Question

X is three times as old as Y was three years ago. After 17 years, Y will be as old as X is today. What is the sum of the ages of X and Y today?

Answer 1

Correct Answer: 43

To determine the present ages of X and Y, let's define variables for logic formulation. Let Y's age today be \( y \), and X's age today be \( x \). According to the problem:
1. X is three times as old as Y was three years ago:
  \( x = 3(y - 3) \)
2. After 17 years, Y will be as old as X is today:
  \( y + 17 = x \)
Now, solve these equations step by step:

Step 1: From equation 1, expand and simplify:
  \( x = 3y - 9 \)   (Equation 3)

Step 2: Substitute Equation 3 in Equation 2:
  \( y + 17 = 3y - 9 \)

Step 3: Solve for \( y \):
  \( y + 17 = 3y - 9 \)
  \( 17 + 9 = 3y - y \)
  \( 26 = 2y \)
  \( y = 13 \)

Step 4: Substitute \( y = 13 \) in Equation 3 to find \( x \):
  \( x = 3(13) - 9 = 39 - 9 = 30 \)

Conclusion: The sum of the ages of X and Y today is:
  \( x + y = 30 + 13 = 43 \)

This sum fits within the provided range of 43 to 43, confirming the solution is correct.