22. A travel agency has booked 231 passengers for a bus trip. Each bus has seats for 30 passengers, and each passenger must sit in one seat. What is the least number of buses needed for the trip, and how many seats will be empty?
Answer: D
Eight buses are needed for the trip, with 21 empty seats.
To accommodate 231 passengers, the travel agency needs at least eight buses since each bus can hold 30 passengers. With eight buses, 240 seats will be available, leaving 21 seats empty after seating all passengers.
A) 10 buses with 31 empty seats
This option is incorrect because it suggests that 10 buses are required, which would provide a total of 300 seats. This is unnecessary, as only eight buses are sufficient to seat all 231 passengers.
B) 9 buses with 21 empty seats
While this option correctly calculates the number of empty seats, it incorrectly states the number of buses required. Nine buses would provide 270 seats, which exceeds the requirement but is still more than the eight buses needed.
C) 8 buses with 31 empty seats
This option incorrectly states the number of empty seats. Eight buses provide 240 seats, which means there are only 21 empty seats, not 31.
D) 8 buses with 21 empty seats
This option accurately reflects the requirement for the trip. Eight buses will accommodate all 231 passengers and leave 21 empty seats, making it the correct answer.
E) 8 buses with 9 empty seats
This option is incorrect because it miscalculates the number of empty seats. With eight buses, there will be 21 empty seats available, not just 9.
Conclusion
The correct answer, option D, accurately represents the least number of buses needed and the number of empty seats. All other options either miscalculate the number of buses required or the number of empty seats available, demonstrating that they do not meet the problem's criteria.