Question

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 5.5%, and the tax in the second city was 9.5%. The total hotel tax paid for the two cities was $665. How much was the hotel charge in each city before First city: Second city:

Answer 1

$\begin{gathered} 1st\:city:\ 261.25 \\ 2nd\:city:\ 403.75 \end{gathered}$

1) We can gather the data that way:

1st city

Hotel Charge before tax: x

tax rate: 5.5%

2nd city

Hotel charge before tax: (x-500)

Tax rate: 9.5%

Hotel tax 1st city + Hotel tax 2nd city = 665

2) Considering that to find the final cost we need to multiply the tax rate by the hotel charge, we can write out the following expression:

$\begin{gathered} 0.055x+0.095(x-500)=665 \\ 0.055x\cdot \:1000+0.095\left(x-500\right)\cdot \:1000=665\cdot \:1000 \\ 55x+95\left(x-500\right)=665000 \\ 55x+95x-47500=665000 \\ 150x-47500=665000 \\ 150x-47500+47500=665000+47500 \\ 150x=712500 \\ \frac{150x}{150}=\frac{712500}{150} \\ x=4750 \end{gathered}$

Now, let's plug into each expression to find the answer:

$\begin{gathered} Hotel\:1st\:city:0.055(4750)=261.25 \\ Hotel\:2nd\:city\:0.095(4750-500)=403.75 \end{gathered}$