To determine Joana's average daily balance for the last month, we will use the weighted average method. Let's break this down step-by-step.
### Step 1: Calculate the Total Sum of Balances
We will first compute the total sum of balances over all days by multiplying each daily balance by the number of days it was maintained and then summing these products.
1. [tex]$\$[/tex]1,000[tex]$ for 9 days: \( 1,000 \times 9 \)
2. $[/tex]\[tex]$750$[/tex] for 10 days: [tex]\( 750 \times 10 \)[/tex]
3. [tex]$\$[/tex]850[tex]$ for 4 days: \( 850 \times 4 \)
4. $[/tex]\[tex]$900$[/tex] for 7 days: [tex]\( 900 \times 7 \)[/tex]
So, the total sum of balances is:
[tex]\[ (1,000 \times 9) + (750 \times 10) + (850 \times 4) + (900 \times 7) \][/tex]
### Step 2: Calculate the Total Number of Days
We add the number of days each balance was maintained to find the total number of days:
[tex]\[ 9 + 10 + 4 + 7 \][/tex]
### Step 3: Calculate the Average Daily Balance
The average daily balance is found by dividing the total sum of balances by the total number of days:
[tex]\[ \text{Average Daily Balance} = \frac{\text{Total Sum of Balances}}{\text{Total Number of Days}} \][/tex]
Now, let's place the given amounts in the correct places in the expression:
[tex]\[ 9(1,000) + 10(750) + 4(850) + 7(900) \][/tex]
The complete expression to find the total sum of balances and the average daily balance is:
[tex]\[ 9(1,000) + 10(750) + 4(850) + 7(900) \][/tex]
From the calculations, we have:
- Total sum of balances: [tex]\( 26,200 \)[/tex]
- Total number of days: [tex]\( 30 \)[/tex]
Thus, the average daily balance is:
[tex]\[ \frac{26,200}{30} = 873.3333333333334 \][/tex]
### Summary
Therefore, Joana's average daily balance for the last month is approximately [tex]\( \$873.33 \)[/tex].
