A theater group made appearances in two countries. The hotel charges before tax in the second country were $500 lower than in the first. The tax on the hotel bill was 5.5% in the first country and 4.5%in the second. After the trip, the total tax paid on accommodation expenses was $477.50 . How much was the hotel bill in the first country before tax?

1ST Country:

Charges before taxes = $X.
Taxes = $0.055X.

2nd Country:
Before taxes = (X-$500).
Taxes = (0.045(X-500).

Taxes = 0.055x + 0.045(x-500) = 477.50,
=.055x + 0.045x - 22.5 = 477.50,
0.1x = 477.50 + 22.50 = 500,
X = $5000 Before taxes in 1st country.

To find the hotel bill in the first country before tax, we can follow these steps:

1. Let's assume the hotel bill in the first country before tax is 'x'.
2. The hotel bill in the second country before tax is then 'x - $500' (as mentioned in the question).
3. The tax rate in the first country is 5.5%, which means the tax amount paid there is 5.5/100 * x.
4. The tax rate in the second country is 4.5%, which means the tax amount paid there is 4.5/100 * (x - $500).
5. The total tax paid on accommodation expenses is given as $477.50, so we can set up the following equation:

(5.5/100 * x) + (4.5/100 * (x - $500)) = $477.50

Now, let's solve the equation to find the hotel bill in the first country before tax.

(5.5/100 * x) + (4.5/100 * (x - $500)) = $477.50

Multiply both sides by 100 to remove the decimals:

5.5x + 4.5(x - $500) = $47750

Distribute the terms:

5.5x + 4.5x - 4.5 * $500 = $47750

Combine like terms:

10x - $2250 = $47750

Add $2250 to both sides:

10x = $50000

Divide by 10:

x = $5000

Therefore, the hotel bill in the first country before tax was $5000.