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March 1st, 2015, 10:44 PM   #1
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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?
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March 1st, 2015, 10:59 PM   #2
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I would write:

$\displaystyle \frac{1}{3}B+\frac{1}{4}(52-B)=16$

$\displaystyle \frac{1}{3}B+13-\frac{1}{4}B=16$

$\displaystyle \frac{1}{12}B=3$

$\displaystyle B=36$
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March 2nd, 2015, 12:22 AM   #3
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Quote:
Originally Posted by Chikis View Post
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?
$\displaystyle b= nr.\ boys, \ \ g=nr.\ girls
\\\;\\
b+g=52\ \ \ (*)
\\\;\\
\dfrac{1}{3}b+\dfrac{1}{4}g = 16|_{\cdot 12}
\\\;\\
4b+3g+12\cdot16
\\\;\\
b+3b+3g = 12\cdot16
\\\;\\
b+3(b+g)=12\cdot16
\\\;\\
b=12\cdot16-3(b+g)\ \stackrel{(*)}{\Longrightarrow}\ b=12\cdot16-3\cdot52
\\\;\\
b=3(4\cdot16-52)=\ 3(64-52)=3\cdot12 = 36 .$
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March 2nd, 2015, 04:49 AM   #4
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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.
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March 2nd, 2015, 05:13 AM   #5
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Quote:
Originally Posted by MarkFL View Post
I would write:

$\displaystyle \frac{1}{3}B+\frac{1}{4}(52-B)=16$

$\displaystyle \frac{1}{3}B+13-\frac{1}{4}B=16$

$\displaystyle \frac{1}{12}B=3$

$\displaystyle B=36$
Why ? Could you please explain?
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March 2nd, 2015, 05:17 AM   #6
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Quote:
Originally Posted by aurel5 View Post
$\displaystyle b= nr.\ boys, \ \ g=nr.\ girls
\\\;\\
b+g=52\ \ \ (*)
\\\;\\
\dfrac{1}{3}b+\dfrac{1}{4}g = 16|_{\cdot 12}
\\\;\\
4b+3g+12\cdot16
\\\;\\
b+3b+3g = 12\cdot16
\\\;\\
b+3(b+g)=12\cdot16
\\\;\\
b=12\cdot16-3(b+g)\ \stackrel{(*)}{\Longrightarrow}\ b=12\cdot16-3\cdot52
\\\;\\
b=3(4\cdot16-52)=\ 3(64-52)=3\cdot12 = 36 .$
How? Could you explain?
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March 2nd, 2015, 06:32 AM   #7
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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.
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March 2nd, 2015, 10:15 AM   #8
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Quote:
Originally Posted by Chikis View Post
How? Could you explain?

Holding your hand over the pencil.

Your hand should be relaxed,
with the fingers and thumb lightly holding the pencil.

So and only so you will see ...
how the green grass grows.
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March 2nd, 2015, 12:05 PM   #9
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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.
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March 3rd, 2015, 01:16 AM   #10
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Just to clarify, what I was referring to was this:

$\displaystyle \frac{1}{3}B + \frac{1}{4}(52-B) = 13$

$\displaystyle \frac{1}{3}B$ is the number of boys who do science.

$\displaystyle (52-B)$ is the number of girls in the class, so

$\displaystyle \frac{1}{4}(52-B)$ 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
Thanks from MarkFL and phrack999
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