A Plumber Charges $\$50$ For Every House Call And An Additional $\$70$ For Each Hour Of Work. For One House Call Yesterday, The Plumber Earned $\$435$. Which Equation Can Be Solved To Find The Number Of Hours The Plumber

Introduction

As a plumber, one's earnings can be influenced by various factors such as the number of house calls made and the hours spent working on each call. In this scenario, we are given that a plumber charges $\$50$ for every house call and an additional $\$70$ for each hour of work. The plumber earned $\$435$ for one house call yesterday. Our goal is to determine the equation that can be solved to find the number of hours the plumber worked.

Understanding the Problem

Let's break down the information provided:

• The plumber charges $\$50$ for every house call.
• The plumber charges an additional $\$70$ for each hour of work.
• The plumber earned $\$435$ for one house call yesterday.

We can represent the total earnings as the sum of the fixed charge for the house call and the variable charge for the hours worked. Let's denote the number of hours worked as $h$. The total earnings can be represented as:

$$\text{Total Earnings} = \text{Fixed Charge} + (\text{Hourly Charge} \times \text{Number of Hours})$$

Setting Up the Equation

We know that the plumber earned $\$435$ for one house call yesterday. We can set up an equation using the information provided:

$$435 = 50 + 70h$$

In this equation, $435$ represents the total earnings, $50$ represents the fixed charge for the house call, and $70h$ represents the variable charge for the hours worked.

Solving for the Number of Hours Worked

To find the number of hours the plumber worked, we need to isolate the variable $h$ in the equation. We can do this by subtracting the fixed charge from both sides of the equation:

$$435 - 50 = 70h$$

This simplifies to:

$$385 = 70h$$

Next, we can divide both sides of the equation by $70$ to solve for $h$:

$$h = \frac{385}{70}$$

Calculating the Number of Hours Worked

Now that we have the equation, let's calculate the number of hours the plumber worked:

$$h = \frac{385}{70}$$

$$h = 5.5$$

Therefore, the plumber worked for $\boxed{5.5}$ hours.

Conclusion

In this scenario, we were given that a plumber charges $\$50$ for every house call and an additional $\$70$ for each hour of work. The plumber earned $\$435$ for one house call yesterday. We set up an equation to find the number of hours the plumber worked and solved for $h$. The result showed that the plumber worked for $\boxed{5.5}$ hours.

Additional Information

• The fixed charge for the house call is $\$50$.
• The hourly charge is $\$70$.
• The total earnings for one house call yesterday was $\$435$.
• The number of hours the plumber worked is $h = 5.5$.

Frequently Asked Questions

• What is the fixed charge for the house call?
• The fixed charge for the house call is $\$50$.
• What is the hourly charge?
• The hourly charge is $\$70$.
• How many hours did the plumber work?
• The plumber worked for $\boxed{5.5}$ hours.

References

• None

Related Topics

• Algebraic equations
• Linear equations
• Solving for variables
• Word problems
  

Introduction

In our previous article, we explored the scenario of a plumber who charges $\$50$ for every house call and an additional $\$70$ for each hour of work. The plumber earned $\$435$ for one house call yesterday. We set up an equation to find the number of hours the plumber worked and solved for $h$. In this Q&A article, we will address some common questions related to the scenario.

Q: What is the fixed charge for the house call?

A: The fixed charge for the house call is $\$50$.

Q: What is the hourly charge?

A: The hourly charge is $\$70$.

Q: How many hours did the plumber work?

A: The plumber worked for $\boxed{5.5}$ hours.

Q: What is the total earnings for one house call yesterday?

A: The total earnings for one house call yesterday was $\$435$.

Q: How do I set up an equation to find the number of hours worked?

A: To set up an equation, you need to represent the total earnings as the sum of the fixed charge for the house call and the variable charge for the hours worked. Let's denote the number of hours worked as $h$. The total earnings can be represented as:

$$\text{Total Earnings} = \text{Fixed Charge} + (\text{Hourly Charge} \times \text{Number of Hours})$$

Q: How do I solve for the number of hours worked?

A: To solve for the number of hours worked, you need to isolate the variable $h$ in the equation. You can do this by subtracting the fixed charge from both sides of the equation and then dividing both sides of the equation by the hourly charge.

Q: What if the plumber worked for a different number of hours?

A: If the plumber worked for a different number of hours, you would need to adjust the equation accordingly. For example, if the plumber worked for $h$ hours, the equation would be:

$$\text{Total Earnings} = \text{Fixed Charge} + (\text{Hourly Charge} \times h)$$

Q: Can I use this equation to find the total earnings for a different number of hours?

A: Yes, you can use this equation to find the total earnings for a different number of hours. Simply plug in the new number of hours and solve for the total earnings.

Q: What if the plumber charges a different amount for the house call?

A: If the plumber charges a different amount for the house call, you would need to adjust the equation accordingly. For example, if the plumber charges $\$x$ for the house call, the equation would be:

$$\text{Total Earnings} = x + (\text{Hourly Charge} \times h)$$

Q: Can I use this equation to find the total earnings for a different hourly charge?

A: Yes, you can use this equation to find the total earnings for a different hourly charge. Simply plug in the new hourly charge and solve for the total earnings.

Conclusion

In this Q&A article, we addressed some common questions related to the scenario of a plumber who charges $\$50$ for every house call and an additional $\$70$ for each hour of work. We provided step-by-step instructions on how to set up an equation to find the number of hours worked and how to solve for the number of hours worked. We also discussed how to adjust the equation for different scenarios.

Additional Information

• The fixed charge for the house call is $\$50$.
• The hourly charge is $\$70$.
• The total earnings for one house call yesterday was $\$435$.
• The number of hours the plumber worked is $h = 5.5$.

Frequently Asked Questions

• What is the fixed charge for the house call?
• The fixed charge for the house call is $\$50$.
• What is the hourly charge?
• The hourly charge is $\$70$.
• How many hours did the plumber work?
• The plumber worked for $\boxed{5.5}$ hours.

References

• None

Related Topics

• Algebraic equations
• Linear equations
• Solving for variables
• Word problems