There were an equal number of boys in Class C and Class D. ⁵₆ of the students in Class C and ¹₅ of the students in Class D are girls. If there are 171 more girls in Class C than in Class D, what is the total number of students in Class C and Class D?
Fraction of the students in Class C that are boys
= 1 - ⁵₆
=  ¹₆

Fraction of the students in Class D that are boys
= 1 - ¹₅
= ⁴₅ 

The number of boys in Class C is equal to the number of boys in Class D. LCM of 1 and 4 is 4. Make the numerators the same. 

 1x46x4 Class C = 45 Class D 
 424 Class C = 45 Class D

Number of boys in each class = 4 u

Total number of students in Class C = 24 u
Total number of students in Class D = 5 u

Number of girls in Class C
= 24 u - 4 u
= 20 u

Number of girls in Class D
= 5 u - 4 u
= 1 u

Number of more girls in Class C than Class D
= 20 u - 1 u
= 19 u

19 u = 171

1 u = 171 ÷ 19 = 9

Total number of students
= 24 u + 5 u
= 29 u
= 29 x 9
= 261

Answer(s): 261