Let's analyze Muriel's transactions step by step to determine the amount of the restaurant bill.
1. Initial Balance:
Muriel's beginning balance is \[tex]$380.29.
2. Transactions:
- Interest Income: \$[/tex]18.10
- Groceries: -\[tex]$61.39
- Paycheck: \$[/tex]476.24
- Gas: -\[tex]$35.00
3. Ending Balance:
Muriel's ending balance is \$[/tex]735.69.
To find the restaurant bill, we need to calculate the net transactions (excluding the restaurant bill) and then see how they influence the beginning balance to result in the ending balance.
4. Calculate total of known transactions:
- Interest Income: \[tex]$18.10
- Groceries: -\$[/tex]61.39
- Paycheck: \[tex]$476.24
- Gas: -\$[/tex]35.00
Summing these transactions, we get:
[tex]\[
18.10 - 61.39 + 476.24 - 35.00 = 397.95
\][/tex]
5. Determine the effective ending balance without the restaurant bill:
We add the sum of these transactions to the beginning balance:
[tex]\[
380.29 + 397.95 = 778.24
\][/tex]
6. Calculate the restaurant bill:
The ending balance should match after including the restaurant bill. The actual ending balance is \[tex]$735.69, so:
\[
778.24 (calculated) - 735.69 (actual) = 42.55
\]
Thus, the restaurant bill must be:
\[
-\$[/tex]42.55
\]
Therefore, Muriel's restaurant bill was \$42.55.
