A theater group made appearances in two states. The hotel charges before tax in the second state were $1000 lower than in the first. The tax on the hotel bill was 4% in the first state and 9% in the second. After the trip, the total tax paid on accommodation expenses was $560 . How much was the hotel bill in the first state before tax?
jkn
To find the hotel bill in the first state before tax, we can follow these steps:
Step 1: Let's assume the hotel bill in the first state before tax is "x" dollars.
Step 2: The hotel charges before tax in the second state are $1000 lower, so the hotel bill in the second state before tax is "x - $1000" dollars.
Step 3: Calculate the tax paid in the first state. The tax rate in the first state is 4%, so the tax paid in the first state is 0.04 * x.
Step 4: Calculate the tax paid in the second state. The tax rate in the second state is 9%, so the tax paid in the second state is 0.09 * (x - $1000).
Step 5: The total tax paid on accommodation expenses is given as $560. So we have the equation: 0.04 * x + 0.09 * (x - $1000) = $560.
Step 6: Solve the equation to find x, which represents the hotel bill in the first state before tax.
Let's solve the equation:
0.04 * x + 0.09 * (x - $1000) = $560
0.04x + 0.09x - 0.09 * $1000 = $560
0.04x + 0.09x - $90 = $560
0.13x - $90 = $560
0.13x = $560 + $90
0.13x = $650
Now, we can solve for x by dividing both sides of the equation by 0.13:
x = $650 / 0.13
x = $5000
Therefore, the hotel bill in the first state before tax was $5000.