Ranjana wants to distribute 540 oranges among some students. If 30 students were more each would get 3 oranges less .find the number of students.

let the no. of students(A)= x
      no. of oranges distributed per one(B)= y

xy=540  eq 1

if A=(x+30)
    B=(y-3)

(x+30)(y-3)=540= xy
xy - 3x + 30y - 90= xy
​-3x + 30y - 90 = 0
-3x - 90 = -30y
-(3x + 90) = -30y
​3x + 90 = 30y  
​
x = (30y - 90)/3
x = 10y - 30   eq- 2

try the equation 2 in equation 1

(10y - 30 )y = 540

10y² - 30y = 540 (divide the equation by 10)

=> y² - 3y = 54
=> ​ y² + 6y - 9y - 54 = 0
=> y(y+6) - 9(y+6)
=> (y - 9) (y+6)

y=9
y= -6

from eq 1 
xy=540
x(9)=540
x=540/9
x=60

                  
ANSWER:- x= 60          
                    y= 9