Chapter: Quadratic Equations· Mathematics Part 1 (Algebra)
Answer: There are 60 students
Let the number of students be \(x\). Each gets \(\dfrac{540}{x}\) bananas.
With \(x + 30\) students each gets \(\dfrac{540}{x + 30}\).
\(\dfrac{540}{x} - \dfrac{540}{x + 30} = 3\)
\(540\left[\dfrac{(x + 30) - x}{x(x + 30)}\right] = 3\)
\(\dfrac{540 \times 30}{x(x + 30)} = 3\)
\(x(x + 30) = 5400\)
\(x^2 + 30x - 5400 = 0\)
\((x + 90)(x - 60) = 0\)
\(x = -90\) (rejected) or \(x = 60\).
Check: \(540 \div 60 = 9\), \(540 \div 90 = 6\), difference 3 ✓.