Janna Is Playing An Online Trivia Game. She Has 50 Points And Earns 2 Points For Each Correct Answer. She Will Advance To The Next Round If Her Score Is Over 68 Points.Which Inequality Can Janna Use To Find How Many More Questions She Must Answer

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Introduction

In this article, we will explore how to use inequalities to solve real-world problems, specifically in the context of an online trivia game. We will use the scenario of Janna, who is playing a trivia game and needs to determine how many more questions she must answer to advance to the next round.

Understanding the Problem

Janna has 50 points and earns 2 points for each correct answer. She will advance to the next round if her score is over 68 points. To find out how many more questions she must answer, we need to set up an inequality that represents the situation.

Setting Up the Inequality

Let's denote the number of questions Janna needs to answer as x. Since she earns 2 points for each correct answer, her total score after answering x questions will be 50 + 2x. We want to find the minimum value of x such that her score is greater than 68.

The Inequality

We can set up the inequality as follows:

50 + 2x > 68

Solving the Inequality

To solve the inequality, we need to isolate the variable x. We can do this by subtracting 50 from both sides of the inequality:

2x > 18

Next, we can divide both sides of the inequality by 2:

x > 9

Interpretation

The inequality x > 9 tells us that Janna needs to answer at least 10 questions to have a score greater than 68. This means that if she answers 9 questions, her score will be 50 + 2(9) = 68, which is not enough to advance to the next round. However, if she answers 10 questions, her score will be 50 + 2(10) = 70, which is more than enough to advance to the next round.

Conclusion

In this article, we used an inequality to solve a real-world problem in the context of an online trivia game. We set up the inequality 50 + 2x > 68, solved it, and found that Janna needs to answer at least 10 questions to have a score greater than 68. This demonstrates how inequalities can be used to model and solve real-world problems.

Real-World Applications

Inequalities have many real-world applications, including:

  • Finance: Inequalities can be used to model investment returns, interest rates, and other financial concepts.
  • Science: Inequalities can be used to model population growth, chemical reactions, and other scientific phenomena.
  • Engineering: Inequalities can be used to model stress, strain, and other engineering concepts.

Tips and Tricks

  • Use inequalities to model real-world problems: Inequalities can be used to model a wide range of real-world problems, including those in finance, science, and engineering.
  • Solve inequalities step-by-step: When solving inequalities, make sure to follow the order of operations and solve the inequality step-by-step.
  • Check your solutions: Always check your solutions to make sure they make sense in the context of the problem.

Common Mistakes

  • Forgetting to check solutions: Make sure to check your solutions to make sure they make sense in the context of the problem.
  • Not following the order of operations: When solving inequalities, make sure to follow the order of operations and solve the inequality step-by-step.
  • Not using inequalities to model real-world problems: Inequalities can be used to model a wide range of real-world problems, including those in finance, science, and engineering.

Conclusion

Q: What is an inequality?

A: An inequality is a mathematical statement that compares two expressions using a relation such as greater than (>), less than (<), greater than or equal to (≥), or less than or equal to (≤).

Q: How do I use inequalities to solve real-world problems?

A: To use inequalities to solve real-world problems, you need to:

  1. Identify the variables: Identify the variables in the problem and what you are trying to solve for.
  2. Set up the inequality: Set up the inequality using the variables and the given information.
  3. Solve the inequality: Solve the inequality using algebraic methods.
  4. Check your solutions: Check your solutions to make sure they make sense in the context of the problem.

Q: What are some common types of inequalities?

A: Some common types of inequalities include:

  • Linear inequalities: Inequalities that can be written in the form ax + b > c, where a, b, and c are constants.
  • Quadratic inequalities: Inequalities that can be written in the form ax^2 + bx + c > d, where a, b, c, and d are constants.
  • Absolute value inequalities: Inequalities that involve absolute values, such as |x| > a, where a is a constant.

Q: How do I solve linear inequalities?

A: To solve linear inequalities, you can use the following steps:

  1. Add or subtract the same value to both sides: Add or subtract the same value to both sides of the inequality to isolate the variable.
  2. Multiply or divide both sides by a constant: Multiply or divide both sides of the inequality by a constant to isolate the variable.
  3. Check your solutions: Check your solutions to make sure they make sense in the context of the problem.

Q: How do I solve quadratic inequalities?

A: To solve quadratic inequalities, you can use the following steps:

  1. Factor the quadratic expression: Factor the quadratic expression to find the roots of the equation.
  2. Use the sign chart method: Use the sign chart method to determine the intervals where the inequality is true.
  3. Check your solutions: Check your solutions to make sure they make sense in the context of the problem.

Q: How do I solve absolute value inequalities?

A: To solve absolute value inequalities, you can use the following steps:

  1. Write two separate inequalities: Write two separate inequalities, one for the positive case and one for the negative case.
  2. Solve each inequality separately: Solve each inequality separately using algebraic methods.
  3. Check your solutions: Check your solutions to make sure they make sense in the context of the problem.

Q: What are some real-world applications of inequalities?

A: Inequalities have many real-world applications, including:

  • Finance: Inequalities can be used to model investment returns, interest rates, and other financial concepts.
  • Science: Inequalities can be used to model population growth, chemical reactions, and other scientific phenomena.
  • Engineering: Inequalities can be used to model stress, strain, and other engineering concepts.

Q: How can I practice solving inequalities?

A: You can practice solving inequalities by:

  • Working on sample problems: Work on sample problems to practice solving inequalities.
  • Using online resources: Use online resources, such as Khan Academy or Mathway, to practice solving inequalities.
  • Seeking help from a tutor: Seek help from a tutor or teacher if you are struggling to solve inequalities.

Conclusion

In this article, we answered some frequently asked questions about inequalities in real-world scenarios. We covered topics such as what an inequality is, how to use inequalities to solve real-world problems, and how to solve different types of inequalities. We also discussed some real-world applications of inequalities and provided tips and tricks for practicing solving inequalities.