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Let's break down the questions in the image to provide detailed solutions.

### Problem Description:
Miguel is estimating his electricity bill. He uses around 700 kWh per month. The utility charges:
- A base fee of $6 per month,
- 6.726 cents per kWh for the first 500 kWh,
- 8.136 cents per kWh for usage over 500 kWh.

#### Part (a) - How much will Miguel pay for 700 kWh of electricity?

1. **Convert the rates to dollars**: 
   - 6.726 cents per kWh = $0.06726 per kWh for the first 500 kWh,
   - 8.136 cents per kWh = $0.08136 per kWh for any additional usage beyond 500 kWh.

2. **Calculate the cost**:
   - For the first 500 kWh:
     \[
     500 \times 0.06726 = 33.63 \text{ dollars}
     \]
   - For the next 200 kWh (since Miguel uses 700 kWh, the extra is 700 - 500 = 200 kWh):
     \[
     200 \times 0.08136 = 16.27 \text{ dollars}
     \]

3. **Add the base fee**:
   \[
   6 \text{ (base fee)} + 33.63 + 16.27 = 55.90 \text{ dollars}
   \]

So, Miguel would pay **$55.90** for 700 kWh of electricity.

---

#### Part (b) - Error in calculating total price for three items: $1.50, 37 cents, and 5 cents.

To solve this, we need to correctly add the three amounts:
1. Convert everything to dollars:
   - $1.50 stays as $1.50,
   - 37 cents = $0.37,
   - 5 cents = $0.05.

2. Add the amounts:
   \[
   1.50 + 0.37 + 0.05 = 1.92 \text{ dollars}
   \]

The correct total is **$1.92**.

---

#### Part (c) - Which is the most likely common error in part (b)?

- **Option 1**: Forgetting to convert cents to dollars (adding 37 and 5 as whole numbers instead of decimals).
  This leads to $1.50 + 37 + 5 = 43.50, which is wrong.

- **Option 2**: Making an addition error such as adding 37 + 5 = 45 instead of 42 cents.
  This leads to $1.50 + 0.45 = $1.95, which is still incorrect but closer.

- **Option 3**: Leaving off the decimal entirely, giving 1.50 + 37 + 5 = $43.50, which is clearly wrong.

The most likely error is **forgetting to convert cents to dollars**, which matches **Option 1**.

---

### Summary of Answers:
1. **Part (a)**: $55.90
2. **Part (b)**: $1.92
3. **Part (c)**: The most likely error is **forgetting to convert the cents to dollars**.

---

Would you like more details on any part? Here are 5 related questions you might find helpful:
1. How can you convert cents to dollars easily in other contexts?
2. What would happen if Miguel used 800 kWh instead of 700 kWh?
3. How do utility companies determine rates for electricity usage beyond a certain threshold?
4. What are some common rounding errors when working with currency?
5. How do fixed base fees affect the overall calculation for utilities?

**Tip**: Always make sure to convert all units to the same base (like converting cents to dollars) before adding them up to avoid common mistakes.

Miguel is moving and wants to estimate what his electricity bill will be in his new apartment. He looks at old bills and sees that he uses around 700 kWh of electricity each month. The utility company charges $6 each month plus 6.726 cents per kWh for the first 500 kWh and 8.136 cents per kWh for any kilowatt-hours above 500.

Learn how to calculate an electricity bill with a base fee and variable rate per kWh. This example covers a monthly usage of 700 kWh with rates of 6.726 cents per kWh for the first 500 kWh and 8.136 cents per kWh for usage beyond 500 kWh. The solution includes step-by-step currency conversion and total cost calculation.

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