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

3%, and the tax in the second city was 9.5%. The total hotel tax paid for the two cities was $580. How much was the hotel charge in each city before tax?
First city:
si
Х
5
?
Second city: 0
I’m

Answer 1

9514 1404 393

Answer:

• first city: $3500
• second city: $5000

Explanation:

Let x and y represent the hotel charges in the two cities. The relations we are given are ...

x - y = -1500 . . . . . . second city hotel charge was 1500 more

0.03x +0.095y = 580 . . . . . total tax paid was 580

Using the first equation, we can write an expression for x:

x = y -1500

Substituting that into the second equation gives ...

0.03(y -1500) +0.095y = 580

0.125y = 625 . . . . . . . add 45 to both sides and simplify

y = 5000 . . . . . . . . . . multiply by 8

x = 5000 -1500 = 3500

The hotel charges were ...

First city: $3500

Second city: $5000