Question

a lecture hall has 108 chairs arranged in rows with the same number of chairs in each row.you eliminate three rows by adding six chairs to each of the other rows.how many rows are they now?how many chairs are in each row?

Answer 1

Answer:

Let initial number of chairs in one row = x

If there are 108 chairs,

Then, the total rows of chairs = $\frac{108}{x}$

According to the question,

When three rows of chairs decreased by 3 when the number of chairs in each row is increased by 6,

Therefore, $\frac{108}{x} - 3 = \frac{108}{x+6}$

$\frac{108}{x} - \frac{108}{x+6}=3$

$108[\frac{1}{x} - \frac{1}{x+6}]=3$

$108[\frac{x+6-x}{x(x+6)}]=3$

$108[\frac{6}{x(x+6)}]=3$

$\frac{216}{x^2+6x}=1$

$216=x^2+6x$

$216-x^2-6x=0$

$x^2+6x-216=0$

⇒  x = 12 or x = -18

But number of chairs can not be negative,

Therefore, the number of chairs in each row = 12

⇒ Total number of rows ( initial) = 108/12 = 9

While new number of rows = 9 - 3 = 6