Real-World Systems of Equations Practice

Question

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Question
Mrs. Gonzalez is going to rent a car for a business trip for one week. The total cost, C
, for Top-Notch Car Rental is $150 plus $0.35 per mile, m
. The total cost, C
, for Fleetwood Car Rental is $200 and $0.10 per mile, m
. Which company is less expensive for a 300-mile trip and by how much? Use 1 for Top-Notch Car Rental and 2 for Fleetwood Car Rental in the answer.(1 point)
The less expensive company is
by $
.

Answer 1

To find out which car rental company is less expensive for a 300-mile trip, we need to calculate the total cost \(C\) for each company based on the given formulas.

For Top-Notch Car Rental:

• Fixed cost: $150
• Variable cost per mile: $0.35
• Total miles: 300

The total cost for Top-Notch Car Rental can be calculated as follows: \[ C = 150 + 0.35m \] Substituting \(m = 300\): \[ C = 150 + 0.35 \times 300 \] \[ C = 150 + 105 \] \[ C = 255 \]

For Fleetwood Car Rental:

• Fixed cost: $200
• Variable cost per mile: $0.10
• Total miles: 300

The total cost for Fleetwood Car Rental is calculated as follows: \[ C = 200 + 0.10m \] Substituting \(m = 300\): \[ C = 200 + 0.10 \times 300 \] \[ C = 200 + 30 \] \[ C = 230 \]

Comparison:

• Total cost for Top-Notch Car Rental: $255
• Total cost for Fleetwood Car Rental: $230

Now to determine which company is less expensive and by how much: Fleetwood Car Rental is less expensive.

To find the difference in cost: \[ \text{Difference} = 255 - 230 = 25 \]

Final Answer: The less expensive company is 2 by $25.