### Question:

Two years ago, I was three times as old as my brother was. In three years, I will be twice as old as my brother. How old is each of us now?

### Answer:

**The older brother is 17, and the younger brother is 7.**

### Explanation

Let’s delve into the age mystery and solve the puzzle step by step to reveal the ages of you and your brother.

Step 1: Setting Up Variables

- Let your current age be “x” years.
- Let your brother’s current age be “y” years.

Step 2: Two Years Ago Comparison Two years ago, your age was (x – 2) years, and your brother’s age was (y – 2) years. The puzzle states that at that time, your age was three times your brother’s age:

Equation 1: x – 2 = 3(y – 2)

Step 3: In Three Years Comparison In three years, your age will be (x + 3) years, and your brother’s age will be (y + 3) years. The puzzle states that at that time, your age will be twice your brother’s age:

Equation 2: x + 3 = 2(y + 3)

Step 4: Solving the System of Equations Now, we have a system of two equations with two variables:

- x – 2 = 3(y – 2)
- x + 3 = 2(y + 3)

Solving these equations simultaneously, we find that your current age “x” is 17 years, and your brother’s current age “y” is 7 years.