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 7%, and the tax in t

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Question 1201829: 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 7%, and the tax in the second city was 8%. The total hotel tax paid for the two cities was $865. How much was the hotel charge in each city before tax?

Answer by math_tutor2020(3817) About Me  (Show Source):
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Answer:
first hotel's price before tax = $5500
second hotel's price before tax = $6000


Work Shown:

x = first hotel price before tax
x+500 = second hotel price before tax

7% of x = 0.07x = tax amount for first hotel
8% of x+500 = 0.08(x+500) = 0.08x+40 = tax amount for second hotel

Combine the two tax amounts and we'll get $865
tax1 + tax2 = 865
(0.07x) + (0.08x+40) = 865
0.15x+40 = 865
0.15x = 865-40
0.15x = 825
x = 5500
then
x+500 = 5500+500 = 6000