Write The Inequality In Standard Form That Describes The Following Situation:Anna Has Up To 311 Minutes To Dedicate To Working Out This Week. It Takes Her 45 Minutes To Complete A Cardio Workout And 26 Minutes To Complete A Weightlifting Workout.Use

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Introduction

Inequality is a fundamental concept in mathematics that helps us describe and analyze various real-world situations. In this article, we will explore how to write an inequality in standard form that describes Anna's workout time. Anna has up to 311 minutes to dedicate to working out this week, and she needs to complete a cardio workout and a weightlifting workout. We will use mathematical modeling to create an inequality that represents this situation.

Understanding the Situation

Anna has a total of 311 minutes to dedicate to working out this week. She needs to complete a cardio workout, which takes 45 minutes, and a weightlifting workout, which takes 26 minutes. We can represent the total time spent on both workouts as the sum of the time spent on each workout. Let's denote the number of cardio workouts as C and the number of weightlifting workouts as W.

Creating the Inequality

We can create an inequality that represents the situation by using the following variables:

  • C: number of cardio workouts
  • W: number of weightlifting workouts
  • Total time: 311 minutes

The total time spent on both workouts can be represented as:

45C + 26W тЙд 311

This inequality states that the total time spent on both workouts is less than or equal to 311 minutes.

Standard Form Inequality

To write the inequality in standard form, we need to isolate the variable on one side of the inequality. In this case, we can isolate C by subtracting 26W from both sides of the inequality:

45C тЙд 311 - 26W

Now, we can divide both sides of the inequality by 45 to isolate C:

C тЙд (311 - 26W) / 45

This is the standard form inequality that represents Anna's workout time.

Interpreting the Inequality

The inequality C тЙд (311 - 26W) / 45 represents the maximum number of cardio workouts Anna can complete in a week, given the time constraint. The right-hand side of the inequality represents the maximum number of cardio workouts Anna can complete, given the time spent on weightlifting workouts.

For example, if Anna completes 5 weightlifting workouts, the maximum number of cardio workouts she can complete is:

C тЙд (311 - 26(5)) / 45 C тЙд (311 - 130) / 45 C тЙд 181 / 45 C тЙд 4.02

This means that Anna can complete at most 4 cardio workouts in a week, given the time constraint.

Conclusion

In this article, we created an inequality in standard form that represents Anna's workout time. We used mathematical modeling to create an inequality that represents the situation, and we interpreted the inequality to understand the maximum number of cardio workouts Anna can complete in a week. This example demonstrates the importance of inequality in mathematics and its application in real-world situations.

Real-World Applications

Inequality is a fundamental concept in mathematics that has numerous real-world applications. Some examples include:

  • Finance: Inequality is used to model financial situations, such as investment returns and loan payments.
  • Science: Inequality is used to model scientific phenomena, such as population growth and chemical reactions.
  • Engineering: Inequality is used to model engineering systems, such as electrical circuits and mechanical systems.

Tips and Tricks

When creating an inequality in standard form, remember to:

  • Isolate the variable: Isolate the variable on one side of the inequality.
  • Simplify the expression: Simplify the expression on the right-hand side of the inequality.
  • Interpret the inequality: Interpret the inequality to understand the situation it represents.

By following these tips and tricks, you can create inequalities in standard form that accurately represent real-world situations.

Practice Problems

Practice creating inequalities in standard form by solving the following problems:

  • A bookstore has a total of 500 books to stock on a shelf. Each book takes up 2 inches of space. If the shelf is 10 feet long, how many books can be stocked on the shelf?
  • A company has a budget of $10,000 to spend on marketing. Each marketing campaign costs $500. If the company wants to spend at most 80% of its budget, how many marketing campaigns can it afford?

