = 3f \Longrightarrow m = \frac{3}{2}f \Longrightarrow m \gt f$$
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May 24th, 2014, 11:49 PM   #8
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Oh, OK. Thank you.
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May 28th, 2014, 04:33 AM   #9
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Or:
A total of 72 * 40 = 2880 points are scored. If all students are male then
a total of (72 + 2) * 40 = 2880 + 80 points are scored, 80 too many.
If a male student is replaced by a female, the total number of points drops by 74 - 69 = 5 points. To drop 80 points, 16 males should be replaced by females which leaves 24 male- and 16 female students.
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