college algebra math question

Question

a theater group made appearances in two cities. the hotel charge before tax in the second city was $500 lower than in the first. the tax in the first city was 4%, and the tax in the second city was 6.5%. the total hotel tax paid for the two cities was "$282.50 ." how much was the hotel charge in each city before tax?

Answer 1

B = A - 500

A = B + 500

.04A + .065B = 282.50

.04(B + 500) + .065B = 282.50

(.04+.065)B + 282.5 - 20

.105B= 262.5

B = 262.50/.105 = $2,500

B = $2,500 in the 2nd city

A= 500+2500 = $3,000 in the 1st city