Step 1 :Let's denote the normal price of a shirt as x.
Step 2 :Since the price of each shirt was reduced by $5, the price Principal Howard paid for each shirt is \(x - 5\).
Step 3 :Given that Principal Howard ordered 116 shirts and paid $928 in total, we can set up the following equation: \(116 * (x - 5) = 928\).
Step 4 :To solve for x, we first distribute 116 to both terms inside the parentheses: \(116x - 116*5 = 928\).
Step 5 :This simplifies to: \(116x - 580 = 928\).
Step 6 :Next, we add $580 to both sides of the equation to isolate 116x: \(116x = 928 + 580\).
Step 7 :This simplifies to: \(116x = 1508\).
Step 8 :Finally, we divide both sides of the equation by 116 to solve for x: \(x = 1508 / 116\).
Step 9 :This simplifies to: \(x = 13\).
Step 10 :So, Brand Blast normally charges $13 for a shirt.
Step 11 :To check our answer, we can substitute x = 13 back into the original equation: \(116 * (13 - 5) = 928\).
Step 12 :This simplifies to: \(116 * 8 = 928\).
Step 13 :Since both sides of the equation are equal, our solution is correct. Brand Blast normally charges $13 for a shirt.
Step 14 :The final answer is \(\boxed{13}\).