Calculating the Total Variable Charge

Oct 13, 2025 by wbrum.org 71 views

Understanding the Problem

In this problem, we are given a gas bill that consists of a variable charge and a fixed charge. The variable charge is $0.60 per 200 cubic meters of gas used, and the fixed charge is a constant amount that is added to the bill regardless of the amount of gas used. We are asked to find the fixed charge, given that the total bill is $178.75 for 55,000 cubic meters of gas.

Breaking Down the Problem

To solve this problem, we need to break it down into smaller steps. First, we need to calculate the total variable charge for 55,000 cubic meters of gas. Then, we can subtract this amount from the total bill to find the fixed charge.

Calculating the Total Variable Charge

The variable charge is $0.60 per 200 cubic meters of gas. To find the total variable charge for 55,000 cubic meters of gas, we need to divide 55,000 by 200 and multiply the result by $0.60.

# Define the variables
gas_used = 55000  # in cubic meters
variable_charge_per_200m3 = 0.60  # in dollars
total_variable_charge = (gas_used / 200) * variable_charge_per_200m3

Finding the Fixed Charge

Now that we have the total variable charge, we can subtract this amount from the total bill to find the fixed charge.

# Define the total bill total_bill = 178.75 # in dollars

fixed_charge = total_bill - total_variable_charge

Solving for the Fixed Charge

Now that we have the code to calculate the fixed charge, we can plug in the values and solve for the fixed charge.

# Define the variables
gas_used = 55000  # in cubic meters
variable_charge_per_200m3 = 0.60  # in dollars
total_bill = 178.75  # in dollars
total_variable_charge = (gas_used / 200) * variable_charge_per_200m3
fixed_charge = total_bill - total_variable_charge
print(f"The fixed charge is $fixed_charge.2f")

Running the Code

When we run the code, we get the following output:

The fixed charge is $13.75

Conclusion

In this problem, we were given a gas bill that consisted of a variable charge and a fixed charge. We were asked to find the fixed charge, given that the total bill was $178.75 for 55,000 cubic meters of gas. We broke down the problem into smaller steps, calculated the total variable charge, and then subtracted this amount from the total bill to find the fixed charge. The fixed charge was found to be $13.75.

Discussion

This problem is a classic example of a linear equation problem. The variable charge is a linear function of the amount of gas used, and the fixed charge is a constant amount that is added to the bill. The problem can be solved using algebraic methods, such as substitution or elimination. However, in this case, we used a more straightforward approach by calculating the total variable charge and then subtracting this amount from the total bill.

Key Concepts

This problem involves the following key concepts:

Linear equations and functions
Algebraic methods, such as substitution and elimination
Real-world applications, such as calculating the cost of goods and services

Glossary

Linear equation: An equation in which the variable appears only in the form of a linear expression, such as x + 2 = 3.
Linear function: A function that can be written in the form f(x) = ax + b, where a and b are constants.
Substitution method: A method of solving linear equations by substituting one expression for another.
Elimination method: A method of solving linear equations by eliminating one variable and solving for the other.
Q&A: Solving for the Fixed Charge in Gas Bills =====================================================

Q: What is the fixed charge in a gas bill?

A: The fixed charge is a constant amount that is added to the bill regardless of the amount of gas used.

Q: How is the fixed charge calculated?

A: The fixed charge is calculated by subtracting the total variable charge from the total bill.

Q: What is the total variable charge?

A: The total variable charge is the amount of money charged for the gas used, based on the rate per unit of gas.

Q: How is the total variable charge calculated?

A: The total variable charge is calculated by multiplying the rate per unit of gas by the total amount of gas used.

Q: What is the rate per unit of gas?

A: The rate per unit of gas is the amount of money charged for each unit of gas used.

Q: How is the rate per unit of gas calculated?

A: The rate per unit of gas is calculated by dividing the total variable charge by the total amount of gas used.

Q: What is the total bill?

A: The total bill is the amount of money paid for the gas used, including the fixed charge and the total variable charge.

Q: How is the total bill calculated?

A: The total bill is calculated by adding the fixed charge and the total variable charge.

Q: What is the formula for calculating the fixed charge?

A: The formula for calculating the fixed charge is:

Fixed Charge = Total Bill - Total Variable Charge

Q: How do I calculate the fixed charge using the formula?

A: To calculate the fixed charge using the formula, you need to know the total bill and the total variable charge. You can then plug these values into the formula to get the fixed charge.

Q: What are some real-world applications of calculating the fixed charge?

A: Some real-world applications of calculating the fixed charge include:

Calculating the cost of goods and services
Determining the fixed charge for a utility bill
Finding the total cost of a trip based on the cost of transportation and accommodations

Q: What are some common mistakes to avoid when calculating the fixed charge?

A: Some common mistakes to avoid when calculating the fixed charge include:

Not accounting for the total variable charge
Not using the correct formula
Not plugging in the correct values

Q: How can I practice calculating the fixed charge?

A: You can practice calculating the fixed charge by using real-world examples or by creating your own problems. You can also use online resources or calculators to help you practice.

Q: What are some additional resources for learning about calculating the fixed charge?

A: Some additional resources for learning about calculating the fixed charge include:

Online tutorials and videos
Math textbooks and workbooks
Online calculators and tools

Q: How can I apply what I've learned about calculating the fixed charge to real-world situations?

A: You can apply what you've learned about calculating the fixed charge to real-world situations by using the formula and techniques to calculate the fixed charge in different scenarios. You can also use the skills you've learned to solve problems and make decisions in your personal and professional life.