A hotel charge for two hotels

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 8.5 % , and the tax in the second city was 7.5 % . The total hotel tax paid for the two cities was $712.5 . How much was the hotel charge in each city before tax?

Answer 1

S= 1500+F

s=8.5% = .085

f = 7.5% = .075

total taxes paid for both = $712.50

s(1500+F)+ f(F) = 712.5

.085(1500) +.085F +.075F = 712.5

.16F = 712.5- 127.5= 585

F=585/.16 = $3656.25 = First Hotel's bill before tax

S= 3656.25+1500= $5156.25 = Second Hotel's before tax bill

.085(5156.25)+ .075(3656.25)

=438.28+ 274.22= 712.5