Each row had 9 chairs at first.

2 chairs from each existing row were removed so each existing row only has 7 chairs left.

The removed chairs are used to make the additional rows.

12 additional rows were made.
So 12 x 7 = 84 chairs. 84 chairs are used to make these new rows.

Since Declan bought another 6 chairs, these 6 chairs were among the 84 used.

84 - 6 = 78

So 78 chairs were removed from the rows of 9 chairs at first.

Since each row had 2 chairs removed at first, 78 ÷ 2 = 39

So there were 39 rows at first.


39 existing rows + 12 new rows = 51 rows

There are 51 rows now.

Since each row has 7 chairs now,

51 x 7 = 357

357 chairs were in the hall for the concert.

At the start, the rows have 9 chairs each.

After the rearrangement with the 6 extra chairs, the rows have 7 chairs each, but there are 12 rows more than before.

For every shift of chairs from a row, 2 chairs are being moved (9 - 7 = 2).

12 extra rows (each containing 7 chairs) means that 12 x 7 = 84 chairs must have occupied the new rows. 6 of the chairs are “new” ones, so the remaining 84 - 6 = 78 chairs must have been moved.

Number of rows being shifted = 78 / 2 = 39

So there are initially 39 rows of 9 chairs. Currently there are 51 rows of 7 chairs.

Check.

39 x 9 + 6 = 351 + 6 = 357
51 x 7 = 357

These tally.

There are currently 357 chairs in the concert hall.