A theatre group made appearances in two cities The hotel cha

A theatre group made appearances in two cities. The hotel charge before tax in the second city was $500 higher than in the first. The tax in the first city was 9%, and the tax in the second city was 5.5%. The total hotel tax paid for the two cities was $788.75. How much was the hotel charge in each city before tax? Note that the ALEKS graphing calculator can be used to make computations easier.

Solution

let hotel charge before tax of first city is x , second city is y

given hotel charge before tax in the second city was 500$ higher than the first

y =500+x

given tax in first city is 9% , second city is 5.5%

(9/100)x +(5.5/100)y =788.75

9x +5.5y =78875

9x +5.5(500+x)=78875

9x +2750 +5.5x =78875

14.5x =76125

x =76125/14.5

x=5250

y =500+x

y =500+5250

y =5750

first city 5250$

second city 5750$