#### In a classroom, the tables were positioned so that there were 5 more rows than columns. Without adding or removing any tables, the arrangement of the tables is changed by removing 5 columns and adding 10 rows. How many people can fit at once in that classroom?Option: 1 315Option: 2 403Option: 3 512Option: 4 204

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

Then the number of rows in the original arrangement is x + 5.

The original number of tables is,

Thus,

$x(x+5)=x^{2}+5x$

After 6 columns are removed, there are columns remaining.

After 12 rows are added, there are rows in the new arrangement.

The new number of chairs is given by,

$(x-5)(x+15)=x^{2}+15x-5x-75\\ (x-5)(x+15)= x^{2}-10x-75\\$

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

So,

$x^{2}+5x= x^{2}-10x-75\\$

By simplifying and solving for x, we get,

$5x=75\\ x=12$

Therefore, the original arrangement had 12 columns and 12 + 5 = 17 rows.

The original number of tables is given by,

$12 \times 17=204$

Therefore, the number of tables is 204.