Question

a number of friends decided to go on a picnic and planned to spend rs.108 on eatables. three of them however did not turn up. as a consequence each one of the remaining had to contribute rs. 3 extra. the number of them who attended the picnic was:------------------

explain please

Answer 1

Let n be the original number of friends

& r = Rs per student

then, nr = 108 ⇒r = 108/n

As 3 friends did not turn up so each friend has to pay Rs 3 extra then;

(n-3) (r+3) = 108

nr + 3n -3r - 9 = 108

n(108/n) + 3n - 3(108/n) -9 = 108

108 + 3n - 3*108/n - 9 = 108

3n - 3*108/n - 9 = 0

3n^2 - 3*108 - 9n = 0

Taking 3 common, we get n^2 - 3n - 108 = 0

Roots of the above quadratic equation =  (3 + √9+432)/2 ; (3-√9+432)/2

(3+√441)/2  ;  (3 - √441)/2

(3+21)/2  ; (3 -21)/2

24/2 ; -18/2

Neglecting the negative value, we have x = 12 Hence the number of friends who attended the picnic = (x-3) = 12-3 = 9

Answer 2

Answer:

let total number of friends be x

then according to questions we can make this equation and solve for x

108/x-3 + 108/x =3

108(x-x-3)/(x)(x-3)=3

(x)(x-3)=108

x^2-3x-108=0

x^2-12x+9x-108=0

(x-12)+9(x-12)=0

(x-12)(x+9)=0

x=12 as x cannot be negative (-9)

Therefore the number of friends who attended the picnic is 12-3=9

so ans is 9. (: