Final answer:
The retailer returns 20% of the damaged inventory which equates to $110. This is 20% of the $550 worth of damaged goods from the original $1,100 inventory purchase.
Step-by-step explanation:
The question asks to calculate the value of the merchandise returned by a retailer. The original purchase of the inventory was $1,100. Given that 50% of the inventory was damaged, the damaged inventory amounts to $550. The retailer decides to return 20% of the damaged inventory for a full refund. Therefore, the value of the merchandise returned is 20% of $550, which amounts to $110.