Question

Chairs in an auditorium are arranged in rows in such a way that the first two rows each have the same number of chairs. The third and fourth rows each have three more chairs than the first and second row; the fifth and sixth rows each have three more chairs than the third and fourth row, etc. The sequence of number of chairs for every second row forms an arithmetic sequence. The first two rows each have 27 chairs, and the last two rows each have 114 chairs.

How many rows of chairs are there?

How can this be? Because the first two rows have the same amount of chairs, and no whole number added by itself equals 27. I'm Confused.

Answer 1

The first 2 rows *each* have 27 chairs.

What we have here is the fact that each pair of rows of chairs has 3 more per row more than the previous pair.

114-27 = 87 = 3*29.

So, there are 30 pairs of rows. The first pair have 27 chairs each, and the 30th pair have 114 chairs each.

Sounds like 60 rows of chairs.

Answer 2

There are 222 chairs in the auditorium. They are arranged in 12 rows. The first 6 rows have 18 chairs per row. The last 6 rows each have an equal number of chairs per row. How many chairs per row do the last 6 rows have?