Final answer:
By calculating the fee per mile and the initial charge from the provided data, Houa would be charged $51.25 for driving 2.5 miles with the rented truck.
Step-by-step explanation:
To determine how much Houa would be charged for driving 2.5 miles with the rented truck, we need to understand the linear relationship between the miles driven (m) and the total cost (C). The information provided shows a linear pattern in cost relative to miles:
- Driving 2 miles costs $50.00
- Driving 3.5 miles costs $53.75
- Driving 8 miles costs $65.00
From these data points, we can calculate the fee per mile by looking at the difference in cost over the difference in distance between any two points. For example, using the 2 miles and 3.5 miles data points:
Fee per mile = (Cost at 3.5 miles - Cost at 2 miles) / (3.5 miles - 2 miles)
Fee per mile = ($53.75 - $50.00) / (3.5 miles - 2 miles)
Fee per mile = $3.75 / 1.5 miles
Fee per mile = $2.50 per mile
To find the initial charge, we now subtract the cost of the miles driven from the total cost for any of the provided data points. Using the 2 miles data point:
Initial charge = Total cost at 2 miles - (Fee per mile × 2 miles)
Initial charge = $50.00 - ($2.50 per mile × 2 miles)
Initial charge = $50.00 - $5.00
Initial charge = $45.00
Now, to calculate the total cost for driving 2.5 miles, we use the initial charge plus the fee per mile for 2.5 miles:
Total cost for 2.5 miles = Initial charge + (Fee per mile × 2.5 miles)
Total cost for 2.5 miles = $45.00 + ($2.50 per mile × 2.5 miles)
Total cost for 2.5 miles = $45.00 + $6.25
Total cost for 2.5 miles = $51.25
Therefore, Houa would be charged $51.25 for driving 2.5 miles with the rented truck.