Final answer:
The sister and brother are the same age.
Step-by-step explanation:
To solve this problem, let's assign variables to represent the ages of the siblings. Let's say the sister's age is x and the brother's age is y. According to the information given, in 2 years the sister will be twice as old as she was 2 years ago, so we can write the equation:
x + 2 = 2(x - 2)
Simplifying the equation, we get:
x + 2 = 2x - 4
Next, let's solve for x:
2 = x - 4
6 = x
Therefore, the sister's age is 6 years old. Now, let's look at the information about the brother. In 3 years, the brother will be three times older than he was 3 years ago, so we can write the equation:
y + 3 = 3(y - 3)
Simplifying the equation, we get:
y + 3 = 3y - 9
Next, let's solve for y:
12 = 2y
6 = y
Therefore, the brother's age is 6 years old. Since they are both the same age, we can conclude that the siblings are the same age.