Finding the Number of Minutes Jeanie Practiced

Oct 13, 2025 by leolavanderia.com.br 44 views

Introduction

In this article, we will explore a real-world problem involving algebraic equations. We will set up and solve an equation to determine the number of minutes Jeanie practiced her violin. This problem requires us to use algebraic thinking and mathematical modeling to solve a practical problem.

Problem Statement

Jeanie practiced her violin for a certain number of minutes. The number of minutes she practiced was 15 less than twice the number of minutes her friend, Brian, practiced. Their total practice time was 120 minutes. We need to set up and solve an equation to determine how many minutes Jeanie practiced her violin.

Setting Up the Equation

Let's denote the number of minutes Brian practiced as x. Since Jeanie practiced 15 less than twice the number of minutes Brian practiced, we can represent the number of minutes Jeanie practiced as 2x - 15. The total practice time of both Jeanie and Brian is 120 minutes. We can set up the equation as follows:

x + (2x - 15) = 120

Simplifying the Equation

To simplify the equation, we can combine like terms:

x + 2x - 15 = 120

Combine the x terms:

3x - 15 = 120

Adding 15 to Both Sides

To isolate the x term, we can add 15 to both sides of the equation:

3x - 15 + 15 = 120 + 15

This simplifies to:

3x = 135

Dividing Both Sides by 3

To solve for x, we can divide both sides of the equation by 3:

3x / 3 = 135 / 3

This simplifies to:

x = 45

Finding the Number of Minutes Jeanie Practiced

Now that we know the number of minutes Brian practiced (x = 45), we can find the number of minutes Jeanie practiced. We can substitute x = 45 into the expression 2x - 15:

2(45) - 15 = 90 - 15

This simplifies to:

Conclusion

In this article, we set up and solved an equation to determine the number of minutes Jeanie practiced her violin. We used algebraic thinking and mathematical modeling to solve a practical problem. We found that Jeanie practiced her violin for 75 minutes.

Key Takeaways

We set up an equation to model the situation involving Jeanie and Brian's practice time.
We simplified the equation by combining like terms and adding 15 to both sides.
We solved for x by dividing both sides of the equation by 3.
We found the number of minutes Jeanie practiced by substituting x = 45 into the expression 2x - 15.

Real-World Applications

This problem has real-world applications in various fields, such as:

Music education: This problem can be used to model the practice time of students learning to play a musical instrument.
Sports: This problem can be used to model the practice time of athletes training for a competition.
Business: This problem can be used to model the production time of a company manufacturing a product.

Future Directions

Introduction

In our previous article, we set up and solved an equation to determine the number of minutes Jeanie practiced her violin. We used algebraic thinking and mathematical modeling to solve a practical problem. In this article, we will answer some frequently asked questions (FAQs) related to the problem.

Q: What is the main concept behind the problem?

A: The main concept behind the problem is algebraic thinking and mathematical modeling. We used an equation to model the situation involving Jeanie and Brian's practice time.

Q: What is the equation that models the situation?

A: The equation that models the situation is x + (2x - 15) = 120, where x represents the number of minutes Brian practiced.

Q: How do we simplify the equation?

A: We simplify the equation by combining like terms and adding 15 to both sides.

Q: What is the value of x?

A: The value of x is 45, which represents the number of minutes Brian practiced.

Q: How do we find the number of minutes Jeanie practiced?

A: We find the number of minutes Jeanie practiced by substituting x = 45 into the expression 2x - 15.

Q: What is the number of minutes Jeanie practiced?

A: The number of minutes Jeanie practiced is 75.

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

A: Some real-world applications of this problem include music education, sports, and business.

Q: Can we use this problem to model other situations?

A: Yes, we can use this problem to model other situations involving algebraic equations and mathematical modeling.

Q: What are some tips for solving algebraic equations?

A: Some tips for solving algebraic equations include:

Simplifying the equation by combining like terms
Adding or subtracting the same value to both sides of the equation
Multiplying or dividing both sides of the equation by the same value
Using inverse operations to isolate the variable

Q: What are some common mistakes to avoid when solving algebraic equations?

A: Some common mistakes to avoid when solving algebraic equations include:

Not simplifying the equation
Not using inverse operations to isolate the variable
Not checking the solution to make sure it is correct

Conclusion

In this article, we answered some frequently asked questions related to the problem of determining the number of minutes Jeanie practiced her violin. We used algebraic thinking and mathematical modeling to solve a practical problem. We hope this article has been helpful in understanding the concepts and techniques involved in solving algebraic equations.

Key Takeaways

We used algebraic thinking and mathematical modeling to solve a practical problem.
We simplified the equation by combining like terms and adding 15 to both sides.
We found the number of minutes Jeanie practiced by substituting x = 45 into the expression 2x - 15.
We identified some real-world applications of this problem.
We provided some tips and common mistakes to avoid when solving algebraic equations.

Future Directions

In the future, we can explore more complex problems involving algebraic equations and mathematical modeling. We can also apply these concepts to real-world problems in various fields, such as science, technology, engineering, and mathematics (STEM).