540 is distributed equally among same students.if there would have been 30 students more each would have received 3 less.find the number of students.
Answers
Step-by-step explanation:
Let the number of students be x.
Total number of oranges = 540/x
∴ the number of oranges each student gets = If there were 30 more students, the total number of students = (x + 30) and the total number of oranges each student gets = (540/(x + 30) According to the given condition, 540/x - 540/(x + 3) = 3
∴ 540{1/x - 1/(x + 30)} = 3
∴ (3+30 - x)/x(x + 3) = 3/540
∴ 30/ x2 + 30x = 3/540
∴ 30 × 540 = 3x2 + 90x
∴ 3x2 + 90x= 16200
∴ x2 + 30x – 5400 = 0 …[Dividing both sides by 3]
∴ x2 + 90x – 60x – 5400 = 0
∴ x(x + 90) – 60(x + 90) = 0
∴ (x + 90) (x – 60) = 0 By using the property, if the product of two numbers is zero, then at least one of them is zero, we get
∴ x + 90 = 0 or x – 60 = 0
∴ x = – 90 or x = 60 But, number of students cannot be negative, x = 60
∴ The total number of students is 60.