Your cousin bought a used car. He paid a total of $12,755 for the car. The total cost includes:

Let's denote the list price of the car as x.

The total cost including 7% sales tax and $450 in additional fees can be expressed as:
Total Cost = x + 0.07x + 450

Given that the total cost is $12,755, we can write:
12,755 = x + 0.07x + 450

Simplifying the equation:
12,755 = 1.07x + 450
12,755 - 450 = 1.07x
12,305 = 1.07x
x = 12,305 / 1.07
x = $11,500

Therefore, the list price of the car your cousin bought is $11,500.