Let \( x \) be the hotel charge before tax in the first city. Then, the hotel charge before tax in the second city would be \( x + 1000 \).
The tax in the first city is calculated as: \[ \text{Tax in first city} = 0.085x \]
The tax in the second city is calculated as: \[ \text{Tax in second city} = 0.055(x + 1000) \]
Given that the total hotel tax paid for the two cities was $790, we can set up the following equation: \[ 0.085x + 0.055(x + 1000) = 790 \]
Now, let's simplify the equation: \[ 0.085x + 0.055x + 0.055 \times 1000 = 790 \] \[ 0.085x + 0.055x + 55 = 790 \] \[ 0.14x + 55 = 790 \]
Next, we will isolate \( x \): \[ 0.14x = 790 - 55 \] \[ 0.14x = 735 \] \[ x = \frac{735}{0.14} = 5250 \]
Thus, the hotel charge before tax in the first city is \( x = 5250 \).
Now we can find the hotel charge in the second city: \[ x + 1000 = 5250 + 1000 = 6250 \]
To summarize:
- The hotel charge in the first city before tax is $5250.
- The hotel charge in the second city before tax is $6250.