To determine Carlos's average daily balance over the course of the last month, we need to follow a methodical approach. Here's a step-by-step solution:
1. Identify the given data:
- 3 days, balance of \[tex]$2460
- 7 days, balance of \$[/tex]1247
- 8 days, balance of \[tex]$1487
- 4 days, balance of \$[/tex]762
- 6 days, balance of \[tex]$1014
2. Calculate the total balance weighted by the number of days:
- This involves multiplying each balance by the number of days it was held.
\[
\text{Weighted balance for 3 days} = 3 \times 2460 = 7380
\]
\[
\text{Weighted balance for 7 days} = 7 \times 1247 = 8729
\]
\[
\text{Weighted balance for 8 days} = 8 \times 1487 = 11896
\]
\[
\text{Weighted balance for 4 days} = 4 \times 762 = 3048
\]
\[
\text{Weighted balance for 6 days} = 6 \times 1014 = 6084
\]
3. Sum the total weighted balances:
\[
7380 + 8729 + 11896 + 3048 + 6084 = 37137
\]
4. Sum the total number of days:
\[
3 + 7 + 8 + 4 + 6 = 28
\]
5. Calculate the average daily balance:
- Divide the total weighted balance by the total number of days.
\[
\text{Average daily balance} = \frac{37137}{28} \approx 1326.3214285714287
\]
6. Round the average daily balance to the nearest penny:
\[
\text{Rounded average daily balance} = 1326.32
\]
Therefore, Carlos’s average daily balance, when rounded to the nearest penny, is \( \$[/tex]1326.32 \).
