Final answer:
The mathematical expression that represents the profit made from selling hats, including the advertising cost, should be 10n - 50, where n stands for the number of hats sold.
Step-by-step explanation:
To represent the situation described, we need a mathematical expression that considers the number of hats sold, the profit made from each hat, and subtracts the cost of advertising. We will use n to represent the number of hats sold. If the amount of money made from each hat is constant, let's consider that as the profit per hat. The advertising cost is a fixed amount that will be subtracted from the total profit.
In mathematical terms, if we multiply the number of hats sold (n) by the profit made for each hat, and then subtract the fixed advertising cost, we get a formula that looks like this:
Profit = (Profit_per_hat * number_of_hats_sold) - Advertising_cost
If the profit per hat is $10 and the advertising cost is $50, the proper expression using n would be:
10n - 50
Therefore, the correct formula to calculate the profit based on the number of hats sold, with each hat making $10 and the advertising cost being $50, is 10n - 50.