There were an equal number of girls in Class Q and Class R. ⁵₆ of the students in Class Q and ¹₄ of the students in Class R are boys. If there are 84 more boys in Class Q than in Class R, what is the total number of students in Class Q and Class R?
Fraction of the students in Class Q that are girls
= 1 - ⁵₆
=  ¹₆

Fraction of the students in Class R that are girls
= 1 - ¹₄
= ³₄ 

The number of girls in Class Q is equal to the number of girls in Class R. LCM of 1 and 3 is 3. Make the numerators the same. 

 1x36x3 Class Q = 34 Class R 
 318 Class Q = 34 Class R

Number of girls in each class = 3 u

Total number of students in Class Q = 18 u
Total number of students in Class R = 4 u

Number of boys in Class Q
= 18 u - 3 u
= 15 u

Number of boys in Class R
= 4 u - 3 u
= 1 u

Number of more boys in Class Q than Class R
= 15 u - 1 u
= 14 u

14 u = 84

1 u = 84 ÷ 14 = 6

Total number of students
= 18 u + 4 u
= 22 u
= 22 x 6
= 132

Answer(s): 132