Oh, this would be so much easier to explain if I could draw t accounts and show you. I haven't yet tried to explain this one in words only. Here goes:
The allowance account is a contra asset account, which reduces the receivables, so it is a credit balance. When you do an actual write off, you credit John Doe's account out of the receivables and debit it out of the allowance account also. i.e. each account is reduced. So that's what the write-offs during the year are going to do to your balance. You need to get this balance first.
With the method you're using, analysis of receivables, the number you got (59,700) is the balance you want to have in the allowance account at year-end. i.e. this is not your adjusting entry, but the balance you want. (You can't journalize a balance.) Here's where a t account would come in handy. You need to look at the balance in the account, and figure out what needs added (credited) to that account to get to the 59,700 balance. That's the number you will use in the entry.
The adjusting entry is always a dr to Bad Debt Expense or Uncollectible Accounts Expense, or whatever you're book is calling it, and a credit to the Allowance account. Remember that expenses are always debits. And this allowance account is a contra asset, making it a credit.
That allowance will then reduce the amount of the receivables. The receivables don't have value if you think you can't collect them. So the estimate of what you think you can't collect reduces that value to a lower net number. (Called net realizable value.) There's actually two ways you can present this on the balance sheet. Hopefully your book has an example of this.
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