My Math Forum How Many Male Students in a Class

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 May 24th, 2014, 04:27 AM #1 Senior Member     Joined: Nov 2010 From: Indonesia Posts: 2,001 Thanks: 132 Math Focus: Trigonometry 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?
 May 24th, 2014, 05:26 AM #2 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 m + f = 40 (74m + 69f) / (m + f) = 72 Take over, rover! Thanks from greg1313 and Haejang
May 24th, 2014, 07:12 AM   #3
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Quote:
 Originally Posted by Denis 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?

 May 24th, 2014, 05:45 PM #4 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond 2m = 3f 2m = 3(40 - m) (from m + f = 40) 2m = 120 - 3m 5m = 120 m = 24. Thanks from Monox D. I-Fly and v8archie
May 24th, 2014, 06:24 PM   #5
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Quote:
 Originally Posted by Monox D. I-Fly 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.

May 24th, 2014, 06:50 PM   #6
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Quote:
 Originally Posted by greg1313 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 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.

 May 24th, 2014, 08:38 PM #7 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,674 Thanks: 2654 Math Focus: Mainly analysis and algebra No, it says that if you double the number of males you get the same number as if you treble the number of females. $$2m = 3f \Longrightarrow m = \frac{3}{2}f \Longrightarrow m \gt f$$
 May 24th, 2014, 11:49 PM #8 Senior Member     Joined: Nov 2010 From: Indonesia Posts: 2,001 Thanks: 132 Math Focus: Trigonometry Oh, OK. Thank you.
 May 28th, 2014, 04:33 AM #9 Math Team   Joined: Apr 2010 Posts: 2,780 Thanks: 361 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. Thanks from Haejang

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