A​ company's charge for electricity is 8.230​¢ per​ kilowatt-hour. In​ addition, each monthly bill contains a customer charge of ​$6.37. If last​ year's bills ranged from a low of ​$55.97 to a high of ​$201.64​, over what range did usage vary​ (in kilowatt-hours)?

We are given the following:

- The electricity rate is 8.230¢ per kilowatt-hour (kWh), which is $ 0.08230 $ dollars per kWh.
- There is a fixed monthly customer charge of $ 6.37 $ dollars.
- The bills range from a low of $ 55.97 $ dollars to a high of $ 201.64 $ dollars.

We need to find the range of usage in kilowatt-hours (kWh).

### Step 1: Setup the formula for the monthly bill

The total bill $ B $ is the sum of the fixed customer charge and the charge based on the number of kilowatt-hours $ x $ used:
\[
B = 6.37 + 0.08230x
\]

### Step 2: Find usage at the low end of the bill range

For the low bill $ B = 55.97 $, we can use the equation:
\[
55.97 = 6.37 + 0.08230x
\]

Solve for $ x $ (kilowatt-hours used):
\[
55.97 - 6.37 = 0.08230x
\]
\[
49.60 = 0.08230x
\]
\[
x = \frac{49.60}{0.08230} \approx 602.19 \, \text{kWh}
\]

### Step 3: Find usage at the high end of the bill range

For the high bill $ B = 201.64 $, we use the same equation:
\[
201.64 = 6.37 + 0.08230x
\]
Solve for $ x $:
\[
201.64 - 6.37 = 0.08230x
\]
\[
195.27 = 0.08230x
\]
\[
x = \frac{195.27}{0.08230} \approx 2372.55 \, \text{kWh}
\]

### Step 4: Conclusion

The usage ranged from approximately $ 602.19 \, \text{kWh} $ to $ 2372.55 \, \text{kWh} $.

---

Do you want more details or have any other questions?

Here are 5 relative questions for you:
1. How do varying rates affect overall electricity consumption?
2. What are the advantages of a fixed customer charge?
3. How can you estimate your average electricity usage based on your bill?
4. How does the cost of electricity compare between different seasons?
5. How would the bill change if the rate per kilowatt-hour increased?

**Tip**: Tracking your monthly energy consumption can help identify patterns that can reduce your overall bill.

A company's charge for electricity is 8.230¢ per kilowatt-hour. In addition, each monthly bill contains a customer charge of $6.37. If last year's bills ranged from a low of $55.97 to a high of $201.64, over what range did usage vary (in kilowatt-hours)?

Discover how to calculate the range of electricity usage based on a company's monthly charge. This example covers linear equations and unit rates. Learn how to solve for kilowatt-hours (kWh) usage when given a fixed customer charge and varying bill amounts, suitable for students in Grades 8-10.

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