Final answer:
Upon solving the equation for when the two car rental plans cost the same, an error has been made as the calculated miles do not match any of the given options (500, 600, 700, 800 miles). Incorrect calculations indicate a mileage of 250 miles, which is not listed. It's best to re-check the calculations or seek further assistance.
Step-by-step explanation:
To find out when the two car rental plans cost the same, we need to set up an equation where the total cost of the first plan equals the total cost of the second plan. Let x be the number of miles driven. The first plan's cost is $52 plus $0.17 per mile, which is expressed as 52 + 0.17x. The second plan's cost is $57 plus $0.15 per mile, written as 57 + 0.15x.
To find the mileage where both plans cost the same, we solve for x in the equation 52 + 0.17x = 57 + 0.15x.
- Subtract 0.15x from both sides: 52 + 0.02x = 57.
- Subtract 52 from both sides: 0.02x = 5.
- Divide both sides by 0.02: x = 5 / 0.02.
- x = 250 miles, which is not an option given in the question, indicating possible miscalculation or misunderstanding.
- If we re-calculate correctly:
- Subtract 0.15x from both sides: 52 + 0.02x = 57.
- Subtract 52 from both sides: 0.02x = 5.
- Divide both sides by 0.02: x = 5 / 0.02.
- x = 250 is not listed in the options.
However, if we re-evaluate our equation and solve it properly, we would find the correct mileage:
- Subtract 0.17x from both sides: 52 = 57 - 0.02x.
- Subtract 57 from both sides: -5 = -0.02x.
- Divide both sides by -0.02: x = 250.
The correct answer should provide one of the options given a, b, c, or d. In this scenario, it appears I have made an error, as my solution does not match any of the provided choices. Therefore, I am unable to confidently provide the correct answer to this question and recommend reviewing your notes or asking your teacher for clarification.