Question 1020623
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In a hall 192 children are made to sit in rows and columns and number of rows is more than column by 4 . What is the number of children in each column
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1.
Try to factor the number 192 into the product of two positive integers with the difference of 4 between them.

Actually, such factorization is unique: 192 = 16*12.

So, the number of columns is 12.


2.
The other way is to solve the problem using equations.

Let x be the (unknown) number of columns.
Then the number of rows is x+4, and your equation is 

x*(x+4) = 192,  or  {{{x^2 + 4x - 192}}} = {{{0}}}.

Now you can apply the quadratic formula or use factoring. Let's factor left side polynomial: 

{{{x^2 + 4x - 192}}} = (x+16)*(x-12).

Then your equation is (x+16)*(x-12) = 0.

Its roots are x = -16 and x = 12.

Only positive x = 12 suits the condition.

<U>Answer</U>. 12 columns.
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