Planned a picnic. The budget was Rs 500. But, 5 of them failed to go and thus the cost of food for each member increase by Rs 5.

Question

How many students attended the picnic?

Answer 1

Let x = original number of planned attendees

Let y = cost per person

 

xy = 500    {equation 1}

(x-5)(y+5) = 500   {equation 2}

 

From equation 2:

xy + 5x - 5y - 25 = 500

We know xy = 500 so

500 + 5x - 5y - 25 = 500

5x - 5y - 25 = 0

5(x-y-5) = 0

x - y - 5 = 0

 

From equation 1:  y = 500/x

 

x - 500/x - 5 = 0

Multiply through by x

x² - 500 - 5x = 0

x² - 5x - 500 = 0

This can be factored.  The factors of -500 that add to -5 are -25(20)

(x-25)(x+20) = 0

x = 25 or x = -20

 

Discarding the negative, x = 25

This was the original planned numbers for attendance.

The actual number that attended was x-5

 

20 students attended