He Also Has A Coupon For $5$ Off His Entire Purchase. Omar Wants To Know How Many Pairs Of Socks He Can Buy.Let $p$ Be The Number Of Pairs Of Socks Omar Buys. Write An Inequality That Represents The Situation: $4p - 5 \leq

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Introduction

In today's world of discounts and promotions, it's essential to understand how to calculate the value of a coupon or a discount. In this article, we will explore a scenario where Omar wants to buy pairs of socks using a coupon that offers a $5 discount on his entire purchase. We will write an inequality that represents the situation and provide a step-by-step solution to help Omar determine how many pairs of socks he can buy.

The Coupon Discount

Omar has a coupon for $5 off his entire purchase. This means that if he buys a certain number of pairs of socks, he will get a discount of $5 on the total price. Let's assume that the price of each pair of socks is $x. Then, the total price of p pairs of socks is $px.

Writing the Inequality

Since Omar has a coupon for $5 off his entire purchase, the total price of p pairs of socks will be reduced by $5. Therefore, the inequality that represents the situation is:

px−5≤20px - 5 \leq 20

where pxpx is the total price of p pairs of socks, and 2020 is the maximum amount Omar is willing to spend.

Simplifying the Inequality

To simplify the inequality, we can add 55 to both sides:

px≤25px \leq 25

This means that the total price of p pairs of socks must be less than or equal to $25.

Finding the Maximum Number of Pairs

Now, we need to find the maximum number of pairs of socks Omar can buy. To do this, we can divide both sides of the inequality by xx:

p≤25xp \leq \frac{25}{x}

This means that the maximum number of pairs of socks Omar can buy is 25x\frac{25}{x}.

Example

Let's say the price of each pair of socks is $5. Then, the maximum number of pairs Omar can buy is:

p≤255=5p \leq \frac{25}{5} = 5

This means that Omar can buy at most 5 pairs of socks.

Conclusion

In this article, we wrote an inequality that represents the situation where Omar wants to buy pairs of socks using a coupon that offers a $5 discount on his entire purchase. We simplified the inequality and found the maximum number of pairs of socks Omar can buy. This example demonstrates how to use mathematical concepts to solve real-world problems.

Mathematical Concepts

  • Inequalities: We used inequalities to represent the situation and simplify the equation.
  • Algebra: We used algebraic concepts, such as addition and division, to simplify the inequality.
  • Problem-solving: We applied mathematical concepts to solve a real-world problem.

Real-World Applications

  • Coupons and discounts: This example demonstrates how to calculate the value of a coupon or a discount.
  • Budgeting: This example shows how to use mathematical concepts to determine how much money can be spent on a particular item.
  • Shopping: This example can be applied to any shopping scenario where a discount or coupon is used.

Future Directions

  • More complex inequalities: We can explore more complex inequalities and how to solve them.
  • Real-world applications: We can apply mathematical concepts to more real-world problems, such as finance, economics, and science.
  • Mathematical modeling: We can use mathematical modeling to represent real-world situations and solve problems.

References

Glossary

  • Inequality: An inequality is a mathematical statement that compares two expressions using a relation such as <, >, ≤, or ≥.
  • Algebra: Algebra is a branch of mathematics that deals with the study of variables and their relationships.
  • Problem-solving: Problem-solving is the process of using mathematical concepts to solve real-world problems.
    Frequently Asked Questions: Understanding the Coupon Discount ================================================================

Q: What is the coupon discount?

A: The coupon discount is a $5 discount on Omar's entire purchase of pairs of socks.

Q: How do I write an inequality to represent the situation?

A: To write an inequality, you need to represent the total price of p pairs of socks, which is $px, and subtract the coupon discount of $5. The resulting inequality is:

px−5≤20px - 5 \leq 20

Q: How do I simplify the inequality?

A: To simplify the inequality, you can add $5 to both sides:

px≤25px \leq 25

This means that the total price of p pairs of socks must be less than or equal to $25.

Q: How do I find the maximum number of pairs of socks Omar can buy?

A: To find the maximum number of pairs of socks Omar can buy, you can divide both sides of the inequality by xx:

p≤25xp \leq \frac{25}{x}

This means that the maximum number of pairs of socks Omar can buy is 25x\frac{25}{x}.

Q: What if the price of each pair of socks is $5?

A: If the price of each pair of socks is $5, then the maximum number of pairs Omar can buy is:

p≤255=5p \leq \frac{25}{5} = 5

This means that Omar can buy at most 5 pairs of socks.

Q: Can I use this method to calculate the value of a coupon or a discount on any item?

A: Yes, you can use this method to calculate the value of a coupon or a discount on any item. Simply represent the total price of the item, subtract the coupon discount, and simplify the inequality.

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

A: Some real-world applications of this method include:

  • Budgeting: This method can be used to determine how much money can be spent on a particular item.
  • Shopping: This method can be used to calculate the value of a coupon or a discount on any item.
  • Finance: This method can be used to calculate the value of a coupon or a discount on financial products, such as loans or investments.

Q: Can I use this method to solve more complex inequalities?

A: Yes, you can use this method to solve more complex inequalities. Simply represent the total price of the item, subtract the coupon discount, and simplify the inequality.

Q: What are some tips for using this method?

A: Some tips for using this method include:

  • Make sure to represent the total price of the item correctly.
  • Subtract the coupon discount from the total price.
  • Simplify the inequality to find the maximum number of pairs of socks Omar can buy.

Q: Can I use this method to solve problems in other areas of mathematics?

A: Yes, you can use this method to solve problems in other areas of mathematics, such as algebra and geometry.

Q: What are some common mistakes to avoid when using this method?

A: Some common mistakes to avoid when using this method include:

  • Not representing the total price of the item correctly.
  • Not subtracting the coupon discount from the total price.
  • Not simplifying the inequality to find the maximum number of pairs of socks Omar can buy.

Q: Can I use this method to solve problems in real-world scenarios?

A: Yes, you can use this method to solve problems in real-world scenarios, such as budgeting, shopping, and finance.

Q: What are some benefits of using this method?

A: Some benefits of using this method include:

  • It can be used to solve problems in real-world scenarios.
  • It can be used to calculate the value of a coupon or a discount on any item.
  • It can be used to determine how much money can be spent on a particular item.

Q: Can I use this method to solve problems in other areas of mathematics?

A: Yes, you can use this method to solve problems in other areas of mathematics, such as algebra and geometry.

Q: What are some limitations of using this method?

A: Some limitations of using this method include:

  • It may not be applicable to all real-world scenarios.
  • It may not be applicable to all types of problems.
  • It may require additional mathematical concepts to solve more complex problems.