First take the 19 teachers out of 406 to get the students. Cut the students into 9 units: 4 are boys, the other 5 are girls.

boys 4/9girls 5/99 units = 387 students

Plain numbers are given; italic underlined numbers are worked out.

  1. Students → 406 − 19 = 387
  2. 9 units → 387
  3. 1 unit → 387 ÷ 9 = 43
  4. Girls − boys → 5 units − 4 units = 1 unit = 43

There are 43 more girls than boys.

Check: boys 172 + girls 215 = 387; 215 − 172 = 43. ✓