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.

  1. 👍
  2. 👎
  3. 👁
  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.

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    An auditorium has 50 rows of seats. The first row has 20 seats, the second row has 21, the third row has 22 seats, and so on, each row having one more seat than the previous row. How many seats are there all together? a. write 2

  2. Math

    An auditorium has 30 rows with 10 seats in the first row, 12 in the second row, 14 in the third row, and so forth. How many seats are in the auditorium My answer is 1170 but the way I figured out the problem was by listing numbers

  3. Math (arithmetic)

    The total seating capacity of an auditorium is 1,065. The first row has 21 seats arithmetic series and each row has one seat more than the row in front of it. How many rows of seats are there in the auditorium?

  4. Math

    If he arranges the chairs and six years of the same morning he has all the chairs left over if he arranges the chairs and four rows of the same link he has 19 years left over how many chairs does Liam have

  1. math

    there are 6 rows with 18 chairs in each row. in the center of the chairs, 4 rows of 6 chairs are brown. the rest of the chairs are blue. how many chairs are blue?

  2. math

    Liam is setting up folding chairs for a meeting. If he arranges the chairs in 5 rows of the same length, he has 5 chairs left over. If he arranges the chairs in 3 rows of that same length, he has 15 left over. How many chairs does

  3. math- Algebra 2

    An auditorium has 49 rows of seats. The first row contains 40 seats. As you move to the rear of the auditorium, each row has 3 more seats than the previous row. * I am pretty sure it involves both arithmetic series and explicit

  4. Math

    One seat in an auditorium is broken. It is in the 3rd row from the front of the auditorium and in the 18th row from the back of the auditorium. There are 12 seats to its left and 17 seats to its right. If every row has the same

  1. Math

    There are 8 rows of chairs in the auditorium. 3 of the rows are empty. What fraction of the rows are empty

  2. math

    bryan is setting chairs in rows for a graduation ceremony. He has 50 black chairs and 60 white chairs. Each row will have the same number of chairs, and each row will have the same color chair. What is the greatest number of

  3. Math

    An auditorium has 400 seats. Each row in the auditorium has 16 seats. In which equation does r represent the number of rows of seats in the auditorium?

  4. Math

    1. Trevor has $65 to spend at the sporting-goods store. He buys 3 cans of tennis balls for $6 each. How many $8 sports towels can Trevor buy? a. 3 towels b. 5 towels ******* c. 6 towels d. 8 towels 2. There are 39 students in the

You can view more similar questions or ask a new question.