SOLUTION: In a class of 52 students 16 are science students. If 1/3 of the boys and 1/4 of the girls assign students, how many boys are in the class?

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Question 1163227: In a class of 52 students 16 are science students. If 1/3 of the boys and 1/4 of the girls assign students, how many boys are in the class?
Found 3 solutions by ankor@dixie-net.com, greenestamps, ikleyn:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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In a class of 52 students 16 are science students.
If 1/3 of the boys and 1/4 of the girls science students, how many boys are in the class?
:
let b = no. of boys
then since the total students is 52,
(52-b) = no. of girls
:
1%2F3b + 1%2F4(52-b) = 16
get rid of the denominators, multiply equation by 12
4b + 3(52-b) = 12 * 16
4b + 156 - 3b = 192
4b - 3b = 192 - 156
b = 36 boys in the class.
:
:
See if that checks out
52 - 36 = 16 girls
1%2F3(36) + 1%2F4(16) =
12 + 4 = 16

Answer by greenestamps(13200) About Me  (Show Source):
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The solution from the other tutor is fine....

Given the way the information is given, I would prefer to use two variables, leading to a solution using elimination.

The total number of students is 52:
(1) b%2Bg+=+52

The total number of science students is 16:
(2) %281%2F3%29b%2B%281%2F4%29g+=+16

Multiply (2) by 4 and compare to (1):

%284%2F3%29b%2Bg+=+64
b%2Bg+=+52
%281%2F3%29b+=+12
b+=+36

ANSWER: There are 36 boys in the class.

CHECK:
36 boys means 16 girls
(1/3)(36)+(1/4)(16) = 12+4 = 16

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
In a class of 52 students 16 are science students.
If 1/3 of the boys and 1/4 of the girls highlight%28cross%28assign%29%29  are  a  Science  students,  how many boys are in the class?
~~~~~~~~~~~~~


            To make an impression  (and to shake your mind),  I can solve the problem differently. 


Let x be  1%2F3  of the boys  and  let y be  1%2F4  of the girls in the class.


Then the number of boys is 3x and the number of girls is 4y.


So we have two equations


     x +  y = 16      (1)

    3x + 4y = 52.     (2)


It is equivalent to  (after multiplying the first equation by 3)


    3x + 3y = 48      (3)

    3x + 4y = 52.     (4)


which implies  (subtracting equation (3) from (4) )


          y = 52 - 48 = 4.


Thus the number of girls in the class is 4*4 = 16,  and the boys are the rest population  52 - 16 = 36.

Solved.

What I did  (introduced the unknowns by a non-standard way)  may work productively and facilitate solutions in many other cases.