The Expression for Total Cost

Oct 13, 2025 by magicalceylontours.com 89 views

Introduction

In this article, we will explore the concept of discounts and taxes in a mathematical context. A store is offering a 15% discount on all shoes, and Ayla purchases shoes and clothes. We will analyze the expression representing her total cost, including 9% tax, and identify the term that represents the cost of the shoes after the discount.

The Expression for Total Cost

The expression for Ayla's total cost is given by:

${ c + (1-0.15)s + 0.09[c + (1-0.15)s] }$

Where:

$c$ represents the cost of the clothes
$s$ represents the cost of the shoes
$0.15$ is the discount rate (15% of the cost of the shoes)
$0.09$ is the tax rate (9% of the total cost)

Breaking Down the Expression

To understand the expression, let's break it down into its components:

The first term, $c$ , represents the cost of the clothes.
The second term, $(1-0.15)s$ , represents the cost of the shoes after the discount. This is because the discount rate is subtracted from 1, which represents the original cost of the shoes.
The third term, $0.09[c + (1-0.15)s]$ , represents the tax on the total cost, including the discounted cost of the shoes.

Identifying the Term Representing the Cost of Shoes

The term that represents the cost of the shoes after the discount is:

${ (1-0.15)s }$

This term is obtained by subtracting the discount rate (0.15) from 1, which represents the original cost of the shoes. The result is then multiplied by the cost of the shoes ( $s$ ).

Why This Term Represents the Cost of Shoes

This term represents the cost of the shoes after the discount because it takes into account the 15% discount on the original cost of the shoes. By subtracting the discount rate from 1, we are effectively reducing the cost of the shoes by 15%. This is the term that is used to calculate the total cost, including tax.

Conclusion

In conclusion, the term that represents the cost of the shoes after the discount is:

${ (1-0.15)s }$

This term is obtained by subtracting the discount rate (0.15) from 1, which represents the original cost of the shoes. The result is then multiplied by the cost of the shoes ( $s$ ). This term is used to calculate the total cost, including tax, and represents the cost of the shoes after the discount.

Mathematical Representation

Mathematically, the expression for the total cost can be represented as:

${ c + (1-0.15)s + 0.09[c + (1-0.15)s] }$

Where:

$c$ represents the cost of the clothes
$s$ represents the cost of the shoes
$0.15$ is the discount rate (15% of the cost of the shoes)
$0.09$ is the tax rate (9% of the total cost)

Taxation and Discounts

In this article, we have explored the concept of discounts and taxes in a mathematical context. We have analyzed the expression representing Ayla's total cost, including 9% tax, and identified the term that represents the cost of the shoes after the discount. This term is:

${ (1-0.15)s }$

Real-World Applications

The concept of discounts and taxes has many real-world applications. For example, when shopping online, customers may encounter discounts and taxes on their purchases. Understanding how to calculate the total cost, including tax, is essential for making informed purchasing decisions.

Conclusion

In conclusion, the term that represents the cost of the shoes after the discount is:

${ (1-0.15)s }$

Final Thoughts

${ (1-0.15)s }$

References

[1] A store is offering a 15% discount on all shoes.
[2] Ayla purchases shoes and clothes.
[3] The expression representing her total cost, including 9% tax, is:

${ c + (1-0.15)s + 0.09[c + (1-0.15)s] }$

Where:

$c$ represents the cost of the clothes
$s$ represents the cost of the shoes
$0.15$ is the discount rate (15% of the cost of the shoes)
$0.09$ is the tax rate (9% of the total cost)

Glossary

Discount: A reduction in the price of a product or service.
Tax: A fee imposed by a government on its citizens or residents.
Cost: The amount of money required to purchase a product or service.
Expression: A mathematical representation of a concept or idea.

FAQs

Q: What is the term that represents the cost of the shoes after the discount? A: The term that represents the cost of the shoes after the discount is:

${ (1-0.15)s }$

This term is obtained by subtracting the discount rate (0.15) from 1, which represents the original cost of the shoes. The result is then multiplied by the cost of the shoes ( $s$ ).

