A bus company has been contracted to transport 330 passengers 440 miles. Each bus will hold 55 passengers. Which inequality represents the solution set that shows the number of buses, b, that the bus company will use to transport the passengers?
To determine the number of buses needed, we will divide the total number of passengers by the number of passengers each bus can hold. However, because we can't have a fraction of a bus and you can't have more passengers than a bus can hold, we will need to round up to the next whole number to ensure that all passengers have a seat.
Given:
- Total number of passengers to transport: 330
- Capacity of one bus: 55 passengers
Let's calculate the number of buses needed by dividing the number of passengers by the capacity of each bus:
330 passengers / 55 passengers/bus = 6 buses
However, this is under the assumption that each passenger will be sitting and no extra buses will be needed for any reason.
When we write the inequality to represent the number of buses needed, we want to ensure that each bus is filled but we also need to cover any scenario where additional buses could be required for some reason (for instance, if not all seats can be filled for a particular trip). Therefore, we define the variable b as the number of buses, and the inequality should reflect that b must be greater than or equal to the number of buses needed for exactly 330 passengers:
b ≥ 330 / 55
Since 330 divided by 55 is 6, the inequality simplifies to:
b ≥ 6
However, since b must be a whole number, and we are dealing with people who cannot be divided amongst buses, we already know that 6 buses will suffice and not more than that would be needed if each bus is utilized to its full capacity. Hence, in reality, the buses needed would be exactly 6 for this scenario, and if we write this as an inequality it would indicate:
b ≥ 6
But keep in mind that b cannot be a fraction, so we are looking for the smallest integer value of b that is greater than or equal to 6. Given that 6 itself is an integer and fulfills this condition, the actual solution would be:
b = 6
Hence, the bus company will use 6 buses to transport the 330 passengers.