# Algebra

posted by lucy

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. Steve

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.

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A rectangular auditorium seats 900 people. The number of seats in each row exceeds the number of rows by 11. Find the number of seats in each row.
The text passage contains a mathematical question about the seating arrangement in a rectangular auditorium. The question asks to find the number of seats in each row, given that the total number of seats is 1960 and the number of seats in each row exceeds the number of rows by 9. An answer is provided, showing the steps to solve the quadratic equation and concluding that there are 40 rows of 49 seats each.
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
system
# Algebra

posted by lucy

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. Steve

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.

## Similar Questions

The seats in a theater are arranged in parallel rows that form a rectangular region. The number of seats in each row of the theater is 16 fewer than the number of rows. How many seats are in each row of a 1161-seat theater?
2. ### math

Determine the seating capacity of an auditorium with 10 rows of seats if there are 10 seats in the first row, 16 seats in the second row, 22 seats in the third row, 28 seats in the forth row, and so on ?
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 formulas …
4. ### 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?
5. ### Discrete Mathematics

Mathematical sequences can be used to model real life applications. Suppose you want to construct a movie theater in your town. The number of seats in each row can be modeled by the formula C_n = 16 + 4n, when n refers to the nth row, …
6. ### Algebra II

A rectangular auditorium seats 900 people. The number of seats in each row exceeds the number of rows by 11. Find the number of seats in each row.
user
The text passage contains a mathematical question about the seating arrangement in a rectangular auditorium. The question asks to find the number of seats in each row, given that the total number of seats is 1960 and the number of seats in each row exceeds the number of rows by 9. An answer is provided, showing the steps to solve the quadratic equation and concluding that there are 40 rows of 49 seats each.

TYPE: SINGLE_QUESTION_WITH_ANSWER