Okay, let's see. The problem is about finding the original price of a shirt that's on sale. The sale price is $14.40, which is 60% off the original. Hmm, so I need to figure out what the original price was before the 60% discount was applied. 

First, I remember that when something is a certain percentage off, the sale price is the original price minus that percentage. So if the shirt is 60% off, then the sale price is 40% of the original price. Because 100% minus 60% is 40%. That makes sense. So, if 40% of the original price equals $14.40, then I can set up an equation to solve for the original price.

Let me write that down. Let’s call the original price "x". Then, 40% of x is equal to $14.40. In mathematical terms, that would be 0.40 * x = 14.40. To find x, I need to divide both sides of the equation by 0.40. So x = 14.40 / 0.40. Let me calculate that. 

14.40 divided by 0.40. Hmm, 0.40 goes into 14.40 how many times? Well, 0.40 times 30 is 12.00, and 0.40 times 36 is 14.40. Wait, no, 0.40 times 36 would be 14.40. Let me check: 36 * 0.40 = 14.40. Yes, that's right. So x is 36. Therefore, the original price was $36. 

Wait, but let me double-check that. If the original price is $36, and it's 60% off, then the discount is 0.60 * 36 = 21.60. Subtracting that from 36 gives 36 - 21.60 = 14.40, which matches the sale price. So that checks out. 

Alternatively, I could think of it as the sale price being 40% of the original. So 40% of x is 14.40, so x is 14.40 divided by 0.40. Which is the same as multiplying 14.40 by 2.5 (since 1/0.40 is 2.5). 14.40 * 2.5. Let me calculate that. 14 * 2.5 is 35, and 0.40 * 2.5 is 1.00. So 35 + 1 = 36. Same result. 

Another way to approach this could be to set up the equation as follows: original price minus 60% of original price equals sale price. So x - 0.60x = 14.40. That simplifies to 0.40x = 14.40, leading to x = 14.40 / 0.40 = 36. Yep, same answer. 

I think that's solid. But let me make sure I didn't make any calculation errors. Let's redo the division. 14.40 divided by 0.40. If I move the decimal places to make it whole numbers, multiply numerator and denominator by 100: 1440 / 40. 40 goes into 1440 how many times? 40*30=1200, 40*36=1440. So 36. Correct. 

Alternatively, breaking down 14.40: 0.40 is 2/5, so dividing by 2/5 is multiplying by 5/2. So 14.40 * 5/2. Let's compute that. 14.40 * 5 = 72.00, divided by 2 is 36.00. Yep. So all methods lead to 36. 

Therefore, the original price was $36. 

I think that's thorough. Checked it multiple ways, different methods to verify. All point to the same answer. So I feel confident that's correct.
Therefore, the original price of the shirt was $\boxed{36}$ dollars.
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