Question

A theater group made appearances in two cities. The hotel charge before tax and the second city was $1500 lower than in the first. The tax in the first city was 3% and the tax in the second city was 5%. The total hotel tax paid for the two cities was $285. How much was the total charge and each city before tax?First city:Second city:

Answer 1

The charge before tax in the first city is $4500

The charge before tax in the second city is $3000

Step-by-step explanation:

Let the charge before tax in the first city = A

let the charge before tax in the second city = B

The percent of tax on the first city = 3% = 0.03

The percent of tax on the second city = 5% = 0.05

The total tax paid for both cities = $285

Writing the equation for the total tax paid for both cities:

3%(A) + 5%(B) = 285

0.03A + 0.05B = 285 ...equation (1)

The hotel charge before tax in the second city = 1500 lower than first city

The hotel charge before tax in the second city = charge before tax in first city - 1500

B = A - 1500 ...equation (2)

substitute for B in (1):

0.03A + 0.05(A - 1500) = 285

0.03A + 0.05A - 75 = 285

0.08A = 285 + 75

0.08A = 360

A = 360/0.08

A = 4500

Substitute for A in (2):

B = 4500 - 1500

B = 3000

The charge before tax in the first city is $4500

The charge before tax in the second city is $3000