A Plumber Charges A $ 45 \$45 $45 Fee To Make A House Call And Then $ 25 \$25 $25 For Each Hour Of Labor. The Plumber Uses An Equation In The Form Y = M X + B Y = Mx + B Y = M X + B To Determine The Amount To Charge Each Customer.What Is The Value Of

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Introduction

When it comes to pricing services, plumbers often use a combination of fixed and variable costs to determine the total amount to charge each customer. In this scenario, a plumber charges a $\$45$ fee to make a house call and then $\$25$ for each hour of labor. To determine the amount to charge each customer, the plumber uses an equation in the form $y = mx + b$, where $y$ is the total amount to charge, $x$ is the number of hours of labor, $m$ is the hourly rate, and $b$ is the fixed fee. In this article, we will uncover the value of $m$ and $b$ in the plumber's pricing equation.

The Plumber's Pricing Equation

The plumber's pricing equation is given by $y = mx + b$, where $y$ is the total amount to charge, $x$ is the number of hours of labor, $m$ is the hourly rate, and $b$ is the fixed fee. In this scenario, the plumber charges $\$25$ for each hour of labor, so the hourly rate $m$ is equal to $\$25$. The fixed fee $b$ is equal to $\$45$, which is the fee charged to make a house call.

Finding the Value of $m$

To find the value of $m$, we need to determine the hourly rate charged by the plumber. In this scenario, the plumber charges $\$25$ for each hour of labor, so the value of $m$ is equal to $\$25$.

Finding the Value of $b$

To find the value of $b$, we need to determine the fixed fee charged by the plumber. In this scenario, the plumber charges a $\$45$ fee to make a house call, so the value of $b$ is equal to $\$45$.

The Plumber's Pricing Equation with $m$ and $b$

Now that we have found the values of $m$ and $b$, we can substitute them into the plumber's pricing equation to get:

$$y = 25x + 45$$

This equation represents the total amount to charge each customer, where $y$ is the total amount to charge, $x$ is the number of hours of labor, and $25x + 45$ is the amount to charge.

Example 1: Calculating the Total Amount to Charge

Suppose the plumber works for 2 hours and charges a $\$45$ fee to make a house call. To calculate the total amount to charge, we can substitute $x = 2$ into the plumber's pricing equation:

$$y = 25(2) + 45$$

$$y = 50 + 45$$

$$y = 95$$

Therefore, the total amount to charge is $\$95$.

Example 2: Calculating the Total Amount to Charge

Suppose the plumber works for 3 hours and charges a $\$45$ fee to make a house call. To calculate the total amount to charge, we can substitute $x = 3$ into the plumber's pricing equation:

$$y = 25(3) + 45$$

$$y = 75 + 45$$

$$y = 120$$

Therefore, the total amount to charge is $\$120$.

Conclusion

In this article, we have uncovered the value of $m$ and $b$ in the plumber's pricing equation. The value of $m$ is equal to $\$25$, which represents the hourly rate charged by the plumber. The value of $b$ is equal to $\$45$, which represents the fixed fee charged by the plumber. We have also used the plumber's pricing equation to calculate the total amount to charge in two different scenarios. By understanding the values of $m$ and $b$, plumbers can use the plumber's pricing equation to determine the amount to charge each customer.

References

• [1] Algebra.com. (n.d.). Linear Equations. Retrieved from https://www.algebra.com/algebra/homework/linear-equations/linear-equations.faq.html
• [2] Khan Academy. (n.d.). Linear Equations. Retrieved from https://www.khanacademy.org/math/algebra/x2f1f4-linear-equations/x2f1f5-linear-equations-intro/v/linear-equations-intro

Further Reading

• [1] Math Is Fun. (n.d.). Linear Equations. Retrieved from https://www.mathisfun.com/algebra/linear-equations.html
• [2] Purplemath. (n.d.). Linear Equations. Retrieved from https://www.purplemath.com/modules/lineareq.htm

Tags

• Plumber's Pricing Equation
• Linear Equations
• Algebra
• Math
• Science
• Technology
• Engineering
• Mathematics
• Linear Equations
• Algebraic Equations
• Math Is Fun
• Purplemath
• Khan Academy
• Algebra.com
  

Introduction

In our previous article, we uncovered the value of $m$ and $b$ in the plumber's pricing equation. The value of $m$ is equal to $\$25$, which represents the hourly rate charged by the plumber. The value of $b$ is equal to $\$45$, which represents the fixed fee charged by the plumber. In this article, we will answer some frequently asked questions about the plumber's pricing equation.

