Select The Correct Answer From Each Drop-down Menu.Ralph Bought A Computer Monitor With An Area Of 384 Square Inches. The Length Of The Monitor Is Six Times The Quantity Of Five Less Than Half Its Width. Complete The Equation That Can Be Used To

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Introduction

In this article, we will delve into a mathematical problem involving a computer monitor. The problem requires us to find the correct equation that represents the relationship between the length and width of the monitor. We will use algebraic expressions and equations to solve this puzzle.

The Problem

Ralph bought a computer monitor with an area of 384 square inches. The length of the monitor is six times the quantity of five less than half its width. We need to complete the equation that can be used to represent this relationship.

Step 1: Define the Variables

Let's define the variables for the width and length of the monitor. We will use the variable w to represent the width and the variable l to represent the length.

Step 2: Write the Equation for the Area

The area of the monitor is given as 384 square inches. We can write an equation to represent this:

A = lw

where A is the area, l is the length, and w is the width.

Step 3: Write the Equation for the Length

The length of the monitor is six times the quantity of five less than half its width. We can write an equation to represent this:

l = 6(1/2(w - 5))

Step 4: Simplify the Equation

We can simplify the equation for the length by multiplying the fraction:

l = 6((w - 5)/2)

l = 3(w - 5)

Step 5: Substitute the Equation for the Length into the Area Equation

We can substitute the equation for the length into the area equation:

A = lw

384 = l(3(w - 5))

Step 6: Simplify the Equation

We can simplify the equation by multiplying the terms:

384 = 3lw - 45l

Step 7: Use the Given Information

We are given that the area of the monitor is 384 square inches. We can use this information to find the value of lw:

lw = 384

Step 8: Substitute the Value of lw into the Equation

We can substitute the value of lw into the equation:

384 = 3lw - 45l

384 = 3(384) - 45l

Step 9: Solve for l

We can solve for l by isolating the term:

384 = 1152 - 45l

-768 = -45l

l = 17

Step 10: Find the Value of w

We can find the value of w by substituting the value of l into the equation for the length:

l = 3(w - 5)

17 = 3(w - 5)

w - 5 = 17/3

w = 5 + 17/3

w = 26/3

Conclusion

In this article, we solved a mathematical puzzle involving a computer monitor. We used algebraic expressions and equations to find the correct equation that represents the relationship between the length and width of the monitor. We defined the variables, wrote the equation for the area, and simplified the equation for the length. We then substituted the equation for the length into the area equation and solved for the value of l. Finally, we found the value of w by substituting the value of l into the equation for the length.

The Final Answer

The final answer is:

l = 17

w = 26/3

Discussion

This problem requires a strong understanding of algebraic expressions and equations. It also requires the ability to simplify complex equations and solve for the value of variables. The problem is a good example of how algebra can be used to solve real-world problems.

Related Topics

  • Algebraic expressions and equations
  • Simplifying complex equations
  • Solving for the value of variables
  • Real-world applications of algebra

References

Introduction

In our previous article, we solved a mathematical puzzle involving a computer monitor. We used algebraic expressions and equations to find the correct equation that represents the relationship between the length and width of the monitor. In this article, we will answer some frequently asked questions about the problem.

Q: What is the area of the monitor?

A: The area of the monitor is given as 384 square inches.

Q: What is the relationship between the length and width of the monitor?

A: The length of the monitor is six times the quantity of five less than half its width.

Q: How do we write the equation for the area of the monitor?

A: We can write the equation for the area of the monitor as:

A = lw

where A is the area, l is the length, and w is the width.

Q: How do we write the equation for the length of the monitor?

A: We can write the equation for the length of the monitor as:

l = 6(1/2(w - 5))

Q: How do we simplify the equation for the length of the monitor?

A: We can simplify the equation for the length of the monitor by multiplying the fraction:

l = 6((w - 5)/2)

l = 3(w - 5)

Q: How do we substitute the equation for the length into the area equation?

A: We can substitute the equation for the length into the area equation:

A = lw

384 = l(3(w - 5))

Q: How do we solve for the value of l?

A: We can solve for the value of l by isolating the term:

384 = 1152 - 45l

-768 = -45l

l = 17

Q: How do we find the value of w?

A: We can find the value of w by substituting the value of l into the equation for the length:

l = 3(w - 5)

17 = 3(w - 5)

w - 5 = 17/3

w = 5 + 17/3

w = 26/3

Q: What is the final answer?

A: The final answer is:

l = 17

w = 26/3

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

A: This problem has many real-world applications, such as:

  • Designing computer monitors and other electronic devices
  • Calculating the area and perimeter of shapes
  • Solving problems involving algebraic expressions and equations

Q: What are some tips for solving this problem?

A: Some tips for solving this problem include:

  • Reading the problem carefully and understanding what is being asked
  • Using algebraic expressions and equations to represent the relationships between the variables
  • Simplifying complex equations and solving for the value of variables
  • Checking the solution to make sure it makes sense in the context of the problem

Conclusion

In this article, we answered some frequently asked questions about the problem of solving the monitor equation. We provided step-by-step solutions to the problem and discussed some real-world applications of the problem. We also provided some tips for solving the problem.

Related Topics

  • Algebraic expressions and equations
  • Simplifying complex equations
  • Solving for the value of variables
  • Real-world applications of algebra

References