Question 1163227
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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 {{{highlight(cross(assign))}}} &nbsp;<U>are &nbsp;a &nbsp;Science</U> &nbsp;students, &nbsp;how many boys are in the class?
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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;To make an impression &nbsp;(and to shake your mind), &nbsp;I can solve the problem differently.



<pre>
Let x be  {{{1/3}}}  of the boys  and  let y be  {{{1/4}}}  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.
</pre>

Solved.


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