A boy was asked his age by his friend. The boy said, “If you subtract 25 times my age from twice the square of my age, you will get three times your age.” If the friend is 14 years old, what is the age of the boy?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 14 years
Let the boy’s age be \(x\) years. His statement gives a quadratic equation; an age must be a positive root.
\(2x^2-25x=3\times14=42\)
\(2x^2-25x-42=0\)
\((x-14)(2x+3)=0\)
\(x=14\) or \(x=-\tfrac{3}{2}\); an age cannot be negative, so the boy is 14 years old