A theater group made appearances in two cities. The hotel charge before tax in the second city was $1000 lower than in the first. The tax in the first city was 5.5% , and the tax in the second city was 5%. The total hotel tax paid for the two cities was $501.25 . How much was the hotel charge in each city before tax?

Question

A theater group made appearances in two cities. The hotel charge before tax in the second city was $1000 lower than in the first. The tax in the first city was 5.5%  , and the tax in the second city was 5%. The total hotel tax paid for the two cities was $501.25 . How much was the hotel charge in each city before tax?

First City:

Second City:

Dr. Jane · Answer

x = first city
y = second city

y = x -1000 hotel charge is 100o less than the first city.
.055x +.05 y = 501.25

replace y in the second equation with x -1000 (You get this from the first equation)

.055x + .05(x -1000) = 501.25

Solve for x get the first city
use the first equation y = x -1000 to find the second city.
Be sure to check your final answers in both of the original equations to make sure you are correct.

Rolner · Answer

x= 5500 y= 4000