# Algebra

A rectangular auditorium seats 1960 people. The number of seats in each row exceeds the number of rows by 9. Find the number of seats in each row.

Thanks!

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2. 👎
3. 👁
1. Ah, but divide by what? If there are r rows, each row has r+9 seats. So,

r(r+9) = 1960
r^2+9r-1960 = 0
factors of 1960 are many, but two which differ by 9 are 40 and 49. So,
(r+49)(r-40) = 0

There are 40 rows of 49 seats.

1. 👍
2. 👎

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The content structure of the provided text is as follows: It starts with a math problem about finding the number of seats in each row of a rectangular auditorium, given the total number of seats and the relationship between the number of seats per row and the number of rows. The text then provides a solution to the problem, explaining the steps and the reasoning behind the solution.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
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# Algebra

A rectangular auditorium seats 1960 people. The number of seats in each row exceeds the number of rows by 9. Find the number of seats in each row.

Thanks!

1. 👍
2. 👎
3. 👁
1. Ah, but divide by what? If there are r rows, each row has r+9 seats. So,

r(r+9) = 1960
r^2+9r-1960 = 0
factors of 1960 are many, but two which differ by 9 are 40 and 49. So,
(r+49)(r-40) = 0

There are 40 rows of 49 seats.

1. 👍
2. 👎

## Similar Questions

1. ### precalculus

The first row of seating in section A of an arena has 7 seats. There are 25 rows in section A, each row containing two more seats than the row preceeding it. How many seats are in section A? How do you use geometric sequence to

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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

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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?

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an auditorium has 50 rows of seats. THe first row has 20 seats, the row has 21 seats, 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?

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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

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a hockey arena has a total seating capacity of 15690.the first row of seats around the rink has 262 seats. the number of seats in each subsequent row increases by 18. how many rows of seats are in the arena?

1. ### math arithmetic sequence and series

A theater has 30 seats in the first row, 33 seats in the second row, 36 seats in the third row, and so on in the same increasing pattern. If the theater has 15 rows of seats, how many seats are in the theater?

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The right side of the orchestra section of the Nederlander Theatre in New York City has 19 rows, and the last row has 27 seats. The number of seats in each row increases by 1 as you move toward the back of the section. How many
user
The content structure of the provided text is as follows: It starts with a math problem about finding the number of seats in each row of a rectangular auditorium, given the total number of seats and the relationship between the number of seats per row and the number of rows. The text then provides a solution to the problem, explaining the steps and the reasoning behind the solution.

TYPE: SINGLE_QUESTION_WITH_ANSWER