Final answer:
To find the cost of a hat, we first calculate the total spent on shirts, subtract that from the total bill, and solve the resulting equation for the price of a hat, which is $10.
Step-by-step explanation:
The student's question relates to a basic algebra problem in which the cost of shirts is given, and the cost of hats needs to be calculated based on the total bill. To solve this, we must set up an equation and solve for the unknown price of a hat.
Let's denote the price of a hat as H. The brother wants 3 shirts and 4 hats, and the sister wants 2 shirts and 2 hats, with each shirt costing $11. The total cost for shirts is thus 3*$11 for the brother plus 2*$11 for the sister, which equals $55. Since the total bill is $115, the cost for all the hats is $115 - $55 = $60.
Now, we can set up the equation for the hats: 4H (brother's hats) + 2H (sister's hats) = $60. Simplifying, we get 6H = $60. Dividing both sides by 6 gives us H = $10. Therefore, a hat costs $10.