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.
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• Students → 406 − 19 = 387
• 9 units → 387
• 1 unit → 387 ÷ 9 = 43
• 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. ✓