Interest rate and tax

Question

A theater group made appearances in two cities. The hotel charge before tax in the second city was  $1000 higher than in the first. The tax in the first city was  7.5%, and the tax in the second city was 9.5% The total hotel tax paid for the two cities was $647.50  How much was the hotel charge in each city before tax?

Answer 1

(x+1000).075 + .095x = 647.5

.075x + .095x = 647.5 - 75 = 572.5

x = 572.5/.17 = 5725/17 = about $336.76 invested at 9.5%

x+1000 = $1,336.75 invested at 7.5%