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

x^{2} – 5x = 500 cross multiplying

x^{2} – 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

x^{2} – 5x – 500 = 0

x^{2} – 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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