Solving a tax rate or interest rate problem using a system of linear equations

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 4%. The total hotel tax paid for the two cities was $591.25. 

How much was the hotel charge in each city before tax?



Answer 1

Well suppose the hotel charges are x, y

Then y = x + 1500

Tax in 1st city = 0.085x

Tax in 2nd city = 0.04 x

So 0.085x + 0.04y = 591.25

85x + 40y = 591250

y = x + 1500

85x + 40 (x+1500) = 591250

125x + 60000 = 591250

125x = 531250

x = 4250

y = 5750

Tax 1 = 361.25

Tax 2 = 230

Total tax = 591.25