Problema Solution
A theater 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 10%, and the tax in the second city was 4.5%. The total hotel tax paid for the two cities was $783.75. How much was the hotel charge in each city before tax?
Answer provided by our tutors
let
x = hotel charge before tax in the first city
y = hotel charge before tax in the second city
hotel charge before tax in the second city was 500 higher than in the first
y = x + 500
tax in the first city is 10% that is 10% of x or (10/100)*x = 0.1*x
tax in the second city is 4.5% that is 4.5% of y or (4.5/100)*y = 0.045*y
the total hotel tax paid for the two cities was $783.75
0.1*x + 0.045*y = 783.75
by solving the system of equations
y = x + 500
0.1*x + 0.045*y = 783.75
we find
x = $5250
y = $5750
First city hotel charge before tax was $5250.
Second city hotel charge before tax was $5750.