Dan Bought X X X Pounds Of Potatoes For $0.85 Per Pound And Y Y Y Pounds Of Grapes For $1.29 Per Pound. The Total Cost Was Less Than $5. Which Inequality Represents His Purchase?A. 1.29 X + 0.85 Y \textless 5 1.29x + 0.85y \ \textless \ 5 1.29 X + 0.85 Y \textless 5 B.

Introduction

In this article, we will explore the concept of inequalities and how they can be used to represent real-world scenarios. We will use the example of Dan's purchase of potatoes and grapes to illustrate how an inequality can be formed to represent a situation where the total cost is less than a certain amount.

Understanding Inequalities

An inequality is a statement that compares two expressions and indicates whether one is greater than, less than, or equal to the other. Inequalities can be used to represent a wide range of situations, from simple comparisons to complex relationships between variables.

Dan's Purchase

Dan bought $x$ pounds of potatoes for $0.85 per pound and $y$ pounds of grapes for $1.29 per pound. The total cost of his purchase was less than $5. We can represent this situation using an inequality.

Forming the Inequality

To form the inequality, we need to consider the cost of each item and the total cost. The cost of the potatoes is $0.85x$ and the cost of the grapes is $1.29y$. The total cost is the sum of these two costs, which is $0.85x + 1.29y$. Since the total cost is less than $5, we can write the inequality as:

$$0.85x + 1.29y < 5$$

Simplifying the Inequality

We can simplify the inequality by multiplying both sides by 100 to eliminate the decimals. This gives us:

$$85x + 129y < 500$$

Analyzing the Inequality

The inequality $85x + 129y < 500$ represents the situation where the total cost of Dan's purchase is less than $5. We can analyze this inequality to understand its implications.

• If $x = 0$, then the inequality becomes $129y < 500$, which means that the cost of the grapes must be less than $500.
• If $y = 0$, then the inequality becomes $85x < 500$, which means that the cost of the potatoes must be less than $500.
• If both $x$ and $y$ are positive, then the inequality represents the situation where the total cost of the potatoes and grapes is less than $500.

Conclusion

In this article, we used the example of Dan's purchase of potatoes and grapes to illustrate how an inequality can be formed to represent a situation where the total cost is less than a certain amount. We formed the inequality $0.85x + 1.29y < 5$ and simplified it to $85x + 129y < 500$. We analyzed the inequality to understand its implications and how it represents the situation.

Answer

Introduction

In our previous article, we explored the concept of inequalities and how they can be used to represent real-world scenarios. We used the example of Dan's purchase of potatoes and grapes to illustrate how an inequality can be formed to represent a situation where the total cost is less than a certain amount. In this article, we will answer some frequently asked questions about Dan's purchase inequality.

Q: What is the purpose of Dan's purchase inequality?

A: The purpose of Dan's purchase inequality is to represent the situation where the total cost of Dan's purchase of potatoes and grapes is less than $5.

Q: How is the inequality formed?

A: The inequality is formed by considering the cost of each item and the total cost. The cost of the potatoes is $0.85x$ and the cost of the grapes is $1.29y$. The total cost is the sum of these two costs, which is $0.85x + 1.29y$. Since the total cost is less than $5, we can write the inequality as:

$$0.85x + 1.29y < 5$$

Q: Can the inequality be simplified?

A: Yes, the inequality can be simplified by multiplying both sides by 100 to eliminate the decimals. This gives us:

$$85x + 129y < 500$$

Q: What does the inequality represent?

A: The inequality represents the situation where the total cost of Dan's purchase of potatoes and grapes is less than $5. We can analyze this inequality to understand its implications.

• If $x = 0$, then the inequality becomes $129y < 500$, which means that the cost of the grapes must be less than $500.
• If $y = 0$, then the inequality becomes $85x < 500$, which means that the cost of the potatoes must be less than $500.
• If both $x$ and $y$ are positive, then the inequality represents the situation where the total cost of the potatoes and grapes is less than $500.

Q: How can the inequality be used in real-world scenarios?

A: The inequality can be used in real-world scenarios where the total cost of a purchase needs to be less than a certain amount. For example, a store may want to limit the total cost of a customer's purchase to $5, and the inequality can be used to represent this situation.

Q: What are some common mistakes to avoid when working with inequalities?

A: Some common mistakes to avoid when working with inequalities include:

• Not considering the direction of the inequality (e.g., less than vs. greater than)
• Not simplifying the inequality when possible
• Not analyzing the inequality to understand its implications
• Not using the inequality to represent real-world scenarios

Conclusion

In this article, we answered some frequently asked questions about Dan's purchase inequality. We discussed the purpose of the inequality, how it is formed, and how it can be simplified. We also analyzed the inequality to understand its implications and how it can be used in real-world scenarios. By avoiding common mistakes and using the inequality correctly, we can represent real-world scenarios and make informed decisions.

Additional Resources

For more information on inequalities and how they can be used to represent real-world scenarios, please see the following resources:

• Inequality Wikipedia Article
• Math Is Fun: Inequalities
• Khan Academy: Inequalities