Q.4 (i) Manisha wants to distribute 540 bananas among some students. If 30 students were more, each would get 3 bananas less. Find the number of students.
Best answer
Answer: 60 students
Let the number of students be \(x\). Each student gets \(\dfrac{540}{x}\) bananas.
If 30 students were more, each would get 3 bananas less :
\(\dfrac{540}{x} - \dfrac{540}{x + 30} = 3\)
Multiplying by \(x(x + 30)\) : \(540(x + 30) - 540x = 3x(x + 30)\)
\(16200 = 3x^2 + 90x\), i.e. \(x^2 + 30x - 5400 = 0\)
\((x + 90)(x - 60) = 0\), so \(x = -90\) or \(x = 60\).
The number of students cannot be negative, hence \(x = 60\).
Check : \(\dfrac{540}{60} = 9\) and \(\dfrac{540}{90} = 6\), and \(9 - 6 = 3\) ✓
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