To calculate Carlos's new balance after recording the check for the gas bill in his check register, we need to follow a sequence of steps:
1. Determine the beginning balance: According to the check register, Carlos's beginning balance is \[tex]$418.95.
2. Record the water bill payment:
- For the first transaction on the check register, Carlos pays a water bill of \$[/tex]28.94.
- Subtract the water bill amount from the beginning balance:
[tex]$ 418.95 - 28.94 = 390.01 $[/tex]
- This results in an intermediate balance of \[tex]$390.01 after the water bill payment.
3. Record the cash gift:
- On the next transaction, Carlos receives a cash gift of \$[/tex]25.00.
- Add the cash gift amount to the intermediate balance after paying the water bill:
[tex]$ 390.01 + 25.00 = 415.01 $[/tex]
- Now, the new balance is \[tex]$415.01.
4. Record the gas bill payment:
- Finally, Carlos writes a check for \$[/tex]44.92 to pay his gas bill.
- Subtract the gas bill amount from the balance after receiving the cash gift:
[tex]$ 415.01 - 44.92 = 370.09 $[/tex]
- This gives the final balance of \$370.09 after paying the gas bill.
So, Carlos's new balance after writing the check for the gas bill is [tex]\( \boxed{370.09} \)[/tex].
