<Question>
If a snack-size tin of peaches has $40$ calories and is $2\%$ of a person's daily caloric requirement, how many calories fulfill a person's daily caloric requirement?
</Question>

<think>
<Plan_1>
Okay, let's see. The problem says that a snack-size tin of peaches has 40 calories and that's 2% of a person's daily caloric requirement. I need to find out how many calories make up the full daily requirement. Hmm, percentages can sometimes be tricky, but let me break it down step by step.

First, I know that 2% corresponds to 40 calories. So, if 2% is 40 calories, then 1% would be half of that, right?
Let me check that. If 2% is 40, dividing both sides by 2 would give 1% equals 20 calories. That makes sense. So 1% is 20 calories.

Then, to find 100%, which is the total daily calories, I just multiply 20 by 100.
That would be 20 * 100 = 2000 calories. Wait, 20 times 100 is indeed 2000. So, does that mean the daily caloric requirement is 2000 calories?

Let me verify this another way to make sure I didn't make a mistake. If 40 calories is 2% of the total, then the total calories (let's call it T) can be found using the equation: 2% of T equals 40. In math terms, that's 0.02 * T = 40. To solve for T, I divide both sides by 0.02.
So T = 40 / 0.02. Let me compute that. Dividing 40 by 0.02 is the same as multiplying 40 by 50, because 1/0.02 is 50. So 40 * 50 = 2000.

Another way to think about it: 0.02 is equivalent to 2/100. So, 40 divided by (2/100) is 40 * (100/2) = 40 * 50 = 2000.
That's consistent. Hmm, maybe I can cross-check with an example. Suppose someone needs 2000 calories a day.

<prompt_1.1> Cross-verify the solution using an example of a daily caloric need. </prompt_1.1>

Wait, but is there any possibility that the question is tricking me? Like, maybe the 2% is not of the total, but something else?

<prompt_1.2> Consider potential tricks in the question and confirm the interpretation. </prompt_1.2>

Alternatively, if I set up a proportion: 2% corresponds to 40 calories, so 100% corresponds to X calories. Therefore, 2/100 = 40/X. Wait, no, actually, setting up proportions can sometimes be confusing. Let me see. If 2% is 40 calories, then 100% would be X. So, the ratio is 2% : 40 calories = 100% : X calories. So, 2/100 = 40/X.

<prompt_1.3> Use proportions to verify the solution. </prompt_1.3>
</Plan_1>

<Execution_1>
<execution_1.1>
Then 2% of 2000 is 0.02 * 2000 = 40. That's exactly what the problem states. So the tin of peaches is 2% of that 2000, which is 40 calories.
</execution_1.1>

<execution_1.2>
Let me re-read the question. "If a snack-size tin of peaches has 40 calories and is 2% of a person's daily caloric requirement, how many calories fulfill a person's daily caloric requirement"? No, the wording seems straightforward. It says 2% of the daily requirement is 40 calories. So the total should be 2000.
</execution_1.2>

<execution_1.3>
Cross-multiplying gives 2X = 40 * 100. So, 2X = 4000, hence X = 2000.
</execution_1.3>
</Execution_1>

<Plan_2>
Based on execution_1.1, execution_1.2, execution_1.3:
I think all the methods are converging to 2000 calories. Let me just confirm with another example.

<prompt_2.1> Confirm the solution with another example. </prompt_2.1>
</Plan_2>

<Execution_2>
<execution_2.1>
If 1% is 20 calories, then 10% would be 200, 50% would be 1000, and so on. So 100% is 2000. That seems correct.
</execution_2.1>
</Execution_2>

<Final_answer>
Therefore, a person's daily caloric requirement is $\boxed{2000}$ calories.
</Final_answer>
</think>