Atheater 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?

First city: $5,500

Second city: $5,000

Step-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 say

0.065x + 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) = 582.50

0.065x + 0.045x - 22.50 = 582.50 (simplifying and adding 22.5 on each side)...

0.11x = 605

x = 5,500

The cost of the first hotel was $5,500

Thus, the cost of the second hotel was $5,000 (x - 500)

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step-by-step explanation: