Question

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 5 % , and the tax in the second city was 8.5 % . The total hotel tax paid for the two cities was $ 836.25 . How much was the hotel charge in each city before tax?

Answer 1

Answer:

In city one, the hotel charges before taxes were $5,250.

In city two, the hotel charges before taxes were $6,750.

Step-by-step explanation:

Let the hotel charge in the first city be x and in the second city be y.

Given that the hotel charge before tax in the second city was $ 1500 higher than in the first. That can be written as:

$y - x = \ 1500$ ...[1]

The tax in the first city was 5 %, and the tax in the second city was 8.5 %.

The total hotel tax paid for the two cities was $ 836.25

5% of x + 8.5% of y = $836.25

$0.05x+0.085y=\ 836.25$...[2]

Now putting value of y from [1] in to [2]:

$y = \ 1500+x$

$0.05x+0.085\times (\ 1500+x)=\ 836.25$

On solving we get :

x = $5,250

Using vakue of x in [1] to find y:

$y=\ 1500+\ 5,250=\ 6,750$

In city one, the hotel charges before taxes were $5,250.

In city two, the hotel charges before taxes were $6,750.