A theater group made appearances in two cities. The hotel charges before tax in the second city were $1,000 lower than in the first. The tax on the hotel bill was 5% in the first city and 4% in the second. After the trip, the total tax paid on accommodation expenses was $387.50. How much was the hotel bill in the first city before tax?

pretax bill in first city = $x : Tax = 5%

pretax bill in second city = x-1000: Tax = 4%
..
0.05x+0.04(x-1000)= 387.50
0.05x+0.04x-40=387.50
0.09x=387.50+40
0.09x=427.50
/0.09
x= $4750 Bill in first city

To solve this problem, we can set up a system of equations. Let's assume the hotel bill in the first city before tax is represented by x.

According to the information given, the hotel bill in the second city before tax is $1,000 lower than the first city, so it can be represented as (x - 1000).

The tax on the hotel bill in the first city is 5%, which means 5% of the hotel bill in the first city is paid as tax. This can be expressed as 0.05x.

Similarly, the tax on the hotel bill in the second city is 4%, which means 4% of the hotel bill in the second city is paid as tax. This can be expressed as 0.04(x - 1000).

Given that the total tax paid on accommodation expenses is $387.50, we can set up the equation:

0.05x + 0.04(x - 1000) = 387.50

Now, we can solve this equation to find the value of x, which represents the hotel bill in the first city before tax.