Let Mark’s current age be x.
Three years ago, Mark’s age was x – 3. The square of his age from that time can be expressed as (x – 3)².
In 9 years, Mark’s age will be x + 9. According to the problem statement, we can set up the following equation:
(x – 3)² = 6 * (x + 9)
Now let’s expand and simplify the equation:
x² – 6x + 9 = 6x + 54
Bringing all terms to one side gives us:
x² – 12x – 45 = 0
This is a quadratic equation. We can solve for x using the quadratic formula:
x = [-b ± √(b² – 4ac)] / 2a
Here, a = 1, b = -12, c = -45.
Calculating the discriminant:
Δ = (-12)² – 4 * 1 * (-45) = 144 + 180 = 324
Now, plug the values into the quadratic formula:
x = [12 ± √324] / 2
√324 = 18
Thus, we have:
x = (12 + 18) / 2 = 15 or x = (12 – 18) / 2 = -3
Since age cannot be negative, we discard x = -3.
Therefore, the current age of Mark is 15 years.