Let's break down the problem step by step.
1. Identify Initial Balance:
The initial balance before the paycheck deposit is recorded in the check register. From the given check register, the initial balance after deducting the garbage service payment of \[tex]$42.48 is:
\[
\text{Balance Initial} = \$[/tex]2636.41
\]
2. Amount of Deposit:
Selma deposits a paycheck amount of:
[tex]\[
\text{Deposit Amount} = \$378.42
\][/tex]
3. Calculate the New Balance:
To determine the new balance, we need to add the deposit amount to the initial balance:
[tex]\[
\text{New Balance} = \text{Balance Initial} + \text{Deposit Amount}
\][/tex]
Substituting the given values:
[tex]\[
= 2636.41 + 378.42
\][/tex]
4. Result:
Hence, the new balance after recording the deposit in the check register would be:
[tex]\[
\text{New Balance} = \$3014.83
\][/tex]
Therefore, Selma's new balance after depositing the paycheck is \$3014.83.
