A theater group made appearances in two cities. The hotel charge before tax in the second city was $500 lower than in the first. The tax in the first city was 6.5% and the tax in the second city was 4.5% The total hotel tax paid for the two cities was $582.50. How much was the hotel charge in each city before tax?

Answer:First city: $5,500Second city: $5,000Step-by-step explanation:Let's define x as the hotel price in the first city and y the hotel price in the second city.  We can start with this equation:y = x - 500 (The hotel before tax in the 2nd city was $500 lower than in the 1st.)Then we can say0.065x + 0.045y = 582.50  (the sum of the tax amounts were $582.50)We place the value of y from the first equation in the second equation:0.065x + 0.045 (x - 500) = 582.500.065x + 0.045x - 22.50 = 582.50 (simplifying and adding 22.5 on each side)...0.11x = 605x = 5,500The cost of the first hotel was $5,500Thus, the cost of the second hotel was $5,000 (x - 500)