A theater group made appearances in two cities.

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 5%

, and the tax in the second city was  3.5%

. The total hotel tax paid for the two cities was $328.75

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

Answer 1

S=1500+F

.05F +.03S = 328.75

.05F +.03(1500+F) = 328.75

.05F +.03F = 328.75-.03(1500)

.08F = 328.75-45 = 283.75

F = 283.75/.08 =$3,546.875= hotel pretax cost in First city

S=$5,046.875 = hotel pretax cost in Second city

.05(3,546.875) + .03(5,046.875)

=177.34375 + 151.3075

=328.75

(no guarantees there's not an arithmetic mistake somewhere, but it came out so well, odds are it may be right-- do a rough estimate: 5% is half 10%. 10% of 3.5 thousand is 350. half 350 is 175. 3% is about 1/3 10%. 10% of 5 thousand is 500. 1/3 of 500 is 133. 175+133 = 315 which is close to 328.75. answer is in the right ball park)