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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: 14,412 Thanks: 1024 
m + f = 40 (74m + 69f) / (m + f) = 72 Take over, rover! 
May 24th, 2014, 07:12 AM  #3 
Senior Member Joined: Nov 2010 From: Indonesia Posts: 2,001 Thanks: 132 Math Focus: Trigonometry  
May 24th, 2014, 05:45 PM  #4 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,934 Thanks: 1128 Math Focus: Elementary mathematics and beyond 
2m = 3f 2m = 3(40  m) (from m + f = 40) 2m = 120  3m 5m = 120 m = 24. 
May 24th, 2014, 06:24 PM  #5 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,654 Thanks: 2632 Math Focus: Mainly analysis and algebra  
May 24th, 2014, 06:50 PM  #6  
Senior Member Joined: Nov 2010 From: Indonesia Posts: 2,001 Thanks: 132 Math Focus: Trigonometry  Quote:
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: 7,654 Thanks: 2632 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. 

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