Solving a tax rate or interest rate problem using a system of linear equations

Question

A theater group made appearances in two cities. The hotel charge before tax in the second city was $1000 lower than in the first. The tax in the first city was 8%, and the tax in the second city was 8.5%. The total hotel tax paid for the two cities was $781.25. 

How much was the hotel charge in each city before tax?

First city:

Second city:

Answer 1

TL;DR

Hotel 1 = $5250

Hotel 2 = $4250

Answer 2

Let S = pretax price for 2nd

F = pretax for 1st

F-S = 1000

8F + 8.5S = 78125

8F -8S = 8000

16.5S = 70125

S = $4,382.81

L = $5,382.81