Conclusion

In this article, we created an inequality in standard form that represents Anna's workout time. We used mathematical modeling to create an inequality that represents the situation, and we interpreted the inequality to understand the maximum number of cardio workouts Anna can complete in a week. This example demonstrates the importance of inequality in mathematics and its application in real-world situations. By following the tips and tricks outlined in this article, you can create inequalities in standard form that accurately represent real-world situations.

Introduction

In our previous article, we explored how to write an inequality in standard form that describes Anna's workout time. We used mathematical modeling to create an inequality that represents the situation and interpreted the inequality to understand the maximum number of cardio workouts Anna can complete in a week. In this article, we will answer some frequently asked questions about standard form inequality.

Q: What is standard form inequality?

A: Standard form inequality is a mathematical expression that represents a situation where one quantity is related to another quantity in a specific way. It is a way to describe a situation using mathematical language.

Q: How do I create a standard form inequality?

A: To create a standard form inequality, you need to:

  1. Identify the variables: Identify the variables involved in the situation.
  2. Create an equation: Create an equation that represents the situation.
  3. Isolate the variable: Isolate the variable on one side of the equation.
  4. Simplify the expression: Simplify the expression on the right-hand side of the equation.

Q: What is the difference between an inequality and an equation?

A: An inequality is a mathematical expression that represents a situation where one quantity is related to another quantity in a specific way, but the relationship is not always true. An equation is a mathematical expression that represents a situation where one quantity is equal to another quantity.

Q: How do I interpret an inequality?

A: To interpret an inequality, you need to:

  1. Understand the variables: Understand the variables involved in the situation.
  2. Understand the relationship: Understand the relationship between the variables.
  3. Determine the solution: Determine the solution to the inequality.

Q: What are some common types of inequalities?

A: Some common types of inequalities include:

  • Linear inequalities: Inequalities that involve a linear expression.
  • Quadratic inequalities: Inequalities that involve a quadratic expression.
  • Polynomial inequalities: Inequalities that involve a polynomial expression.

Q: How do I solve a linear inequality?

A: To solve a linear inequality, you need to:

  1. Isolate the variable: Isolate the variable on one side of the inequality.
  2. Simplify the expression: Simplify the expression on the right-hand side of the inequality.
  3. Determine the solution: Determine the solution to the inequality.

Q: What are some real-world applications of standard form inequality?

A: Some real-world applications of standard form inequality include:

  • Finance: Inequality is used to model financial situations, such as investment returns and loan payments.
  • Science: Inequality is used to model scientific phenomena, such as population growth and chemical reactions.
  • Engineering: Inequality is used to model engineering systems, such as electrical circuits and mechanical systems.

Q: How do I practice creating standard form inequalities?

A: To practice creating standard form inequalities, you can:

  • Work on problems: Work on problems that involve creating standard form inequalities.
  • Use online resources: Use online resources, such as math websites and apps, to practice creating standard form inequalities.
  • Seek help: Seek help from a teacher or tutor if you need assistance.

Conclusion

In this article, we answered some frequently asked questions about standard form inequality. We covered topics such as creating standard form inequalities, interpreting inequalities, and solving linear inequalities. We also discussed some real-world applications of standard form inequality and provided tips on how to practice creating standard form inequalities. By following the tips and tricks outlined in this article, you can become proficient in creating standard form inequalities and apply them to real-world situations.

Practice Problems

Practice creating standard form inequalities by solving the following problems:

  • A bookstore has a total of 500 books to stock on a shelf. Each book takes up 2 inches of space. If the shelf is 10 feet long, how many books can be stocked on the shelf?
  • A company has a budget of $10,000 to spend on marketing. Each marketing campaign costs $500. If the company wants to spend at most 80% of its budget, how many marketing campaigns can it afford?

Additional Resources

For additional resources on standard form inequality, check out the following websites:

  • Mathway: A math problem solver that can help you create standard form inequalities.
  • Khan Academy: A website that provides video lessons and practice problems on standard form inequality.
  • Math Open Reference: A website that provides interactive math lessons and practice problems on standard form inequality.