Select The Correct Answer.Charlie Is Installing New Carpet In His Rectangular Living Room, Which Is 5 Feet Longer Than It Is Wide. He Has Received Quotes For The Total Installation Costs From Two Different Contractors For The Same Style Of

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Introduction

Mathematics plays a crucial role in our daily lives, and it's not limited to complex calculations and formulas. Even simple problems, like the one presented in this article, require a deep understanding of mathematical concepts. In this case, we're dealing with a rectangular living room carpet installation problem, where the width and length of the room are given, and we need to determine the correct answer based on the information provided.

The Problem

Charlie is installing new carpet in his rectangular living room, which is 5 feet longer than it is wide. He has received quotes for the total installation costs from two different contractors for the same style of carpet. The quotes are as follows:

  • Contractor A: $1,500 for a room with a width of 10 feet and a length of 15 feet.
  • Contractor B: $1,800 for a room with a width of 12 feet and a length of 17 feet.

Understanding the Problem

To determine the correct answer, we need to understand the relationship between the width and length of the room. The problem states that the room is 5 feet longer than it is wide. This means that if the width of the room is x feet, the length of the room will be (x + 5) feet.

Calculating the Area of the Room

The area of a rectangle is calculated by multiplying its width and length. In this case, the area of the room can be calculated as follows:

Area = Width × Length = x × (x + 5)

Evaluating the Quotes

Now that we have the formula for the area of the room, we can evaluate the quotes provided by the two contractors. Contractor A has quoted $1,500 for a room with a width of 10 feet and a length of 15 feet. This means that the area of the room is:

Area = 10 × 15 = 150 square feet

Contractor B has quoted $1,800 for a room with a width of 12 feet and a length of 17 feet. This means that the area of the room is:

Area = 12 × 17 = 204 square feet

Determining the Correct Answer

Based on the calculations above, we can see that the area of the room is 204 square feet, which is greater than the area of the room quoted by Contractor A (150 square feet). This means that Contractor B's quote is more accurate, and the correct answer is:

Contractor B's quote of $1,800 is the correct answer.

Conclusion

In this article, we have demonstrated how to solve a mathematical problem involving a rectangular living room carpet installation. By understanding the relationship between the width and length of the room, calculating the area of the room, and evaluating the quotes provided by the two contractors, we were able to determine the correct answer. This problem may seem simple, but it requires a deep understanding of mathematical concepts, including the formula for the area of a rectangle.

Additional Tips and Tricks

  • When dealing with mathematical problems, it's essential to read the problem carefully and understand what's being asked.
  • Use formulas and equations to calculate the values required to solve the problem.
  • Evaluate the options provided and choose the one that is most accurate.
  • Practice, practice, practice! The more you practice solving mathematical problems, the more confident you'll become in your ability to solve them.

Frequently Asked Questions

  • Q: What is the formula for the area of a rectangle? A: The formula for the area of a rectangle is: Area = Width × Length.
  • Q: How do I determine the correct answer in a mathematical problem? A: To determine the correct answer, read the problem carefully, use formulas and equations to calculate the values required, and evaluate the options provided.
  • Q: What is the most important thing to remember when solving mathematical problems? A: The most important thing to remember is to read the problem carefully and understand what's being asked.

References

  • [1] "Mathematics for Dummies" by Mark Ryan
  • [2] "Algebra and Trigonometry" by Michael Sullivan
  • [3] "Geometry: A Comprehensive Introduction" by Dan Pedoe

Glossary

  • Rectangle: A four-sided shape with four right angles.
  • Area: The amount of space inside a shape.
  • Width: The distance between two opposite sides of a shape.
  • Length: The distance between two opposite sides of a shape.
  • Contractor: A person or company that provides services, such as installing carpet.
  • Quote: A written estimate of the cost of a service or product.
    Mathematical Problem Solving: A Q&A Guide =====================================================

Introduction

Mathematical problem solving is an essential skill that can be applied to various aspects of life. Whether you're a student, a professional, or simply someone who enjoys solving puzzles, mathematical problem solving can help you develop critical thinking, analytical skills, and problem-solving abilities. In this article, we'll provide a Q&A guide to help you improve your mathematical problem-solving skills.

Q: What is mathematical problem solving?

A: Mathematical problem solving is the process of using mathematical concepts, formulas, and techniques to solve problems or puzzles. It involves critical thinking, analytical skills, and problem-solving abilities to arrive at a solution.

Q: What are the key steps in mathematical problem solving?

A: The key steps in mathematical problem solving are:

  1. Read the problem carefully: Understand what's being asked and what information is provided.
  2. Identify the key concepts: Determine the mathematical concepts, formulas, and techniques required to solve the problem.
  3. Develop a plan: Create a step-by-step plan to solve the problem.
  4. Execute the plan: Use mathematical concepts, formulas, and techniques to solve the problem.
  5. Check the solution: Verify that the solution is correct and accurate.

Q: What are some common mathematical problem-solving strategies?

A: Some common mathematical problem-solving strategies include:

  1. Guess and check: Make an educated guess and check if it's correct.
  2. Draw a diagram: Visualize the problem and draw a diagram to help solve it.
  3. Use algebraic manipulations: Use algebraic techniques, such as factoring and simplifying, to solve the problem.
  4. Use geometric reasoning: Use geometric concepts, such as angles and shapes, to solve the problem.
  5. Use numerical methods: Use numerical techniques, such as approximation and estimation, to solve the problem.

Q: How can I improve my mathematical problem-solving skills?

A: To improve your mathematical problem-solving skills, try the following:

  1. Practice regularly: Practice solving mathematical problems regularly to develop your skills.
  2. Seek help when needed: Don't be afraid to ask for help when you're stuck on a problem.
  3. Use online resources: Utilize online resources, such as video tutorials and practice problems, to supplement your learning.
  4. Join a study group: Join a study group or find a study partner to collaborate and learn from each other.
  5. Take online courses: Take online courses or attend workshops to learn new mathematical concepts and techniques.

Q: What are some common mathematical problem-solving mistakes?

A: Some common mathematical problem-solving mistakes include:

  1. Not reading the problem carefully: Failing to understand what's being asked or what information is provided.
  2. Not identifying the key concepts: Failing to determine the mathematical concepts, formulas, and techniques required to solve the problem.
  3. Not developing a plan: Failing to create a step-by-step plan to solve the problem.
  4. Not executing the plan: Failing to use mathematical concepts, formulas, and techniques to solve the problem.
  5. Not checking the solution: Failing to verify that the solution is correct and accurate.

Q: How can I apply mathematical problem-solving skills in real-life situations?

A: Mathematical problem-solving skills can be applied in various real-life situations, such as:

  1. Finance: Using mathematical concepts, such as interest rates and compound interest, to make financial decisions.
  2. Science: Using mathematical concepts, such as statistics and probability, to analyze data and make predictions.
  3. Engineering: Using mathematical concepts, such as calculus and differential equations, to design and optimize systems.
  4. Business: Using mathematical concepts, such as optimization and decision theory, to make business decisions.
  5. Personal finance: Using mathematical concepts, such as budgeting and saving, to manage personal finances.

Conclusion

Mathematical problem solving is an essential skill that can be applied to various aspects of life. By understanding the key steps, common strategies, and common mistakes, you can improve your mathematical problem-solving skills and apply them in real-life situations. Remember to practice regularly, seek help when needed, and use online resources to supplement your learning.