A theater group made appearances in two cities. The hotel charge before tax in the second city was \( \$ 500 \) lower than in the first. The tax in the first city was \( 7 \% \), and the tax in the second city was \( 8.5 \% \). The total hotel tax paid for the two cities was \( \$ 461.25 \). How much was the hotel charge in each city before tax? Note that the ALEKS graphing calculator can be used to make computations easier. First city: Second city:
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Let's set the hotel charge before tax in the first city as \( x \). Therefore, the hotel charge in the second city would be \( x - 500 \). The total tax paid can be represented with the tax rates given: For the first city: \[ \text{Tax} = 0.07x \] For the second city: \[ \text{Tax} = 0.085(x - 500) \] Now, we can set up the equation for the total tax: \[ 0.07x + 0.085(x - 500) = 461.25 \] Expanding the equation gives: \[ 0.07x + 0.085x - 42.5 = 461.25 \] Combining like terms results in: \[ 0.155x - 42.5 = 461.25 \] Adding 42.5 to both sides leads to: \[ 0.155x = 503.75 \] Dividing both sides by 0.155 gives: \[ x = \frac{503.75}{0.155} \approx 3248.39 \] Thus, the hotel charge before tax in the first city is approximately \( \$ 3248.39 \). For the second city, we calculate: \[ x - 500 \approx 3248.39 - 500 \approx 2748.39 \] Therefore, the hotel charges before tax are approximately: First city: \( \$ 3248.39 \) Second city: \( \$ 2748.39 \) The theater group's choice of cities could reflect their understanding of historic performance trends. Cities with vibrant arts scenes host more theatre-goers, benefitting local businesses and raising cultural awareness. They may also choose cities based on logistics - travel costs and audience size, impacting their overall performance profitability. Tax strategies vary widely across regions! Cities often have unique tax structures which could affect total expenses. For traveling groups, knowing the local tax rates can help in budget planning. For instance, this group's experience highlights how fluctuations in tax percentages can significantly impact overall costs; always be informed before booking to avoid surprises!
