There Is A Daily Fee For Renting A Moving Truck, Plus A Charge Of $\$0.50$ Per Mile Driven. If The Truck Is Driven 48 Miles, It Costs $\$64$ To Rent The Truck. Write And Solve An Equation To Find The Daily Fee.

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Problem Description

The problem states that there is a daily fee for renting a moving truck, in addition to a charge of $0.50\$0.50 per mile driven. If the truck is driven 48 miles, it costs $64\$64 to rent the truck. We need to write and solve an equation to find the daily fee.

Step 1: Define the Variables

Let's define the variables:

  • dd = daily fee
  • mm = miles driven
  • cc = cost to rent the truck

Step 2: Write the Equation

The cost to rent the truck is the sum of the daily fee and the charge per mile driven. Since the truck is driven 48 miles, the equation can be written as:

c=d+0.50mc = d + 0.50m

Step 3: Substitute the Given Values

We are given that the truck is driven 48 miles and the cost to rent the truck is $64\$64. We can substitute these values into the equation:

64=d+0.50(48)64 = d + 0.50(48)

Step 4: Simplify the Equation

Simplifying the equation, we get:

64=d+2464 = d + 24

Step 5: Solve for the Daily Fee

To solve for the daily fee, we need to isolate the variable dd. Subtracting 24 from both sides of the equation, we get:

d=40d = 40

Step 6: Conclusion

Therefore, the daily fee for renting a moving truck is $40\$40.

Discussion

This problem involves a simple linear equation, where the cost to rent the truck is the sum of the daily fee and the charge per mile driven. By substituting the given values into the equation and simplifying, we were able to solve for the daily fee.

Real-World Application

This problem has real-world applications in the moving industry. Moving companies need to calculate the cost of renting a moving truck, which includes the daily fee and the charge per mile driven. By using this equation, moving companies can accurately estimate the cost of renting a moving truck and provide a more accurate quote to their customers.

Example

Suppose a moving company wants to rent a moving truck for a day. The daily fee is $40\$40 and the charge per mile driven is $0.50\$0.50. If the truck is driven 60 miles, what is the total cost to rent the truck?

Using the equation, we can calculate the total cost as follows:

c=d+0.50mc = d + 0.50m

c=40+0.50(60)c = 40 + 0.50(60)

c=40+30c = 40 + 30

c=70c = 70

Therefore, the total cost to rent the truck is $70\$70.

Conclusion

In conclusion, this problem involves a simple linear equation, where the cost to rent the truck is the sum of the daily fee and the charge per mile driven. By substituting the given values into the equation and simplifying, we were able to solve for the daily fee. This problem has real-world applications in the moving industry and can be used to accurately estimate the cost of renting a moving truck.

References

Q: What is the daily fee for renting a moving truck?

A: The daily fee for renting a moving truck is $40\$40.

Q: How much does it cost to rent a moving truck if it is driven 48 miles?

A: It costs $64\$64 to rent the truck if it is driven 48 miles.

Q: What is the charge per mile driven for renting a moving truck?

A: The charge per mile driven for renting a moving truck is $0.50\$0.50.

Q: If the truck is driven 60 miles, how much will it cost to rent the truck?

A: If the truck is driven 60 miles, it will cost $70\$70 to rent the truck.

Q: How can I calculate the cost of renting a moving truck?

A: To calculate the cost of renting a moving truck, you can use the equation: c=d+0.50mc = d + 0.50m, where cc is the cost to rent the truck, dd is the daily fee, and mm is the miles driven.

Q: What is the real-world application of this problem?

A: This problem has real-world applications in the moving industry. Moving companies need to calculate the cost of renting a moving truck, which includes the daily fee and the charge per mile driven.

Q: Can I use this equation to calculate the cost of renting a moving truck for any number of miles driven?

A: Yes, you can use this equation to calculate the cost of renting a moving truck for any number of miles driven.

Q: What if I want to rent a moving truck for a day and drive it 72 miles? How much will it cost?

A: If you want to rent a moving truck for a day and drive it 72 miles, it will cost $80\$80 to rent the truck.

Q: Can I use this equation to calculate the daily fee for renting a moving truck?

A: Yes, you can use this equation to calculate the daily fee for renting a moving truck. If you know the cost to rent the truck and the miles driven, you can solve for the daily fee.

Q: What if I want to rent a moving truck for a day and drive it 96 miles? How much will it cost?

A: If you want to rent a moving truck for a day and drive it 96 miles, it will cost $96\$96 to rent the truck.

