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?

Rationale

8 buses with 21 empty seats.

To accommodate 231 passengers, the travel agency requires a minimum of 8 buses, as 8 x 30 equals 240 seats, leaving 21 seats unoccupied. This calculation ensures that all passengers have a seat while minimizing the number of buses used.

A (10 buses with 31 empty seats) YOUR ANSWER

Using 10 buses would provide 300 total seats (10 x 30), which is more than necessary for 231 passengers. While this option does ensure all passengers are seated, it is not the least number of buses required, as 8 buses suffice.

B (9 buses with 21 empty seats) YOUR ANSWER

Nine buses would yield 270 seats (9 x 30), indeed accommodating all 231 passengers with 39 empty seats. However, this exceeds the requirement of 8 buses, making it an inefficient choice.

C (8 buses with 31 empty seats) YOUR ANSWER

While 8 buses provide enough seats for the passengers, the calculation shows that 8 x 30 equals 240 seats, leaving only 21 empty. This option incorrectly states the number of empty seats.

D (8 buses with 21 empty seats) CORRECT

This is the correct choice. With 8 buses, there are 240 seats available, allowing for 231 passengers to be seated, resulting in 21 empty seats.

E (8 buses with 9 empty seats) YOUR ANSWER

This option incorrectly underestimates the number of empty seats. Eight buses yield 240 seats, and with 231 passengers, there are actually 21 seats left unoccupied, not 9.

Conclusion

The most efficient way to transport 231 passengers is by using 8 buses, which provides 240 seats and results in 21 empty seats. All other options either overestimate the number of buses needed or miscalculate the number of empty seats, highlighting the importance of accurate calculations in logistical planning.

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?

8 buses with 21 empty seats.

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