Quadratic Equation

let the number of students=x

Amount each student pays = y .So x y = 240 , y = 240/x

4 students of the group failed to go

Now number of students = x -4 and each one pays y+5

(x-4) (y+5) = 240

(x - 4) (240 / x    +5 ) = 240

(x -4 ) ( 240 + 5x)  = 240 x

240 x + 5 x² - 960 -20 x =  240 x

5x²  - 20x  - 960  =  0

x²  -  4x  - 192 = 0

x²  - 12x  +  8x  -  192  =  0

X( x - 12 )  + 8 ( x - 12 )  =  0

(x + 8 ) ( x - 12)  =  0

x = -8 , 12

The number of students  who went for the picnic  can not be negative , so x = 12

The number of students  who went for the picnic   = 12