Gary: The balance in his check register is $500 and the balance in his bank statement is $500.
Gail: The balance in her check register is $400 and the balance in her bank statement is $500.
Gavin: The balance in his check register is $500 and the balance in his bank statement is $510.
3 Answers

Well your balance in your register and your balance in your bank statement have to be the same for it to be correctly balanced, so it would be Gary.

Not enough information to tell.
For example, suppose Gail had a $500 balance in her register yesterday, but then she wrote a check for $100. The balance in her register would be $400, and the balance on her statement would be $500, but her checkbook would still be correctly balanced.
And suppose Gary wrote a check yesterday for $200 but forgot to write it down in his register. Then his checkbook would NOT be in balance, even though he has the same number in his register as the number that appears in his statement.

Gggggggggaaaaaarrrryyyyyyyyyyy