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?

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)   (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 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
:
b + (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
(36) + (16) =
12 + 4 = 16
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

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)

The total number of science students is 16:
(2)

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

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)   (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 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 of the boys and let y be 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.

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