Elena Walked 20 Minutes More Than Lin. Jada Walked Twice As Long As Elena. Jada Walked For 90 Minutes. The Equation $2(x+20) = 90$ Describes This Situation. Match Each Expression With The Statement In The Story It Represents.A. $x$B.

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Introduction

In this article, we will delve into a mathematical problem that involves solving an equation to determine the time each person walked. The problem is presented in a story format, making it engaging and easy to understand. We will break down the problem, identify the variables, and solve the equation to find the solution.

The Story

Elena walked 20 minutes more than Lin. Jada walked twice as long as Elena. Jada walked for 90 minutes. The equation 2(x+20)=902(x+20) = 90 describes this situation.

Breaking Down the Problem

Let's analyze the problem step by step:

  • Elena walked 20 minutes more than Lin. This means that if Lin walked for x minutes, Elena walked for x + 20 minutes.
  • Jada walked twice as long as Elena. This means that if Elena walked for x + 20 minutes, Jada walked for 2(x + 20) minutes.
  • Jada walked for 90 minutes. This is the given information.

Identifying the Variables

From the problem, we can identify the variables:

  • x: the time Lin walked
  • x + 20: the time Elena walked
  • 2(x + 20): the time Jada walked

Solving the Equation

The equation 2(x+20)=902(x+20) = 90 describes the situation. To solve for x, we need to isolate the variable x.

Step 1: Distribute the 2

Distribute the 2 to the terms inside the parentheses:

2(x+20)=2x+402(x+20) = 2x + 40

Step 2: Set up the Equation

Set up the equation by equating the expression to 90:

2x+40=902x + 40 = 90

Step 3: Subtract 40 from Both Sides

Subtract 40 from both sides to isolate the term with x:

2x=502x = 50

Step 4: Divide Both Sides by 2

Divide both sides by 2 to solve for x:

x=25x = 25

Conclusion

We have solved the equation and found the value of x, which represents the time Lin walked. Now, let's match each expression with the statement in the story it represents.

Matching the Expressions

A. xx B. x+20x + 20 C. 2(x+20)2(x + 20)

  • A. xx: represents the time Lin walked
  • B. x+20x + 20: represents the time Elena walked
  • C. 2(x+20)2(x + 20): represents the time Jada walked

Discussion

This problem is a great example of how math can be used to solve real-world problems. By breaking down the problem into smaller steps and identifying the variables, we were able to solve the equation and find the solution. This type of problem is commonly seen in algebra and is an essential part of mathematical problem-solving.

Tips and Variations

  • To make this problem more challenging, you can add more variables or change the equation.
  • To make this problem easier, you can provide more information or simplify the equation.
  • You can also use this problem as a starting point to explore other mathematical concepts, such as graphing or systems of equations.

Conclusion

Introduction

In our previous article, we solved the equation 2(x+20)=902(x+20) = 90 to determine the time each person walked. Now, let's answer some frequently asked questions about the problem and provide additional insights.

Q&A

Q: What is the time Lin walked?

A: Lin walked for x minutes, which we found to be 25 minutes.

Q: What is the time Elena walked?

A: Elena walked for x + 20 minutes, which is 25 + 20 = 45 minutes.

Q: What is the time Jada walked?

A: Jada walked for 2(x + 20) minutes, which is 2(25 + 20) = 2(45) = 90 minutes.

Q: Why did we need to distribute the 2 in the equation?

A: We needed to distribute the 2 to simplify the equation and isolate the variable x.

Q: Why did we subtract 40 from both sides of the equation?

A: We subtracted 40 from both sides to isolate the term with x and make it easier to solve for x.

Q: Why did we divide both sides of the equation by 2?

A: We divided both sides by 2 to solve for x and find the value of the variable.

Q: What is the relationship between the time Lin walked and the time Elena walked?

A: The time Elena walked is 20 minutes more than the time Lin walked.

Q: What is the relationship between the time Elena walked and the time Jada walked?

A: The time Jada walked is twice as long as the time Elena walked.

Q: How can we use this problem to practice other mathematical concepts?

A: We can use this problem to practice graphing, systems of equations, and other algebraic concepts.

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

A: This problem can be used to model real-world situations, such as determining the time it takes to complete a task or the cost of a product.

Additional Insights

  • This problem is a great example of how math can be used to solve real-world problems.
  • By breaking down the problem into smaller steps and identifying the variables, we were able to solve the equation and find the solution.
  • This type of problem is commonly seen in algebra and is an essential part of mathematical problem-solving.

Tips and Variations

  • To make this problem more challenging, you can add more variables or change the equation.
  • To make this problem easier, you can provide more information or simplify the equation.
  • You can also use this problem as a starting point to explore other mathematical concepts, such as graphing or systems of equations.

Conclusion

In conclusion, this problem is a great example of how math can be used to solve real-world problems. By breaking down the problem into smaller steps and identifying the variables, we were able to solve the equation and find the solution. This type of problem is commonly seen in algebra and is an essential part of mathematical problem-solving.