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The problem in the image involves calculating the average daily balance for a credit card account. Here's a breakdown of the information provided:

- Initial balance on 7/8: $456.
- A purchase of $112 was made on 7/16.
- A payment of $342 was made on 7/28.
- The billing date is 8/8.

### Step-by-Step Solution for Average Daily Balance

1. **Initial Balance Period (7/8 - 7/16):**
   From 7/8 to 7/16, the balance is $456 for 8 days.
   \[
   \text{Balance for this period} = 456 \times 8 = 3648
   \]

2. **Balance After Purchase (7/16 - 7/28):**
   After the purchase on 7/16, the new balance becomes $456 + 112 = 568$. This balance remains from 7/16 to 7/28 (12 days).
   \[
   \text{Balance for this period} = 568 \times 12 = 6816
   \]

3. **Balance After Payment (7/28 - 8/8):**
   After the payment of $342 on 7/28, the new balance is $568 - 342 = 226$. This balance lasts for 11 days from 7/28 to 8/8.
   \[
   \text{Balance for this period} = 226 \times 11 = 2486
   \]

4. **Total Average Daily Balance Calculation:**
   The total number of days is $8 + 12 + 11 = 31$ days.
   \[
   \text{Total balance sum} = 3648 + 6816 + 2486 = 12950
   \]
   The average daily balance is:
   \[
   \frac{12950}{31} \approx 417.74
   \]

Thus, the **average daily balance** is approximately **$417.74**.

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Do you need any further details or clarification on this solution? Here are five related questions for further exploration:

1. How would the average daily balance change if the purchase had been larger?
2. What is the significance of average daily balance in credit card billing cycles?
3. How is interest applied based on the average daily balance?
4. How does making payments earlier in the cycle affect the balance?
5. Could the result be different if there were additional purchases after 7/28?

**Tip:** When calculating average daily balance, it's important to consider each transaction's impact on the balance for the appropriate number of days.

A credit card account has a $456 balance on 7/8. A purchase of $112 was made on 7/16 and a payment of $342 was made on 7/28. The billing date is 8/8. Find the average daily balance.

Learn how to calculate the average daily balance for a credit card account with transactions including purchases and payments. This detailed step-by-step guide is ideal for students in Grades 9-12.

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