540 is distributed equally among some students if there would have been 30 students more it would have received three less find the number of students
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Total = 540
Initial student = x
Initial orange for 1 student = n
nx = 540
(n - 3)(x + 30) = 540
nx = (n - 3)(x + 30)
nx = nx + 30n - 3x - 90
30n = 3x + 90
x = over the pic 1
30n-903
x = 10n - 30
∵ nx = 540
n(10n - 30) = 540
n(n - 3) = 54
n2 - 3n - 54 = 0
n2 - 9n + 6n - 54 = 0
n(n - 9) + 6(n - 9) = 0
(n - 9)(n + 6) = 0
⇒ n - 9 = 0 or n + 6 = 0
⇒ n = 9 or n = - 6
But number of students cannot be negative.
∵ nx = 540 ⇒ x = over the pic 2
5409 ⇒ x = 60
∴ number of students = 60 students.
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