Step 1 :Let \( s \) represent the number of students, \( a \) represent the number of adults, \( b \) represent the number of buses, \( t \) represent the total number of people, and \( p \) represent the number of people per bus.
Step 2 :We are given \( s = 267 \), \( a = 21 \), and \( b = 9 \).
Step 3 :First, we find the total number of people going on the trip by adding the number of students and adults: \( t = s + a \).
Step 4 :Substitute the given values into the equation: \( t = 267 + 21 \).
Step 5 :Simplify to find the total number of people: \( t = 288 \).
Step 6 :Next, we divide the total number of people by the number of buses to find the number of people per bus: \( p = \frac{t}{b} \).
Step 7 :Substitute the values into the equation: \( p = \frac{288}{9} \).
Step 8 :Simplify to find the number of people per bus: \( p = 32 \).
Step 9 :\(\boxed{32}\)