There were an equal number of girls in Class H and Class J. ⁵₆ of the students in Class H and ¹₃ of the students in Class J are boys. If there are 54 more boys in Class H than in Class J, what is the total number of students in Class H and Class J?
Fraction of the students in Class H that are girls
= 1 - ⁵₆
=  ¹₆

Fraction of the students in Class J that are girls
= 1 - ¹₃
= ²₃ 

The number of girls in Class H is equal to the number of girls in Class J. LCM of 1 and 2 is 2. Make the numerators the same. 

 1x26x2 Class H = 23 Class J 
 212 Class H = 23 Class J

Number of girls in each class = 2 u

Total number of students in Class H = 12 u
Total number of students in Class J = 3 u

Number of boys in Class H
= 12 u - 2 u
= 10 u

Number of boys in Class J
= 3 u - 2 u
= 1 u

Number of more boys in Class H than Class J
= 10 u - 1 u
= 9 u

9 u = 54

1 u = 54 ÷ 9 = 6

Total number of students
= 12 u + 3 u
= 15 u
= 15 x 6
= 90

Answer(s): 90