prompter: When I was four, my sister was half my age. Now I am 28, how old is my sister?

assistant: When you were 4 your sister was 2 years old, since she was half your age. That means she is 2 years younger. Age difference always stays the same. So, to find your sister's age we need to subtract 2 from your current age(28).
28-2=26
Your sister is 26 years old.

assistant: When you were four your sister was two, so now that you are 28 your sister would be 26.

prompter: Correct.  I’m glad you can do the math.

assistant: If you were 4 years old and your sister was half your age then she would have been 4/2 = 2 years old. Now if you are 28 years old, she would be 28-26 = 2 years younger than you, so she would be 28-2 = 26 years old.

prompter: This seems overly complex, can you please repeat that but without any calculations.

assistant: Your sister is 26 years old.

prompter: How did you work this out? My initial thought is that my sister is 14 years old.

assistant: The first part of your initial question states that when you were 4, your sister was half your age, meaning that she was 4 / 2 = 2 years old.
Now you are 28, meaning that 24 years have passed since you were 4.
This means that your sister is now 2 + 24 = 26 years old.

assistant: If your sister was half your age when you were four, then she was 4 / 2 = 2 years old.

Since you are now 28 years old, your sister is now 28 - (4 - 2) = 26 years old.

assistant: So when you were 4 years old if your sister had half your age that means, she was 2 at the time. That means that the age diference is 2 years, wich will stay constant in time. So if you are now 28, Simply take 2 away and that leaves us with the factual response. 26 Years old. Your initial thought was wrong.

assistant: When you were four your sister was half your age and therefore two years old.

This means she was born between one and three years after you for there to be at least one day when she was two and you four.

If you are now 28 she is at most three and at least one year older than you, depending on how your birthdays are arranged. As the question is phrased to ask for one particular answer I answered 26.

prompter: That is correct. Can you explain how you came to the right conclusion?

assistant: When you were 4, your sister was 2, which is half your age, and 2 years younger than you. Since you both age at the same rate, we can find find your sisters age when you are 28 by subtracting 2 and getting 26.

assistant: You state that at the age of 4 you're sister was half you're age. So 4 divided by 2 is 2, therefore she is 2 years younger than you. If you are now 28, then she is 26.

assistant: When you were four, your sister was half your age, which means she was two years old.
Since the same amount of years pass for both of you as you get older, the difference of two years between you and your sister remains.
Therefore if you are 28, your sister is still 2 years younger, which implies she is 26 years old.

This, of course, assumes a simplified case in which we don't take into account birthday dates. In reality the difference in age can be off by 1 year depending on whose birthday comes first.

prompter: Thanks! Can you briefly explain the rationale behind that answer?