Complete The Equation To Show The Relationship Between The Number Of Buses, $x$, And The Number Of People That Can Be Transported, $y$.$\[ \begin{array}{|c|c|} \hline \text{Buses} & \text{People Transported} \\ \hline 5 & 225

Introduction

In this article, we will explore the relationship between the number of buses and the number of people that can be transported. This is a classic problem in mathematics, and it can be solved using algebraic equations. We will start by analyzing the given data and then use it to form an equation that represents the relationship between the number of buses and the number of people transported.

Analyzing the Given Data

The given data shows that when there are 5 buses, 225 people can be transported. This information can be used to form an equation that represents the relationship between the number of buses and the number of people transported.

Forming the Equation

Let's assume that the number of buses is represented by the variable $x$ and the number of people transported is represented by the variable $y$. We know that when there are 5 buses, 225 people can be transported. This can be represented by the equation:

$$y = kx$$

where $k$ is a constant that represents the number of people that can be transported per bus.

Finding the Value of $k$

We can use the given data to find the value of $k$. When there are 5 buses, 225 people can be transported. This can be represented by the equation:

$$225 = k(5)$$

To find the value of $k$, we can divide both sides of the equation by 5:

$$k = \frac{225}{5}$$

$$k = 45$$

Writing the Equation

Now that we have found the value of $k$, we can write the equation that represents the relationship between the number of buses and the number of people transported:

$$y = 45x$$

This equation shows that the number of people transported is directly proportional to the number of buses. For every bus, 45 people can be transported.

Solving for $x$

If we know the number of people transported, we can use the equation to find the number of buses. For example, if 900 people are transported, we can use the equation to find the number of buses:

$$900 = 45x$$

To find the value of $x$, we can divide both sides of the equation by 45:

$$x = \frac{900}{45}$$

$$x = 20$$

This means that 20 buses are needed to transport 900 people.

Solving for $y$

If we know the number of buses, we can use the equation to find the number of people transported. For example, if there are 15 buses, we can use the equation to find the number of people transported:

$$y = 45(15)$$

$$y = 675$$

This means that 675 people can be transported with 15 buses.

Conclusion

In this article, we have explored the relationship between the number of buses and the number of people that can be transported. We have formed an equation that represents this relationship and used it to solve for the number of buses and the number of people transported. This equation can be used to plan transportation for large groups of people and to ensure that everyone has a safe and comfortable ride.

Real-World Applications

The equation we have formed has many real-world applications. For example, it can be used to plan transportation for large events such as concerts, festivals, and sporting events. It can also be used to plan transportation for large groups of people such as tourists, students, and workers.

Limitations

While the equation we have formed is useful, it has some limitations. For example, it assumes that each bus has the same capacity and that the number of people transported is directly proportional to the number of buses. In reality, the capacity of each bus may vary and the number of people transported may not be directly proportional to the number of buses.

Future Research

There are many areas of future research that could be explored. For example, researchers could investigate the relationship between the number of buses and the number of people transported in different scenarios such as urban and rural areas. They could also investigate the impact of different factors such as traffic congestion and road conditions on the number of people transported.

Conclusion

In conclusion, the equation we have formed represents the relationship between the number of buses and the number of people that can be transported. It can be used to plan transportation for large groups of people and to ensure that everyone has a safe and comfortable ride. While it has some limitations, it is a useful tool for understanding the relationship between the number of buses and the number of people transported.

Q: What is the equation that represents the relationship between the number of buses and the number of people transported?

A: The equation that represents the relationship between the number of buses and the number of people transported is:

$$y = 45x$$

This equation shows that the number of people transported is directly proportional to the number of buses. For every bus, 45 people can be transported.

Q: How do I use the equation to find the number of buses needed to transport a certain number of people?

A: To use the equation to find the number of buses needed to transport a certain number of people, you can rearrange the equation to solve for x:

$$x = \frac{y}{45}$$

For example, if you want to transport 900 people, you can plug in the value of y and solve for x:

$$x = \frac{900}{45}$$

$$x = 20$$

This means that 20 buses are needed to transport 900 people.

Q: How do I use the equation to find the number of people that can be transported with a certain number of buses?

A: To use the equation to find the number of people that can be transported with a certain number of buses, you can plug in the value of x and solve for y:

$$y = 45x$$

For example, if you have 15 buses, you can plug in the value of x and solve for y:

$$y = 45(15)$$

$$y = 675$$

This means that 675 people can be transported with 15 buses.

Q: What are some real-world applications of the equation?

A: The equation has many real-world applications, including:

• Planning transportation for large events such as concerts, festivals, and sporting events
• Planning transportation for large groups of people such as tourists, students, and workers
• Estimating the number of buses needed to transport a certain number of people
• Estimating the number of people that can be transported with a certain number of buses

Q: What are some limitations of the equation?

A: The equation assumes that each bus has the same capacity and that the number of people transported is directly proportional to the number of buses. In reality, the capacity of each bus may vary and the number of people transported may not be directly proportional to the number of buses.

Q: Can the equation be used to plan transportation for different scenarios such as urban and rural areas?

A: While the equation can be used to plan transportation for different scenarios, it may not be accurate in all cases. For example, in urban areas, the number of people transported may be affected by factors such as traffic congestion and road conditions. In rural areas, the number of people transported may be affected by factors such as the availability of buses and the distance between destinations.

Q: Can the equation be used to estimate the cost of transportation?

A: While the equation can be used to estimate the number of buses needed to transport a certain number of people, it cannot be used to estimate the cost of transportation. The cost of transportation will depend on factors such as the cost of buses, fuel, and maintenance, as well as the cost of hiring drivers and other personnel.

Q: Can the equation be used to plan transportation for different types of vehicles such as cars and trucks?

A: While the equation can be used to plan transportation for different types of vehicles, it may not be accurate in all cases. For example, the capacity of cars and trucks may vary, and the number of people transported may not be directly proportional to the number of vehicles.

Conclusion

In conclusion, the equation that represents the relationship between the number of buses and the number of people transported is a useful tool for planning transportation for large groups of people. However, it has some limitations and should be used in conjunction with other factors such as traffic congestion and road conditions to ensure accurate estimates.