Irrecoverable Debts and Allowances Example 2 and 3

Can you please explain the flaw in my understanding of these examples.
I managed to follow the example in the lectures, but am struggling to understand why my general equation fails.

Following the examples, I am expecting to find a reliable relationship between the values used on the Statement of Financial Position and the Statement of Profit/Loss, such that I can use the available values on one statement to derive and check my calculated values for the other statement.

From Example 2, I supposed that:
Statement of Profit or Loss: Initial Receivables Value – Calculated Expenses
Should be Equal to:
Statement of Financial Position : Final receivables value – Calculated allowances

Is this assumption valid and correct?

So that, given two values from either statement, I could calculate the third value, and then perform a check between the two statements that my results are consistent.

Using Example 2:

Statement of Profit or Loss: Initial Receivables Value (from the question) – Calculated Expenses
Statement of Profit or Loss data: $82,000 – $20,560 = $61,440

Statement of Financial Position : Final receivables value – Calculated allowances
Statement of Profit or Loss data: $74,000 – $12,560 = $61,440

Using Example 3: The assertion above does not work, but I am struggling to see why:

Statement of Profit or Loss: Initial Receivables Value (from the question) – Calculated Expenses
Statement of Profit or Loss data: ($261,000 – $238,000) – $6,488 = $16,512
$23,000 – $6,488 = $16,512

Statement of Financial Position : Final receivables value – Calculated allowances
Statement of Financial position data: $87,200 – $9,248 = $77,952

Assuming the SOFP calculation and my initial assertion are correct:
Initial Receivables Value – Calculated Expenses = Final receivables value – Calculated allowances

Initial Receivables Value = Final calculated receivables value – Calculated allowances + Calculated Expenses
= $87,200 – $9,248 + $6,488
= $84,440

This value is not provided in the example, nor do I get it at any stage, as a value for the receivables.