In a primary school the average weight of male students is 65.9 kg and the average weight of female students is 57 kg. If the average weight of all the students (both male and female) is 60.3 kg and the number of male students in the school is 66, what is the number of female students in the school?

Let the number of female students be x
Let the weight of female students = 57x
Number of male students = 66
Total weights of male students = 65.9 × 66
The average weight of all the students = 60.3 kg
Total weights of all the students = 60.3 (66 + x)

According to the given information,
Then,
⇒ 60.3 (66 + x) = 66 × 65.9 + 57x
⇒ 60.3 × 66 + 60.3x = 66 × 65.9 + 57x
⇒ 60.3x - 57x = 66 (65.9 - 60.3)
⇒ 3.3x = 66 × 5.6

∴ x = (66 × 5.6)/3.3
⇒ x = 2 × 56
⇒ x = 112