Question

In 2 years, my sister will be twice as old as she was 2 years ago, and in 3 years my brother will be three times older than he was 3 years ago. Which sibling is older?

Answer 1

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.