Q: What is the tax rate in this scenario? A: The tax rate in this scenario is 9% of the total cost.
Q: What is the discount rate in this scenario? A: The discount rate in this scenario is 15% of the cost of the shoes.
A Store's Offer: Calculating the Total Cost of Ayla's Purchase - Q&A ====================================================================

Introduction

In our previous article, we explored the concept of discounts and taxes in a mathematical context. We analyzed the expression representing Ayla's total cost, including 9% tax, and identified the term that represents the cost of the shoes after the discount. In this article, we will answer some frequently asked questions (FAQs) related to this topic.

Q&A

Q: What is the term that represents the cost of the shoes after the discount?

A: The term that represents the cost of the shoes after the discount is:

${ (1-0.15)s }$

This term is obtained by subtracting the discount rate (0.15) from 1, which represents the original cost of the shoes. The result is then multiplied by the cost of the shoes ( $s$ ).

Q: What is the tax rate in this scenario?

A: The tax rate in this scenario is 9% of the total cost.

Q: What is the discount rate in this scenario?

A: The discount rate in this scenario is 15% of the cost of the shoes.

Q: How do I calculate the total cost, including tax?

A: To calculate the total cost, including tax, you can use the following expression:

${ c + (1-0.15)s + 0.09[c + (1-0.15)s] }$

Where:

$c$ represents the cost of the clothes
$s$ represents the cost of the shoes
$0.15$ is the discount rate (15% of the cost of the shoes)
$0.09$ is the tax rate (9% of the total cost)

Q: What is the difference between a discount and a tax?

A: A discount is a reduction in the price of a product or service, while a tax is a fee imposed by a government on its citizens or residents.

Q: Can I apply multiple discounts to a single purchase?

A: Yes, you can apply multiple discounts to a single purchase. However, the discounts must be applied in a specific order, and the total discount must not exceed 100%.

Q: How do I calculate the total discount on a single purchase?

A: To calculate the total discount on a single purchase, you can use the following expression:

${ \text{Total Discount} = \text{Discount 1} + \text{Discount 2} + \cdots + \text{Discount n} }$

Where:

$\text{Discount 1}$ , $\text{Discount 2}$ , $\ldots$ , $\text{Discount n}$ are the individual discounts applied to the purchase

Q: Can I apply a discount to a product that is already on sale?

A: Yes, you can apply a discount to a product that is already on sale. However, the total discount must not exceed 100%.

Q: How do I calculate the total cost of a purchase, including multiple discounts and taxes?

A: To calculate the total cost of a purchase, including multiple discounts and taxes, you can use the following expression:

${ \text{Total Cost} = \text{Cost of Product} \times (1 - \text{Discount 1}) \times (1 - \text{Discount 2}) \times \cdots \times (1 - \text{Discount n}) + \text{Tax} }$

Where:

$\text{Cost of Product}$ is the original cost of the product
$\text{Discount 1}$ , $\text{Discount 2}$ , $\ldots$ , $\text{Discount n}$ are the individual discounts applied to the product
$\text{Tax}$ is the tax rate applied to the product

Conclusion

In conclusion, we have answered some frequently asked questions related to the concept of discounts and taxes in a mathematical context. We hope that this article has provided you with a better understanding of how to calculate the total cost of a purchase, including multiple discounts and taxes.

References

[1] A store is offering a 15% discount on all shoes.
[2] Ayla purchases shoes and clothes.
[3] The expression representing her total cost, including 9% tax, is:

${ c + (1-0.15)s + 0.09[c + (1-0.15)s] }$

Where:

$c$ represents the cost of the clothes
$s$ represents the cost of the shoes
$0.15$ is the discount rate (15% of the cost of the shoes)
$0.09$ is the tax rate (9% of the total cost)

Glossary

Discount: A reduction in the price of a product or service.
Tax: A fee imposed by a government on its citizens or residents.
Cost: The amount of money required to purchase a product or service.
Expression: A mathematical representation of a concept or idea.

FAQs

Q: What is the term that represents the cost of the shoes after the discount? A: The term that represents the cost of the shoes after the discount is:

${ (1-0.15)s }$

This term is obtained by subtracting the discount rate (0.15) from 1, which represents the original cost of the shoes. The result is then multiplied by the cost of the shoes ( $s$ ).

Q: What is the tax rate in this scenario? A: The tax rate in this scenario is 9% of the total cost.
Q: What is the discount rate in this scenario? A: The discount rate in this scenario is 15% of the cost of the shoes.