Multiple choice

$A$'s age is twice as $B$'s age. $4$ years ago, $A$ was three times as old as $B$. Find their present ages.

  1. $30$ years and $15$ years
  2. $20$ years and $10$ years
  3. $10$ years and $5$ years
  4. $16$ years and $ 8$ years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let B's age be x, so A's age is 2x. Four years ago, A was 2x-4 and B was x-4. The equation 2x-4 = 3(x-4) simplifies to 2x-4 = 3x-12, so x = 8. Thus, B is 8 and A is 16.

AI explanation

Let the present age of B be x years; then A's present age is 2x years. Four years ago, A's age was (2x - 4) years and B's age was (x - 4) years. Setting up the equation from the given condition gives 2x - 4 = 3 times (x - 4), which simplifies to 2x - 4 = 3x - 12. Solving this yields x = 8, meaning B is 8 years old; A is twice as old, making A 16 years old.

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