Question

A theater group made appearances in two cities. The hotel charge before tax in the second city was $1000 higher than in the first. The tax in the first city was

9%, and the tax in the second city was 8.5%. The total hotel tax paid for the two cities was $1047.50. 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 1

Explanation:

Let x be the hotel charge before tax in the first city. Then, the hotel charge before tax in the second city is x + 1000.

The tax paid in the first city is 9% of x, which is 0.09x. The tax paid in the second city is 8.5% of (x + 1000), which is 0.085(x + 1000).

The total tax paid for the two cities is $1047.50, so we can set up the following equation:

0.09x + 0.085(x + 1000) = 1047.50

Simplifying and solving for x, we get:

0.09x + 0.085x + 85 = 1047.50

0.175x = 962.50

x = 5500

Therefore, the hotel charge before tax in the first city is $5500, and the hotel charge before tax in the second city is $6500.

Note that these are just the charges before tax. To find the total cost including tax, we need to add the tax paid in each city to these amounts.

In the first city, the tax paid is 9% of $5500, which is $495. In the second city, the tax paid is 8.5% of $6500, which is $552.50.

So, the total cost including tax in the first city is $5995, and the total cost including tax in the second city is $7052.50.