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.
