A Store Offers A $\$10$ Sale On Fish Tanks And A $15\%$ Discount On The Purchase Price. Let $x$ Represent The Price In Dollars, And Let $f(x) = X - 10$ And $g(x) = 0.85x$ Represent The

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Introduction

When it comes to purchasing fish tanks, many people are excited to bring home their new aquatic friends. However, the initial cost of the tank can be a significant expense. To make the purchase more affordable, a store offers a $10 sale on fish tanks and a 15% discount on the purchase price. In this article, we will analyze the sale using mathematical functions and determine the final price of the fish tank.

Understanding the Sale

Let's break down the sale offered by the store. The store is offering a $10 sale on fish tanks, which means that the price of the tank will be reduced by $10. Additionally, the store is offering a 15% discount on the purchase price. This means that the customer will receive a discount of 15% off the original price of the tank.

Mathematical Representation

To represent the sale mathematically, we can use two functions: f(x) and g(x). The function f(x) represents the price of the tank after the $10 sale, and the function g(x) represents the price of the tank after the 15% discount.

Function f(x)

The function f(x) represents the price of the tank after the $10 sale. This function can be represented as:

f(x) = x - 10

where x is the original price of the tank in dollars.

Function g(x)

The function g(x) represents the price of the tank after the 15% discount. This function can be represented as:

g(x) = 0.85x

where x is the original price of the tank in dollars.

Combining the Functions

To find the final price of the tank, we need to combine the two functions. We can do this by substituting the expression for f(x) into g(x).

g(f(x)) = g(x - 10) = 0.85(x - 10)

Simplifying the Expression

To simplify the expression, we can distribute the 0.85 to the terms inside the parentheses.

g(f(x)) = 0.85x - 8.5

Conclusion

In conclusion, the final price of the fish tank after the $10 sale and 15% discount can be represented by the expression 0.85x - 8.5, where x is the original price of the tank in dollars.

Example

Let's say the original price of the tank is $100. To find the final price, we can substitute x = 100 into the expression.

g(f(100)) = 0.85(100) - 8.5 = 85 - 8.5 = 76.5

Therefore, the final price of the fish tank after the $10 sale and 15% discount is $76.50.

Real-World Application

The mathematical analysis of the sale can be applied to real-world scenarios. For example, a customer may be considering purchasing a fish tank that costs $150. After the $10 sale and 15% discount, the final price of the tank would be:

g(f(150)) = 0.85(150) - 8.5 = 127.5 - 8.5 = 119

Therefore, the final price of the fish tank after the $10 sale and 15% discount is $119.

Limitations

One limitation of this analysis is that it assumes that the $10 sale and 15% discount are applied sequentially. In reality, the discounts may be applied simultaneously, which could result in a different final price.

Future Research

Future research could involve exploring the impact of different discount structures on the final price of the fish tank. For example, a store may offer a 20% discount on the purchase price, but only if the customer purchases a certain type of fish food. This could result in a more complex mathematical analysis, but would provide valuable insights into the impact of different discount structures on the final price of the fish tank.

Conclusion

In conclusion, the mathematical analysis of the sale offered by the store provides valuable insights into the impact of the $10 sale and 15% discount on the final price of the fish tank. By combining the two functions, we can determine the final price of the tank after the sale. This analysis can be applied to real-world scenarios and provides a useful tool for customers to make informed purchasing decisions.

References

Introduction

In our previous article, we analyzed the sale offered by a store on fish tanks using mathematical functions. We determined that the final price of the fish tank after the $10 sale and 15% discount can be represented by the expression 0.85x - 8.5, where x is the original price of the tank in dollars. In this article, we will answer some frequently asked questions about the sale and provide additional insights into the mathematical analysis.

Q&A

Q: What is the final price of the fish tank after the $10 sale and 15% discount?

A: The final price of the fish tank after the $10 sale and 15% discount can be represented by the expression 0.85x - 8.5, where x is the original price of the tank in dollars.

Q: How does the $10 sale affect the final price of the fish tank?

A: The $10 sale reduces the price of the fish tank by $10. This means that if the original price of the tank is $100, the price after the $10 sale would be $90.

Q: How does the 15% discount affect the final price of the fish tank?

A: The 15% discount reduces the price of the fish tank by 15% of the original price. This means that if the original price of the tank is $100, the price after the 15% discount would be $85.

Q: Can I apply the $10 sale and 15% discount simultaneously?

A: Yes, you can apply the $10 sale and 15% discount simultaneously. However, the order in which you apply the discounts may affect the final price of the fish tank.

Q: What is the impact of different discount structures on the final price of the fish tank?

A: Different discount structures can have a significant impact on the final price of the fish tank. For example, a store may offer a 20% discount on the purchase price, but only if the customer purchases a certain type of fish food. This could result in a more complex mathematical analysis, but would provide valuable insights into the impact of different discount structures on the final price of the fish tank.

Q: Can I use this analysis to determine the final price of other items?

A: Yes, you can use this analysis to determine the final price of other items that are subject to similar discounts. However, you will need to adjust the mathematical functions to reflect the specific discounts and prices of the item.

Q: What are some real-world applications of this analysis?

A: This analysis has several real-world applications, including:

  • Determining the final price of items after discounts
  • Analyzing the impact of different discount structures on the final price of items
  • Developing pricing strategies for businesses
  • Creating mathematical models to predict the behavior of complex systems

Conclusion

In conclusion, the mathematical analysis of the sale offered by the store provides valuable insights into the impact of the $10 sale and 15% discount on the final price of the fish tank. By answering some frequently asked questions and providing additional insights into the mathematical analysis, we hope to have provided a better understanding of the sale and its implications.

References