Total passengers = 390. Economy : Business = 11 : 2.<br><br>
[[model:questions/solutions/q10505.png]]<br><br>
Total units = 11 + 2 = 13 units<br>
&bull; 13 units → 390<br>
&bull; 1 unit → 390 ÷ 13 = 30<br>
&bull; Economy = 11 units = 11 × 30 = 330<br>
&bull; Business = 2 units = 2 × 30 = 60<br><br>
Now find those who did NOT check baggage:<br>
Economy &mdash; checked : didn't check = 4 : 1, so didn't check (economy) = \( \frac{1}{5} \) × 330 = 66<br>
Business &mdash; checked : didn't check = 9 : 1, so didn't check (business) = \( \frac{1}{10} \) × 60 = 6<br><br>
Total passengers who did not check baggage = 66 + 6 = 72<br>
Check: Checked economy = 264, checked business = 54. 66 + 6 + 264 + 54 = 390. ✓<br><br>
Final Answer: 72