Question

A group of girls planned a picnic. The total budget for food was Rs.2400. Due to illness, 10 girls could not go to the picnic. So, the contribution by each girl towards food increased by Rs. 8. How many girls had planned to go to picnic initially

Answer 1

Let the number of students be x and cost per sudent y

xy=2400 y = 2400/x

(x-10) ( y+8 )= 2400

xy + 8x-10y-80 =2400

2400+8x- 10×2400/x -80 = 2400

8x^2-80x-24000

x^2-10x-300

x = ( + 50, -60)

x= 50

Answer 2

Step-by-step explanation:

Total budget for food is Rs.2400

Let the the number of girls who had planned to go initially be x

Let the previous amount of money to be given by each girl be y

So, xy=2400

=> y= 2400/x -----> (1)

Now, as 10 could not go, the remaining girls become (x-10)

And their contribution towards food increased by Rs.8, so Rs.(y+8)

At the present situation,

(x-10)(y+8) = 2400

=> ( xy+ 8x -10y - 80) = 2400

=> { (x. 2400/x) + 8x - 10(2400/x) - 80} = 2400

=> { 2400 + 8x - 24000/x - 80 } = 2400

=> ( 8x^2 - 2400)/x +2320 = 2400

=> ( 8x^2 - 2400)/x = 2400-2320

=> ( 8x^2 - 2400) = 80x

=> 8x^2 - 80x -2400 =0

=> x^2 - 10x - 300 =0

( By quadratic formulae)

x = 23 or x= -13

Therefore, the number of girls that had planned to go initially is 23

{Sorry for making it look so complicated ^-^}

Hope it meets the needful