On may 31, the cash account of bottle's r us had a normal balance of $5,000. during may, the account was debited for a total of $12,200 and credited for a total of $11,500. what was the balance in the cash account at the beginning of may?

Since there are no special paameters mentioned to solve the problem, algebra will be employed.

What we have so far:
Total debit = $12,200
Total credit = $11,500
Total transactions = Total credit - Total debit
Final balance = $5,000

To solve:
Let us use the working equation: Initial Balance = Final Balance + |Total Transactions|
Initial Balance  =  $5,000 + |$11,500 - $12,200|
Initial Balance  =  $5,000 + |-$700| <--- remember that -$700 is an absolute value which makes it positive.
Initial Balance  =  $5,700 <--- What we are looking for.

Checking:
Early May: $5,700
Around May : $5,700 - Total Debit (Assumption)
Around May : $5,700 - $12,200 = -$6,500 (Assumption)
Around May: -$6,500 + Total Credit (Assumption)
Around May: -$6,500 + $11,500 = $5,000 (Assumption)
31st of May: $5,000 <--- Proven

∴The answer is: $5,700, the initial balance at the beginning of May.