Culegere Matematica Clasa A 9 A !!exclusive!! -

“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.

He checked twice. No mistake. He checked the answer key at the back—it only said “Impossible. Explain why.” culegere matematica clasa a 9 a

Andrei stared at the page. For the first time, the culegere wasn’t asking for a number. It was asking for a reason . He wrote in his notebook: “Easy,” Andrei muttered

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.” He solved it: (3x + 12 = 2x + 24 \Rightarrow x = 12)

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.

But the next problem stopped him cold. Problem 790: A different father is four times as old as his son. In 18 years, he will be only twice as old. But the sum of their current ages is a prime number. Find their ages.

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.