<Question>
A shirt's sale price is marked $\$14.40$, which is $60\%$ off the original price. How many dollars was the original price of the shirt?
</Question>

<think>
<Plan_1>
Okay, so I need to figure out the original price of the shirt when it's on sale for $14.40, which is 60% off. Let me start by understanding what the problem is saying. The sale price is 60% off, which means the customer pays 40% of the original price because 100% minus 60% discount equals 40%. So, $14.40 is 40% of the original price. My task is to find the original price.

Hmm, percentages can sometimes be tricky, but I remember that percentage problems can often be solved by setting up an equation. Let me recall the basic formula: 

If a part is a certain percentage of a whole, then part = percentage × whole. In this case, the part is the sale price ($14.40), the percentage is 40% (since that's what's left after the discount), and the whole is the original price we need to find.

So, translating that into an equation: 
Sale Price = (Percentage) × (Original Price)

But I need to remember that percentages should be converted to decimals when doing calculations. 40% is equivalent to 0.40 in decimal form. So plugging in the numbers:
14.40 = 0.40 × Original Price

To find the Original Price, I need to solve for it. That means dividing both sides of the equation by 0.40:
Original Price = 14.40 / 0.40

Let me compute that.
Dividing 14.40 by 0.40. Well, 0.40 goes into 14.40 how many times? Let's see. 0.40 times 30 is 12.00, and 0.40 times 36 is 14.40. Wait, no, 0.40 times 30 is 12, 0.40 times 35 is 14, so 0.40 times 36 is 14.40. So 14.40 divided by 0.40 is 36. Therefore, the original price was $36.

Let me check that again to be sure. If the original price is $36, and the discount is 60%, then the discount amount is 0.60 × 36 = $21.60. Subtracting that from the original price: 36 - 21.60 = 14.40, which matches the sale price given. So that seems correct.

But wait, let me go through the steps again just to make sure I didn't skip anything. The sale price is 60% off, so that's 100% - 60% = 40% of the original price.
So, 40% of original price = $14.40. Therefore, original price = $14.40 / 0.4 = $36. Yep, that's the same result. So both methods confirm that the original price was $36.

I think that's solid. But maybe there's another way to approach this problem for verification. Let's try using fractions instead of decimals. 40% is equivalent to 2/5. So if 2/5 of the original price is $14.40, then the original price would be $14.40 divided by (2/5), which is the same as multiplying by 5/2.

<prompt_1.1> Use fractions to verify the solution as described in the above plan. </prompt_1.1>

Alternatively, thinking in terms of proportions. If 40% corresponds to $14.40, then 1% would correspond to 14.40 / 40 = 0.36 dollars. Therefore, 100% would be 0.36 × 100 = $36. Again, the same answer.
</Plan_1>

<Execution_1>
<execution_1.1>
Let's compute 14.40 ÷ (2/5). 

First, 14.40 divided by 2 is 7.20. Then, 7.20 multiplied by 5 is 36. So that's another way to get the original price as $36.
</execution_1.1>
</Execution_1>

<Final_answer>
Therefore, the original price of the shirt was $\boxed{\$36}$.
</Final_answer>
</think>