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 higher than in the first. The tax in the first city was 3.5%, and the tax in the second city was 3%. The total hotel tax paid for the two cities was $387.50. 

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

First city:

Second city:

Answer 1

Say the pre-tax charge in the first city was c. We are given that the charge in the second city was c + 1000.

The tax paid in the first city was c·0.035; the tax in the second city was (c + 1000) · 0.03.

The total tax paid was c·(0.035 + 0.03) + 1000 · 0.03 = c·0.065 + 30 = 387.50, so we're told.

Subtract 30 from both sides and divide by 0.065 to get c = 5500. That's the pre-tax charge in the first city, and in the second city we have 6500.