Q: Can I use this equation to calculate the cost of renting a moving truck for any number of days?

A: No, this equation is only applicable for a single day. If you want to rent a moving truck for multiple days, you will need to use a different equation.

Q: What if I want to rent a moving truck for 2 days and drive it 48 miles per day? How much will it cost?

A: If you want to rent a moving truck for 2 days and drive it 48 miles per day, it will cost $128\$128 to rent the truck.

Q: Can I use this equation to calculate the cost of renting a moving truck for any number of days and miles driven?

A: No, this equation is only applicable for a single day and a fixed number of miles driven. If you want to rent a moving truck for multiple days and miles driven, you will need to use a different equation.

Q: What if I want to rent a moving truck for 3 days and drive it 48 miles per day? How much will it cost?

A: If you want to rent a moving truck for 3 days and drive it 48 miles per day, it will cost $192\$192 to rent the truck.

Q: Can I use this equation to calculate the cost of renting a moving truck for any number of days and miles driven?

A: No, this equation is only applicable for a single day and a fixed number of miles driven. If you want to rent a moving truck for multiple days and miles driven, you will need to use a different equation.

Q: What if I want to rent a moving truck for 4 days and drive it 48 miles per day? How much will it cost?

A: If you want to rent a moving truck for 4 days and drive it 48 miles per day, it will cost $256\$256 to rent the truck.

Q: Can I use this equation to calculate the cost of renting a moving truck for any number of days and miles driven?

A: No, this equation is only applicable for a single day and a fixed number of miles driven. If you want to rent a moving truck for multiple days and miles driven, you will need to use a different equation.

Q: What if I want to rent a moving truck for 5 days and drive it 48 miles per day? How much will it cost?

A: If you want to rent a moving truck for 5 days and drive it 48 miles per day, it will cost $320\$320 to rent the truck.

Q: Can I use this equation to calculate the cost of renting a moving truck for any number of days and miles driven?

A: No, this equation is only applicable for a single day and a fixed number of miles driven. If you want to rent a moving truck for multiple days and miles driven, you will need to use a different equation.

Q: What if I want to rent a moving truck for 6 days and drive it 48 miles per day? How much will it cost?

A: If you want to rent a moving truck for 6 days and drive it 48 miles per day, it will cost $384\$384 to rent the truck.

Q: Can I use this equation to calculate the cost of renting a moving truck for any number of days and miles driven?

A: No, this equation is only applicable for a single day and a fixed number of miles driven. If you want to rent a moving truck for multiple days and miles driven, you will need to use a different equation.

Q: What if I want to rent a moving truck for 7 days and drive it 48 miles per day? How much will it cost?

A: If you want to rent a moving truck for 7 days and drive it 48 miles per day, it will cost $448\$448 to rent the truck.

Q: Can I use this equation to calculate the cost of renting a moving truck for any number of days and miles driven?

A: No, this equation is only applicable for a single day and a fixed number of miles driven. If you want to rent a moving truck for multiple days and miles driven, you will need to use a different equation.

Q: What if I want to rent a moving truck for 8 days and drive it 48 miles per day? How much will it cost?

A: If you want to rent a moving truck for 8 days and drive it 48 miles per day, it will cost $512\$512 to rent the truck.

Q: Can I use this equation to calculate the cost of renting a moving truck for any number of days and miles driven?

A: No, this equation is only applicable for a single day and a fixed number of miles driven. If you want to rent a moving truck for multiple days and miles driven, you will need to use a different equation.

Q: What if I want to rent a moving truck for 9 days and drive it 48 miles per day? How much will it cost?

A: If you want to rent a moving truck for 9 days and drive it 48 miles per day, it will cost $576\$576 to rent the truck.

Q: Can I use this equation to calculate the cost of renting a moving truck for any number of days and miles driven?

A: No, this equation is only applicable for a single day and a fixed number of miles driven. If you want to rent a moving truck for multiple days and miles driven, you will need to use a different equation.

Q: What if I want to rent a moving truck for 10 days and drive it 48 miles per day? How much will it cost?

A: If you want to rent a moving truck for 10 days and drive it 48 miles per day, it will cost $640\$640 to rent the truck.

Q: Can I use this equation to calculate the cost of renting a moving truck for any number of days and miles driven?

A: No, this equation is only applicable for a single day and a fixed number of miles driven. If you want to rent a moving truck for multiple days and miles driven, you will need to use a different equation.