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To calculate the total charge for collecting $4500 in past-due child support with the given fee structure, you would first calculate the collection fee based on the amount collected.
First, calculate 18% of $4500:
18% of $4500 = 0.18 x $4500 = $810
Then, add the $15 application fee:
$810 + $15 = $825
Therefore, the total charge for collecting $4500 in past-due child support would be $825.