Question 1167588
This is a weighted average problem. To find the overall average price of the textbook, you need to multiply the average price for each period by its corresponding sales proportion (weight) and sum the results.

The overall average price ($\bar{P}$) is calculated as:
$$\bar{P} = (\text{Price}_{\text{Start}} \times \text{Proportion}_{\text{Start}}) + (\text{Price}_{\text{End}} \times \text{Proportion}_{\text{End}}) + (\text{Price}_{\text{Other}} \times \text{Proportion}_{\text{Other}})$$

Here are the values:
| Time Period | Sales Proportion ($w_i$) | Average Price ($P_i$) |
| :--- | :--- | :--- |
| Start-of-term | $0.45$ | $\$82.52$ |
| End-of-term | $0.31$ | $\$49.12$ |
| Other | $0.24$ | $\$65.23$ |

**Calculation:**
$$\bar{P} = (0.45 \times \$82.52) + (0.31 \times \$49.12) + (0.24 \times \$65.23)$$

```python?code_reference&code_event_index=2
# Define the data
proportions = [0.45, 0.31, 0.24]
prices = [82.52, 49.12, 65.23]

# Calculate the weighted average price
weighted_average_price = sum(p * w for p, w in zip(prices, proportions))

# Print the result
print(f"Start-of-term contribution: {proportions[0] * prices[0]}")
print(f"End-of-term contribution: {proportions[1] * prices[1]}")
print(f"Other contribution: {proportions[2] * prices[2]}")
print(f"Weighted Average Price: {weighted_average_price}")

```

```text?code_stdout&code_event_index=2
Start-of-term contribution: 37.134
End-of-term contribution: 15.2272
Other contribution: 15.6552
Weighted Average Price: 68.0164

```

The average price of the textbook over all seasons is **$68.02**.

This is calculated by taking the **weighted average** of the prices, using the sales proportion for each period as the weight:

$$\begin{aligned} \text{Average Price} &= (0.45 \times \$82.52) + (0.31 \times \$49.12) + (0.24 \times \$65.23) \\ &= \$37.134 + \$15.2272 + \$15.6552 \\ &= \$68.0164\end{aligned}$$

Rounding to two decimal places, the average price is **$68.02**.