Question

ben is 12 years older than ishaan. ben and ishaan first met two years ago. three years ago, ben was 4 times as old as ishaan. how old is ishaan now?

Explanation:

Step1: Define Variables

Let \( I \) be Ishaan's current age, and \( B \) be Ben's current age.

Step2: Set Up Equations

From "Ben is 12 years older than Ishaan", we have \( B = I + 12 \).
Three years ago, Ishaan's age was \( I - 3 \), and Ben's age was \( B - 3 \). From "Three years ago, Ben was 4 times as old as Ishaan", we get \( B - 3 = 4(I - 3) \).

Step3: Substitute and Solve

Substitute \( B = I + 12 \) into \( B - 3 = 4(I - 3) \):
\( (I + 12) - 3 = 4(I - 3) \)
Simplify left side: \( I + 9 = 4I - 12 \)
Subtract \( I \) from both sides: \( 9 = 3I - 12 \)
Add 12 to both sides: \( 21 = 3I \)
Divide by 3: \( I = 7 \)

Answer:

7