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.