March 1st, 2015, 09:44 PM  #1 
Senior Member Joined: Jan 2012 Posts: 721 Thanks: 7  How many boys are in the class?
In a class of 52 students, 16 are science students. If 1/3 of the boys and 1/4 of the girls are science students, how many boys are in the class? Total no of student in class = 52 no of science student = 16 no of non science student = 52  16 = 36 1/3 of the boys = science students 1/4 of the girls = science students How do I know the number of girls or boys in non science class? 
March 1st, 2015, 09:59 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 466 Math Focus: Calculus/ODEs 
I would write: $\displaystyle \frac{1}{3}B+\frac{1}{4}(52B)=16$ $\displaystyle \frac{1}{3}B+13\frac{1}{4}B=16$ $\displaystyle \frac{1}{12}B=3$ $\displaystyle B=36$ 
March 1st, 2015, 11:22 PM  #3  
Senior Member Joined: Apr 2014 From: Europa Posts: 571 Thanks: 176  Quote:
\\\;\\ b+g=52\ \ \ (*) \\\;\\ \dfrac{1}{3}b+\dfrac{1}{4}g = 16_{\cdot 12} \\\;\\ 4b+3g+12\cdot16 \\\;\\ b+3b+3g = 12\cdot16 \\\;\\ b+3(b+g)=12\cdot16 \\\;\\ b=12\cdot163(b+g)\ \stackrel{(*)}{\Longrightarrow}\ b=12\cdot163\cdot52 \\\;\\ b=3(4\cdot1652)=\ 3(6452)=3\cdot12 = 36 .$  
March 2nd, 2015, 03:49 AM  #4 
Math Team Joined: Apr 2010 Posts: 2,778 Thanks: 361 
Alternatively, similar to MarkFL's method, Suppose all students are girls. Then, there are 52 girls and 13 are science students. Replacing one girl with one boy adds 1/3  1/4 = 1/12 science student. We lack 16  13 = 3 sciencestudent. So replace 3 / (1/12) = 3 * 12 = 36 girls with 36 boys and we have 36 boys and (52  36 = 16) girls. 
March 2nd, 2015, 04:13 AM  #5 
Senior Member Joined: Jan 2012 Posts: 721 Thanks: 7  
March 2nd, 2015, 04:17 AM  #6  
Senior Member Joined: Jan 2012 Posts: 721 Thanks: 7  Quote:
 
March 2nd, 2015, 05:32 AM  #7 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,103 Thanks: 704 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
Look at the first equation of MarkFL's method and ask yourself what each term represents. For example, what might B mean? What does $\displaystyle \frac{1}{3}B$ represent? If you do this, you'll realise that it's quite obvious how the equation is derived. We could tell you straight, but you'd probably kick yourself. 
March 2nd, 2015, 09:15 AM  #8 
Senior Member Joined: Apr 2014 From: Europa Posts: 571 Thanks: 176  
March 2nd, 2015, 11:05 AM  #9 
Global Moderator Joined: Dec 2006 Posts: 18,962 Thanks: 1606 
Clearly, 1/4 of the boys and 1/4 of the girls would total 1/4 of 52, which is 13. As 1/3 of the boys exceeds 1/4 of the boys by 1/12 of the boys, 1/12 of the boys is equivalent to 3 boys, and so there are 36 boys. 
March 3rd, 2015, 12:16 AM  #10 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,103 Thanks: 704 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
Just to clarify, what I was referring to was this: $\displaystyle \frac{1}{3}B + \frac{1}{4}(52B) = 13$ $\displaystyle \frac{1}{3}B$ is the number of boys who do science. $\displaystyle (52B)$ is the number of girls in the class, so $\displaystyle \frac{1}{4}(52B)$ refers to the number of girls who do science. $\displaystyle 13$ is the total number of people who do science. Therefore, the first equation of MarkFL's answer is: number of boys who do science + number of girls who do science = total number of people who do science. The rest is just simplification to get a result. It's a nice answer 

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