Question

384 conference attendees need to take tour shuttles into the city. If each bus can carry a maximum of 26 passengers, then what is the minimum number of shuttle trips required to transport all the passengers?

Short answer

The minimum number of shuttle trips required to transport all 384 conference attendees, given each shuttle can carry a maximum of 26 passengers, is \( \lceil \frac{384}{26} \rceil = 15 \) trips.

Step-by-step solution

Identify the given information

The problem states that there are 384 conference attendees who need to be transported, and each shuttle bus can carry a maximum of 26 passengers.

Calculate the number of shuttle bus trips needed by dividing the total number of attendees by the maximum number of passengers per shuttle

To find the minimum number of shuttle bus trips needed, we'll divide the total number of attendees (384) by the maximum number of passengers per shuttle (26): \( \frac{384}{26} = 14.76923076923077 \)

Round up the result

Since we cannot have a partial shuttle bus trip, we should round up the result obtained in the previous step. This means we need at least 15 shuttle trips to transport all the conference attendees. The minimum number of shuttle trips required to transport all 384 conference attendees is 15.

Key concepts

Division in Math

Division is one of the fundamental operations in mathematics, essential to numerous calculations and problem-solving scenarios. In essence, dividing two numbers means calculating how many times the divisor fits into the dividend. When tackling a problem which involves division, such as figuring out the minimum number of shuttle trips required to transport a certain number of people, we rely on this operation to determine an answer that indicates the number of times one operation, like a shuttle trip, must be repeated to reach a certain goal.

Using the problem at hand as an example, by dividing the total number of attendees, which is 384, by the maximum number of passengers per shuttle, 26, we can establish the minimum number of shuttle trips needed. However, when we carry out this division, we often encounter quotients that are not whole numbers. This leads us to the next critical aspect when dealing with division problems, especially in practical applications: rounding numbers.

Rounding Numbers

Rounding numbers is a mathematical technique used to simplify figures, making them easier to work with or comprehend. The decision to round up or down depends on the context of the problem. For numerical values with a fractional part, we can round them to the nearest whole number, but in the context of a problem where partial values do not make practical sense – such as partial shuttle trips in our example – it is essential to round up to ensure that the solution is realistic and fulfills the requirement.

In the shuttle bus problem, the division yielded a quotient of approximately 14.77, which means that making 14 trips would not be enough to transport all attendees. Therefore, we round up to the nearest whole number, which is 15, representing the minimum number of shuttle trips required to transport all 384 conference attendees without leaving anyone behind. Rounding up is critical here to align the mathematical solution with the practical application of the result.

Word Problem Strategies

When confronted with word problems, it's important to have a strategic approach for systematically translating a written scenario into a mathematical equation that can be solved. A powerful strategy is to start by identifying and writing down all the given information. In our example, the important details are the total number of attendees (384) and the maximum number of passengers per shuttle (26).

After identifying the key variables, the next step is to determine what's being asked—in this case, the minimum number of shuttle trips to transport all attendees. Then, set up an equation or operation, such as a division, that utilizes the given information to find the answer. It's also vital to interpret the result in the context of the problem, which will dictate whether you need to apply additional steps, such as rounding the numbers. Armed with these strategies, you can tackle word problems with greater confidence and precision.