To determine Alexandra's beginning odometer reading, we need to break down the problem step by step.

1. Calculate the number of gallons used during the trip:

We are told the total cost of the gas was $35.28, and the price per gallon is $2.45. To find out how many gallons she used, we divide the total bill by the price per gallon:

$\text{Gallons used} = \frac{\text{Total cost}}{\text{Price per gallon}} = \frac{35.28}{2.45} = 14.4 \text{ gallons}$

2. Calculate the number of miles driven:

Next, we use the car's fuel efficiency, which is 25 miles per gallon, to find the total number of miles Alexandra drove. Multiply the gallons used by the miles per gallon:

$\text{Miles driven} = \text{Gallons used} \times \text{Miles per gallon} = 14.4 \times 25 = 360 \text{ miles}$

3. Determine the beginning odometer reading:

The final odometer reading after the trip was 13,020.5 miles, and Alexandra drove 360 miles. Therefore, the beginning odometer reading can be found by subtracting the distance driven from the final reading:

$\text{Beginning odometer reading} = 13,020.5 - 360 = 12,660.5 \text{ miles}$

Final Answer:

The beginning odometer reading was 12,660.5 miles.

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Would you like further clarification on any step? Here are some related questions:

1. How would the result change if the car's fuel efficiency were different?
2. How could we calculate the total cost if Alexandra had driven a longer distance?
3. What happens if the price per gallon were higher?
4. How can we convert miles to kilometers in this problem?
5. What is the formula for calculating total fuel cost in any trip?

Tip: Always check the units for consistency when doing calculations like this.