**Mathematics Problem: Calculate the Pre-Tax Nightly Cost**Including a 9% sales tax, an inn charges $207.10 per night. Find the inn’s nightly cost before tax is added.*Given Data and Solution Explanation:*1. To find the base cost (cost before tax), let $ x $ be the base cost.2. The total cost including tax is calculated by adding the tax directly to the base cost.3. The tax rate given is 9%, so mathematically this would be: \[ \text{Total Cost} = x + (0.09 \times x) \] This simplifies to: \[ \text{Total Cost} = x (1 + 0.09) \] \[ 207.10 = x (1.09) \]4. To solve for $ x $: \[ x = \frac{207.10}{1.09} \] \[ x \approx 190 \] Therefore, the inn's nightly cost before the tax is approximately **$190.00**.**Note:** The calculation shows how to reverse the tax added on a price to determine the original cost of the service or product before tax.*(The above transcription is based on a problem displayed in a document on the computer screen shown in the image. The additional content on the screen and surrounding objects like sticky notes and keyboard are not related to the problem and therefore are not included in this educational transcription.)*

Given: Sales tax is 9% and inn charges per night is $207.10 To find the inn charges per night before…

Answered: Including a 9% sales tax, an inn…

Math

Algebra

Including a 9% sales tax, an inn charges $207.10 per night. Find the inn's nightly cost before tax is added. KM KOM

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

**Mathematics Problem: Calculate the Pre-Tax Nightly Cost**

Including a 9% sales tax, an inn charges $207.10 per night. Find the inn’s nightly cost before tax is added.

*Given Data and Solution Explanation:*
1. To find the base cost (cost before tax), let $ x $ be the base cost.
2. The total cost including tax is calculated by adding the tax directly to the base cost.
3. The tax rate given is 9%, so mathematically this would be:
\[ \text{Total Cost} = x + (0.09 \times x) \]
This simplifies to:
\[ \text{Total Cost} = x (1 + 0.09) \]
\[ 207.10 = x (1.09) \]
4. To solve for $ x $:
\[ x = \frac{207.10}{1.09} \]
\[ x \approx 190 \]

Therefore, the inn's nightly cost before the tax is approximately **$190.00**.

**Note:** The calculation shows how to reverse the tax added on a price to determine the original cost of the service or product before tax.

*(The above transcription is based on a problem displayed in a document on the computer screen shown in the image. The additional content on the screen and surrounding objects like sticky notes and keyboard are not related to the problem and therefore are not included in this educational transcription.)*

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