Answer :

Let x be the number of students who planned picnic

Original cost of food for each member =


5 students failed to attend the picnic, so (x – 5) students attended the picnic


New cost of food for each member =


According to the question



taking LCM



x2 – 5x = 500 cross multiplying


x2 – 5x – 500 = 0


Using the splitting middle term – the middle term of the general equation is divided in two such values that:


Product = a.c


For the given equation a = 1 b = – 5 c = – 500


= 1. – 500 = – 500


And either of their sum or difference = b


= – 5


Thus the two terms are – 25 and 20


Sum = – 25 + 20 = – 5


Product = – 25.20 = – 500


x2 – 5x – 500 = 0


x2 – 25x + 20x – 500 = 0


x(x – 25) + 20(x – 25) = 0


(x + 20) (x – 25) = 0


(x + 20) = 0 or (x – 25) = 0


x = – 20 or x = 25


x cannot be negative thus x = 25


The number of students who planned picnic = x – 5 = 25 – 5 = 20


Cost of food for each member =


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