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  • In a conference room, the chairs were positioned so that there were six more rows than columns. Without adding or removing any chairs, the arrangement of the chairs is changed by removing

In a conference room, the chairs were positioned so that there were six more rows than columns. Without adding or removing any chairs, the arrangement of the chairs is changed by removing 6 columns and adding 12 rows. How many people can fit at once in that conference room?

Option: 1

332


Option: 2

432


Option: 3

542

 


Option: 4

652


Answers (1)

best_answer

Let the number of columns in the original arrangement be x. 

Then the number of rows in the original arrangement is x + 6.

The original number of chairs is,

Thus,

x(x+6)=x^{2}+6x

After 6 columns are removed, there are  x-6  columns remaining. 

After 12 rows are added, there  x+6+12=x+18   are rows in the new arrangement.

The new number of chairs is given by,

(x-6)(x+18)=x^{2}+12x-108

Since no chairs were added or removed, the number of chairs in the original arrangement must be equal to the number of chairs in the new arrangement. 

So,

x^{2}+6x=x^{12}+12x-108

By simplifying and solving for x, we get,

6x=108

x=18

Therefore, the original arrangement had 18 columns and 18 + 6 = 24 rows.

The original number of chairs is given by,

18\times 24=432

Therefore, the number of chairs is 432.

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