Equation Modeling the Total Cost

Oct 13, 2025 by wbrum.org 60 views

Introduction

Renting a car can be a convenient and enjoyable way to travel, especially for road trips. However, it's essential to understand the costs involved to make informed decisions. In this article, we'll explore the total cost of renting a car, including a flat fee and a daily rate.

The Cost of Renting a Car

To rent a car, there is a flat fee of $50, plus $32 per day. We can model the total cost, denoted as ${ c }$ , for renting the car for ${ d }$ days using an equation.

Equation Modeling the Total Cost

Let's denote the total cost as ${ c }$ and the number of days as ${ d }$ . The flat fee is $50, and the daily rate is $32. We can write the equation as:

${ c = 50 + 32d }$

This equation represents the total cost of renting the car for ${ d }$ days.

Understanding the Equation

The equation ${ c = 50 + 32d }$ is a linear equation, where ${ c }$ is the dependent variable (the total cost), and ${ d }$ is the independent variable (the number of days). The equation has two components:

Flat Fee: The flat fee of $50 is a constant value that is added to the total cost.
Daily Rate: The daily rate of $32 is multiplied by the number of days to calculate the total cost.

Example: Calculating the Total Cost

Let's say Franklin is traveling with his family on a road trip and wants to rent a car for 5 days. Using the equation ${ c = 50 + 32d }$ , we can calculate the total cost as follows:

${ c = 50 + 32(5) }$ ${ c = 50 + 160 }$ ${ c = 210 }$

Therefore, the total cost of renting the car for 5 days is $210.

Graphing the Equation

We can graph the equation ${ c = 50 + 32d }$ to visualize the relationship between the total cost and the number of days. The graph will be a straight line with a positive slope, indicating that the total cost increases as the number of days increases.

Conclusion

In conclusion, the total cost of renting a car can be modeled using the equation ${ c = 50 + 32d }$ . This equation represents the flat fee and the daily rate, and it can be used to calculate the total cost for a given number of days. By understanding this equation, we can make informed decisions when renting a car for a road trip.

Real-World Applications

The equation ${ c = 50 + 32d }$ has real-world applications in various industries, such as:

Car Rental Companies: Car rental companies use this equation to calculate the total cost of renting a car for a given number of days.
Travel Agencies: Travel agencies use this equation to estimate the total cost of a road trip, including car rental fees.
Financial Institutions: Financial institutions use this equation to calculate the total cost of a loan or credit card payment.

Tips and Variations

Here are some tips and variations to consider when using the equation ${ c = 50 + 32d }$ :

Discounts: Some car rental companies offer discounts for long-term rentals. We can modify the equation to include a discount factor.
Additional Fees: Some car rental companies charge additional fees for services such as insurance or fuel. We can modify the equation to include these fees.
Non-Linear Relationships: In some cases, the relationship between the total cost and the number of days may be non-linear. We can use a non-linear equation to model this relationship.

Conclusion

Q: What is the total cost of renting a car for 3 days?

A: To calculate the total cost of renting a car for 3 days, we can use the equation ${ c = 50 + 32d }$ . Plugging in ${ d = 3 }$ , we get:

${ c = 50 + 32(3) }$ ${ c = 50 + 96 }$ ${ c = 146 }$

Therefore, the total cost of renting a car for 3 days is $146.

Q: How much will I save if I rent a car for 7 days instead of 5 days?

A: To calculate the savings, we need to calculate the total cost of renting a car for 7 days and 5 days, and then subtract the two amounts.

For 7 days:

${ c = 50 + 32(7) }$ ${ c = 50 + 224 }$ ${ c = 274 }$

For 5 days:

${ c = 50 + 32(5) }$ ${ c = 50 + 160 }$ ${ c = 210 }$

The savings is $274 - $210 = $64.

Q: What is the daily rate of the car rental company?

A: The daily rate of the car rental company is $32.

Q: How much will I pay if I rent a car for 10 days and get a 10% discount?

A: To calculate the total cost with a 10% discount, we need to first calculate the total cost without the discount, and then apply the discount.

For 10 days:

${ c = 50 + 32(10) }$ ${ c = 50 + 320 }$ ${ c = 370 }$

A 10% discount is $370 \times 0.10 = $37.

The total cost with the discount is $370 - $37 = $333.

Q: Can I use this equation to calculate the total cost of renting a car for a fraction of a day?

A: Yes, you can use this equation to calculate the total cost of renting a car for a fraction of a day. However, you need to round up to the nearest whole number of days, as you cannot rent a car for a fraction of a day.

For example, if you want to rent a car for 3.5 days, you would round up to 4 days, and then calculate the total cost using the equation.

Q: How can I modify the equation to include additional fees?

A: To modify the equation to include additional fees, you can add the additional fees to the total cost. For example, if the car rental company charges an additional $20 per day for insurance, you can modify the equation as follows:

${ c = 50 + 32d + 20d }$ ${ c = 50 + 52d }$

This equation includes the daily rate of $32 and the additional fee of $20 per day.

Q: Can I use this equation to calculate the total cost of renting a car for multiple cars?

A: Yes, you can use this equation to calculate the total cost of renting multiple cars. However, you need to multiply the total cost of one car by the number of cars.

For example, if you want to rent 2 cars for 5 days each, you would calculate the total cost of one car using the equation, and then multiply the result by 2.

Conclusion

In conclusion, the equation ${ c = 50 + 32d }$ is a simple and effective way to model the total cost of renting a car for a given number of days. By understanding this equation, we can make informed decisions when renting a car for a road trip.