A theater group made appearances in two cities. The hotel charge before tax in the second city was US$1000 lower than in the first. The tax in the first city was 5%, and the tax in the second city was 5,5%. The total hotel tax paid for the two cities was US$286,25. How much was the hotel charge in each city before tax?

Let's denote the hotel charge before tax in the first city as $x$ and in the second city as $y$.

From the problem, we know:

1. The hotel charge before tax in the second city was $1000 lower than in the first city. $y = x - 1000$

2. The tax in the first city was 5%, and the tax in the second city was 5.5%.

3. The total hotel tax paid for the two cities was $286.25.

The tax paid in the first city is: $0.05x$

The tax paid in the second city is: $0.055y$

The total tax paid is: $0.05x + 0.055y = 286.25$

Now, substitute $y$ from the first equation into the second equation: $0.05x + 0.055(x - 1000) = 286.25$

Simplify and solve for $x$: $0.05x + 0.055x - 55 = 286.25$ $0.105x - 55 = 286.25$ $0.105x = 341.25$ $x = \frac{341.25}{0.105}$ $x = 3250$

Now, substitute $x$ back into the equation for $y$: $y = x - 1000$ $y = 3250 - 1000$ $y = 2250$

Therefore, the hotel charge before tax in the first city was $3250, and in the second city, it was$2250.