a theater group made appearances in two cities. the hotel charge before tax in the second city was $1500…

a theater group made appearances in two cities. the hotel charge before tax in the second city was $1500 higher than in the first. the tax in the first city was 9.5%, and the tax in the second city was 4.5%. the total hotel tax paid for the two cities was $487.50. how much was the hotel charge in each city before tax? note that the aleks graphing calculator can be used to make computations easier. first city: $ second city: $

a theater group made appearances in two cities. the hotel charge before tax in the second city was $1500 higher than in the first. the tax in the first city was 9.5%, and the tax in the second city was 4.5%. the total hotel tax paid for the two cities was $487.50. how much was the hotel charge in each city before tax? note that the aleks graphing calculator can be used to make computations easier. first city: $ second city: $

Answer

Explanation:

Step1: Let the hotel - charge before tax in the first city be $x$.

The hotel - charge before tax in the second city is $x + 1500$.

Step2: Calculate the tax in each city.

The tax in the first city is $0.095x$. The tax in the second city is $0.045(x + 1500)$.

Step3: Set up an equation based on the total tax.

The total tax is $487.50$, so $0.095x+0.045(x + 1500)=487.50$. Expand the equation: $0.095x+0.045x+67.5 = 487.50$. Combine like - terms: $0.14x+67.5 = 487.50$. Subtract 67.5 from both sides: $0.14x=487.50 - 67.5=420$. Solve for $x$: $x=\frac{420}{0.14}=3000$.

Step4: Find the hotel - charge before tax in each city.

The hotel - charge before tax in the first city, $x = 3000$. The hotel - charge before tax in the second city, $x + 1500=3000 + 1500 = 4500$.

Answer:

First city: $$3000$ Second city: $$4500$