2025 NASS PRELIMS P2 Q3

The front wheel of a tricycle has circumference \(x\text{ cm}\). Each rear wheel has circumference \(50\text{ cm}\) less. The tricycle travels \(15\text{ m}\).

1. Write an expression in (x) for the number of revolutions of the front wheel.[1]
2. Write an expression in (x) for the number of revolutions of each rear wheel.[1]
3. Each rear wheel makes 2.5 more revolutions than the front wheel. Form an equation in \(x\) and show that it simplifies to \(x^2-50x-30000=0\).[2]
4. Solve \(x^2-50x-30000=0\).[3]
5. Find the diameter of the front wheel.[1]