A theater group made appearances in two cities.

Question

A theater group made appearances in two cities. The hotel charge before tax in the second city was $1500 lower than in the first. The tax in the first city was 9.5%, and the tax in the second city was  9%. The total hotel tax paid for the two cities was $420. How much was the hotel charge in each city before tax?

Answer 1

We have 2 unknowns, so we must have 2 equations to solve this.

Let x=pre-tax amt in city 1

y=pre-tax amt in city 2

Eq. I: y = x - 1500

Eq. II Amount of total tax = $420

9.5%x + 9.0%y = 420

.095x + .090y = 420

Using the value for y from Eq. I in Eq. II we can solve for x:

.095x + .090y = 420 Eq. II

.095x + .090(x-1500) = 420 substitute for y

.095x + .090x - 135 = 420 distributive property

.185x = 420 + 135 combine like-terms

.185x = 555 simplify

x = 555/.185 divide both sides by .185 to isolate x

x = 3000

Using Eq. I we can solve for y:

y = x - 1500 Eq. I

y = 3000 - 1500 substitute for x

y = 1500

Therefore, the pre-tax amount from city 1 was $3000 and from city 2 was $1500.