Let d and m represent the daily and per-mile charges, respectively.
.. 3d +300m = 111.00 . . . . . . barney's charges
.. 5d +600m = 193.00 . . . . . mary's charges
You can double the first equation and subtract the second to find
.. d = 29
Then
.. m = (111 -3*29)/300 = 0.08
Best Rentals charges $29 per day and $0.08 per mile.