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 9.5%. The total hotel tax paid for the two cities was $430. How much was the hotel charge in each city before tax?

Question

Mathematics

Tristan Patterson

6 November, 01:17

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 9.5%. The total hotel tax paid for the two cities was $430. How much was the hotel charge in each city before tax?

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Answers (1)

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Nickolas Bradshaw · Answer 1

The hotel charge in city one before tax is $3750 and the hotel charge in city two before tax is $2250.

tep-by-step explanation:

Let a = the charge in 1st city before taxes

Let b = the charge in 2nd city before taxes

Based on the information given. We can have the following equation (1).

y = x - 1500 ... (1).

Interms of the information given, the following is formulated based on taxed paid.

0.065x + 0.06y = 378.75 ... (2).

Now we substitute equation (1) into (2).

0.065x + 0.06 (x - 1500) = 378.75

0.065x + 0.06x - 90 = 378.75

0.125x - 90 = 378.75

0.125x = 468.75

Therefor x=3750

Now x value into equation (1)

y = 3750 - 1500

y = 2250

The hotel charge in city one before tax is $3750 and the hotel charge in city two before tax is $2250.