Let's break down the problem step by step:
Step 1: Determine the initial balance
From the given check register, the beginning balance is [tex]\(\$862.74\)[/tex].
Step 2: Record the debit transaction (Medical Bill)
A medical bill has been recorded as a debit of [tex]\(\$41.56\)[/tex] on 5/3. To update the balance after this debit:
[tex]\[
\text{New Balance} = \text{Beginning Balance} - \text{Medical Bill}
\][/tex]
[tex]\[
\text{New Balance} = \$862.74 - \$41.56 = \$821.18
\][/tex]
So, after paying the medical bill, the balance is [tex]\(\$821.18\)[/tex].
Step 3: Record the deposit transaction (Check deposited by Lyle)
Lyle deposited a check of [tex]\(\$75.26\)[/tex]. To update the balance after this deposit:
[tex]\[
\text{New Balance} = \text{Balance after Medical Bill} + \text{Deposit}
\][/tex]
[tex]\[
\text{New Balance} = \$821.18 + \$75.26 = \$896.44
\][/tex]
So, after depositing the check, the new balance is [tex]\(\$896.44\)[/tex].
Thus, Lyle's new balance after recording all the transactions is [tex]\(\$896.44\)[/tex].
