Question

On teachers day ,4800sweets were to be equaly distributed among a certain no . of childers .but on that day 100 childrens were absent .hence,each childrn got 4 sweetes extra.how many childrens were origunaly supposed to be there?

Answer 1

Hi.

Here is your answers---

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Let the number of children who are originally supposed to be in teachers day program be x.

Number of Sweets which is to be originally distributed = 4800/x.

Numbers of children Absent = 100
Numbers of children who attained was present in teacher's day = (x - 100)                                                                                                               Children.

Number of Sweets which will be  distributed to one children = 4800/(x-100)

As per as Questions,

 4800/(x - 100) - 4800/x = 4

[4800x - 4800(x - 100) ] = 4(x² -100x)
  1200( x - x + 100) = x² - 100x
   x² - 100x - 120000 = 0

    Splitting the Middle Term,

   x² - 400x + 300x -120000 = 0
   x(x - 400) + 300(x - 400) = 0
   (x + 300)(x - 400) = 0

  By Zero Product Rule,

x = -300                                 x = 400

Since, x =-300 cannot be possible. Thus, number of Children who are originally supposed to be there in the teacher's day is 400.

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Hope it helps.

Have a nice day.