Question

A theater group made appearances in two cities. The hotel charge before tax in the second city was $500 higher than in the first. The tax in the first city was 5.5%, and the tax in the second city was 7.5%. The total hotel tax paid for the two cities was $492.50. How much was the hotel charge in each city before tax?

Answer 1

The amount before tax at the first hotel be x = $3500

The amount at the second hotel will be x+500 = $4000

Explanation:

Let the amount before tax at the first hotel be x

The amount at the second hotel will be x+500

The tax in the first city was 5.5% = 0.055

the tax in the second city was 7.5% = 0.075

Hence, we have

0.055(x) + 0.075(x + 500) = $492.50

0.055x + 0.075x +37.5 = 492.50

0.13x = 492.50 -37.5

0.13x = 455

x = 455/0.13

x = $3500

The amount before tax at the first hotel be x = $3500

The amount at the second hotel will be x+500 = $3500 + $500

= $4000