Q: What is the plumber's pricing equation?

A: The plumber's pricing equation is given by $y = mx + b$, where $y$ is the total amount to charge, $x$ is the number of hours of labor, $m$ is the hourly rate, and $b$ is the fixed fee.

Q: What is the value of $m$ in the plumber's pricing equation?

A: The value of $m$ is equal to $\$25$, which represents the hourly rate charged by the plumber.

Q: What is the value of $b$ in the plumber's pricing equation?

A: The value of $b$ is equal to $\$45$, which represents the fixed fee charged by the plumber.

Q: How do I use the plumber's pricing equation to calculate the total amount to charge?

A: To use the plumber's pricing equation, you need to substitute the value of $x$ into the equation. For example, if the plumber works for 2 hours, you would substitute $x = 2$ into the equation:

$$y = 25(2) + 45$$

$$y = 50 + 45$$

$$y = 95$$

Therefore, the total amount to charge is $\$95$.

Q: What if the plumber works for a fraction of an hour?

A: If the plumber works for a fraction of an hour, you can still use the plumber's pricing equation. For example, if the plumber works for 1.5 hours, you would substitute $x = 1.5$ into the equation:

$$y = 25(1.5) + 45$$

$$y = 37.5 + 45$$

$$y = 82.5$$

Therefore, the total amount to charge is $\$82.50$.

Q: Can I use the plumber's pricing equation to calculate the number of hours of labor?

A: Yes, you can use the plumber's pricing equation to calculate the number of hours of labor. To do this, you need to rearrange the equation to solve for $x$. For example, if the total amount to charge is $\$120$, you can substitute $y = 120$ into the equation:

$$120 = 25x + 45$$

$$75 = 25x$$

$$3 = x$$

Therefore, the plumber works for 3 hours.

Q: What if the plumber charges a different hourly rate?

A: If the plumber charges a different hourly rate, you need to update the value of $m$ in the plumber's pricing equation. For example, if the plumber charges $\$30$ per hour, you would update the value of $m$ to $30$:

$$y = 30x + 45$$

Q: What if the plumber charges a different fixed fee?

A: If the plumber charges a different fixed fee, you need to update the value of $b$ in the plumber's pricing equation. For example, if the plumber charges a $\$50$ fixed fee, you would update the value of $b$ to $50$:

$$y = 25x + 50$$

Conclusion

In this article, we have answered some frequently asked questions about the plumber's pricing equation. We have also provided examples of how to use the plumber's pricing equation to calculate the total amount to charge and the number of hours of labor. By understanding the plumber's pricing equation, plumbers can use it to determine the amount to charge each customer.

References

• [1] Algebra.com. (n.d.). Linear Equations. Retrieved from https://www.algebra.com/algebra/homework/linear-equations/linear-equations.faq.html
• [2] Khan Academy. (n.d.). Linear Equations. Retrieved from https://www.khanacademy.org/math/algebra/x2f1f4-linear-equations/x2f1f5-linear-equations-intro/v/linear-equations-intro

Further Reading

• [1] Math Is Fun. (n.d.). Linear Equations. Retrieved from https://www.mathisfun.com/algebra/linear-equations.html
• [2] Purplemath. (n.d.). Linear Equations. Retrieved from https://www.purplemath.com/modules/lineareq.htm

Tags

• Plumber's Pricing Equation
• Linear Equations
• Algebra
• Math
• Science
• Technology
• Engineering
• Mathematics
• Linear Equations
• Algebraic Equations
• Math Is Fun
• Purplemath
• Khan Academy
• Algebra.com