A theater group made appearances in two cities. The hotel charge before tax in the second city was
$500 lower than in the first. The tax in the first city was
6%, and the tax in the second city was 4.5% The total hotel tax paid for the two cities was $292.50
. How much was the hotel charge in each city before tax?
F = S + 500
.06F + .045S = 292.50
Substitute S+500 for F in the second equation and solve for S. Insert that value into the first equation to solve for F. Check by putting both values into the second equation.
To find the hotel charges in each city before tax, we can use algebraic equations. Let's denote the hotel charge in the first city before tax as "x".
According to the given information, the hotel charge in the second city before tax is $500 lower than in the first city. So, the hotel charge in the second city before tax can be expressed as "x - $500".
Next, we need to calculate the tax amount for each city. In the first city, the tax rate is 6%, which means the tax amount is 6% of the hotel charge in the first city, or 0.06x.
Similarly, in the second city, the tax rate is 4.5%, which means the tax amount is 4.5% of the hotel charge in the second city, or 0.045(x - $500).
Based on the given information, the total hotel tax paid for the two cities is $292.50. We can set up the equation:
0.06x + 0.045(x - $500) = $292.50
To solve for x, we can simplify and solve the equation step by step:
0.06x + 0.045x - 0.045($500) = $292.50
0.105x - $22.50 = $292.50
0.105x = $292.50 + $22.50
0.105x = $315
Dividing both sides of the equation by 0.105:
x = $315 / 0.105
x = $3000
Therefore, the hotel charge in the first city before tax is $3000.
Substituting this value back into the expression for the hotel charge in the second city:
x - $500 = $3000 - $500 = $2500
Thus, the hotel charge in the second city before tax is $2500.
Therefore, the hotel charge in the first city before tax is $3000, and the hotel charge in the second city before tax is $2500.