The total owners' equity on a company's balance sheet reflects the value of the owners' claims against the company's assets after liabilities have been deducted. When the company sells inventory for cash, it increases both its cash account and its owners' equity, provided there are no costs of goods sold affecting this transaction.
In this scenario, when inventory is sold for $55 in cash, it increases the cash balance, thereby increasing the total assets. If the inventory that was sold was originally recorded at $25 (for context, though this is not directly stated in the question), the sale contributes $55 in revenue. The profit from this transaction, which is the difference between the sale price and the cost of the inventory, will also subsequently increase the owners' equity.
If the original owners' equity was $45 before the transaction, selling the inventory increases it by the profit made from the sale. However, if the owner’s equity was originally given as $45 and the sale of inventory is assumed to have not been accounted for (or is accounted separately), then it simply remains at that level when assessing the balance sheet without calculating additional revenues or expenses from the whole financial picture.
Thus, if the stated owners' equity is $45, and without additional context to change