Problema Solution
A theater group made appearances in two cities. The hotel charge before tax in the second city was $1000 higher than in the first. The tax in the first city was 9.5% , and the tax in the second city was 8.5% . The total hotel tax paid for the two cities was $985 . 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 $1,000 higher than in the first means:
y = x + 1000
Tax in the first city was 9.5%, that is, the tax amount was: 0.95x
Tax in the second city is 8.5%, that is, the tax amount was: 0.85y
The total hotel tax paid for the two cities was $985:
0.95*x + 0.85*y = 985
We need to solve the following system of equations
y = x + 1000
0.95*x + 0.85*y = 985
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x = $75
y = $1,075
First city hotel charge before tax was $75.
Second city hotel charge before tax was $1075.