Chapter4: Systems Of Linear Equations
Section4.3: Solve Mixture Applications With Systems Of Equations
Problem 4.60TI: The manufacturer of a weight training bench spends $120 to build each bench and sells them for $170....
Related questions
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.)*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fffc517a8-8d25-4dba-b5b9-bbe3039266d7%2Ff05b249a-acfa-466b-81f6-d76b273d64e5%2Frjmjv8f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**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.)*
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
Recommended textbooks for you
Elementary Algebra
Algebra
ISBN:
9780998625713
Author:
Lynn Marecek, MaryAnne Anthony-Smith
Publisher:
OpenStax - Rice University
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Elementary Algebra
Algebra
ISBN:
9780998625713
Author:
Lynn Marecek, MaryAnne Anthony-Smith
Publisher:
OpenStax - Rice University
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Intermediate Algebra
Algebra
ISBN:
9781285195728
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning