Question

A theater group made appearances in two cities. The hotel charge before tax in the second city was $1500 lower than in the first. The tax in the first city was 7.5%, and the tax in the second city was 6.5%. The total hotel tax paid for the two cities was $707.50. How much was the hotel charge in each city before tax?First city:Second city:Solve by tax rate or interest rate using system of linear equations

Answer 1

For this problem, we are given the value of a hotel charge before taxes, then we are informed of the taxes on two hotels in different cities, and the total value paid for these taxes. We need to create a system of linear equations for the situation and determine the value of the charges before taxes for each city.

We know the total value paid in taxes, therefore we have:

$\begin{gathered} 0.075\cdot x+0.065\cdot y=707.5\\ \\ y=x-1500 \end{gathered}$

We can solve the second equation, and then replace the found value for y on the first equation. We have:

$\begin{gathered} 0.075\cdot x+0.065\cdot(x-1500)=707.5\\ \\ 0.075\cdot x+0.065x-97.5=707.5\\ \\ 0.14x=805\\ \\ x=\frac{805}{0.14}=5750\\ \\ y=5750-1500=4250 \\ \\ \\ \\ \end{gathered}$

They spent $5750 on the first city and $4250 on the second city.