In Logan's New Apartment, Logan's Bedroom Is 144 Square Feet Smaller Than His Living Room. Logan's Bedroom Has An Area Of 180 Square Feet.Let $r$ Represent The Area Of Logan's Living Room. Which Equation Models The Problem?A. $r - 144 =

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Solving the Mystery of Logan's Apartment

The Problem

Logan has just moved into a new apartment, and he's excited to explore his new space. However, he's noticed that his bedroom is significantly smaller than his living room. Specifically, his bedroom is 144 square feet smaller than his living room. Logan's bedroom has an area of 180 square feet. We need to find the area of Logan's living room, represented by the variable rr.

Understanding the Problem

Let's break down the information given in the problem. We know that Logan's bedroom has an area of 180 square feet, and it's 144 square feet smaller than his living room. This means that the area of his living room is 180 + 144 = 324 square feet. However, we're asked to represent the area of his living room using the variable rr. Therefore, we need to find an equation that models this situation.

Modeling the Problem

To model the problem, we need to create an equation that represents the relationship between the area of Logan's living room and the area of his bedroom. Since the area of his bedroom is 180 square feet, and it's 144 square feet smaller than his living room, we can represent the area of his living room as r=180+144r = 180 + 144. However, we need to express this in terms of the variable rr.

The Equation

The equation that models the problem is r−144=180r - 144 = 180. This equation represents the relationship between the area of Logan's living room and the area of his bedroom. The variable rr represents the area of Logan's living room, and the constant 180 represents the area of his bedroom.

Solving the Equation

To solve the equation, we need to isolate the variable rr. We can do this by adding 144 to both sides of the equation. This gives us:

r−144+144=180+144r - 144 + 144 = 180 + 144

Simplifying the equation, we get:

r=324r = 324

Therefore, the area of Logan's living room is 324 square feet.

Conclusion

In this problem, we used algebraic equations to model the relationship between the area of Logan's living room and the area of his bedroom. We represented the area of his living room using the variable rr and created an equation that models the situation. By solving the equation, we found that the area of Logan's living room is 324 square feet.

Key Takeaways

  • Algebraic equations can be used to model real-world problems.
  • Variables can be used to represent unknown values in an equation.
  • Equations can be solved by isolating the variable.

Further Exploration

  • What if the area of Logan's bedroom was 200 square feet instead of 180 square feet? How would this affect the equation?
  • What if the area of Logan's living room was 300 square feet instead of 324 square feet? How would this affect the equation?
  • Can you think of other real-world problems that can be modeled using algebraic equations?
    Q&A: Solving the Mystery of Logan's Apartment

Frequently Asked Questions

We've received many questions about the problem of Logan's apartment, and we're happy to provide answers. Here are some of the most frequently asked questions:

Q: What is the area of Logan's living room?

A: The area of Logan's living room is 324 square feet.

Q: How do we know that the area of Logan's living room is 324 square feet?

A: We know that the area of Logan's living room is 324 square feet because we solved the equation r−144=180r - 144 = 180. By adding 144 to both sides of the equation, we found that r=324r = 324.

Q: What is the relationship between the area of Logan's living room and the area of his bedroom?

A: The area of Logan's living room is 144 square feet larger than the area of his bedroom. This means that if we know the area of his bedroom, we can find the area of his living room by adding 144 to the area of his bedroom.

Q: Can we use this equation to find the area of Logan's living room if we know the area of his bedroom?

A: Yes, we can use this equation to find the area of Logan's living room if we know the area of his bedroom. For example, if the area of his bedroom is 200 square feet, we can find the area of his living room by adding 144 to 200, which gives us 344 square feet.

Q: What if the area of Logan's bedroom is not 180 square feet, but 200 square feet? How would this affect the equation?

A: If the area of Logan's bedroom is 200 square feet, we would need to adjust the equation accordingly. The new equation would be r−144=200r - 144 = 200. By solving this equation, we would find that r=344r = 344.

Q: Can we use this equation to find the area of Logan's living room if we know the area of his bedroom is 300 square feet?

A: Yes, we can use this equation to find the area of Logan's living room if we know the area of his bedroom is 300 square feet. The equation would be r−144=300r - 144 = 300. By solving this equation, we would find that r=444r = 444.

Q: Can we use this equation to find the area of Logan's living room if we know the area of his bedroom is 250 square feet?

A: Yes, we can use this equation to find the area of Logan's living room if we know the area of his bedroom is 250 square feet. The equation would be r−144=250r - 144 = 250. By solving this equation, we would find that r=394r = 394.

Q: Can we use this equation to find the area of Logan's living room if we know the area of his bedroom is 150 square feet?

A: Yes, we can use this equation to find the area of Logan's living room if we know the area of his bedroom is 150 square feet. The equation would be r−144=150r - 144 = 150. By solving this equation, we would find that r=294r = 294.

Conclusion

We hope these questions and answers have helped you understand the problem of Logan's apartment. Remember, algebraic equations can be used to model real-world problems, and variables can be used to represent unknown values in an equation. By solving the equation, we can find the solution to the problem.

Key Takeaways

  • Algebraic equations can be used to model real-world problems.
  • Variables can be used to represent unknown values in an equation.
  • Equations can be solved by isolating the variable.
  • The area of Logan's living room is 144 square feet larger than the area of his bedroom.

Further Exploration

  • What if the area of Logan's bedroom was 100 square feet instead of 180 square feet? How would this affect the equation?
  • What if the area of Logan's living room was 400 square feet instead of 324 square feet? How would this affect the equation?
  • Can you think of other real-world problems that can be modeled using algebraic equations?