we know that
1) Initial Balance=$109
2) She deposited $344
new balance=109+344=$453
3) wrote checks for $141, $73, $185, $39, and $59
total checks=141+73+185+39+59=$497
$497 > $453 -------> overdrawn
so
New balance=453-497=-$44
a $10 service charge is deducted
so
New balance=-44-10=-$54
4) she made a deposit of $65
New balance=-54+65=$21
therefore
At the end of the month, Dixie's balance was $21