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

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

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

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* (\$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.