The question is:
How many rows of 15 chairs were there in the hall at first?
So we let N = the number of rows of 15 chairs there were in the hall at first.
All the chairs in the hall were arranged in rows of 15.
Therefore there were 15N chairs.
When the chairs were arranged in rows of 10, there were 4 more rows,
that's (N+4) rows of 10 each, or 10(N+4) chairs in the rows
and 5 chairs left over,
so we add 5 more to that, and that gives
10(N+4)+5
chairs after they were rearranged in rows of 10. So the number
of chairs when they were arranged in rows of 15 must equal the
number of chairs when they were arranged in rows of 10. So the
equation is:
15N = 10(N+4)+5
15N = 10N+40+5
15N = 10N+45
5N = 45
N = 9
Checking:
There were 9 row of 15 each in the beginning, which is 9×15 or 135 chairs
Then when they were arranged in 9+4 or 13 rows of 10 each, those rows
contained 13×10 or 130 chairs, and the 5 left over makes 135. So it checks.
Edwin