One rainy Thursday, he flipped to a random page. Problem 789: A father is three times as old as his son. In 12 years, he will be twice as old. Find their ages.
“Easy,” Andrei muttered. Let the son be x , the father 3x . In 12 years: (3x + 12 = 2(x + 12)). He solved it: (3x + 12 = 2x + 24 \Rightarrow x = 12). Father 36, son 12. Done. culegere matematica clasa a 9 a
But by October, the culegere had become a symbol of failure. Problem 347: Solve the system of equations . He’d stare at the two innocent-looking lines until the x’s and y’s blurred. Problem 512: Study the monotonicity of the function . The arrows (↑ for increasing, ↓ for decreasing) felt like personal accusations. One rainy Thursday, he flipped to a random page
He felt a strange thrill. The problem hadn’t tricked him—it had invited him to think beyond the formula. For the first time, math felt less like memorizing and more like investigating. Find their ages
He checked twice. No mistake. He checked the answer key at the back—it only said “Impossible. Explain why.”
He wrote the equations: let son = s , father = f . (f = 4s) (f + 18 = 2(s + 18) \Rightarrow 4s + 18 = 2s + 36 \Rightarrow 2s = 18 \Rightarrow s = 9, f = 36.) Sum = (9 + 36 = 45), which is not prime. A contradiction.
Andrei hated the culegere . Its thick, blue cover—creased at the spine, coffee-stained on the back—sat on his desk like a small, mute tyrant. His father had bought it in September with the best intentions: “Three problems every night, and you’ll be top of the class.”