Algebra II

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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.

  • Algebra II -

    Total # of seats = 900
    # of rows = R
    # of seats = S

    So according to the question, if we have R rows then we have R+11 seats

    Total # of seats = # of rows * # of seats/row
    900 = R * (R+11)
    900 = R^2 + 11R
    0 = R^2 + 11R -900
    0 = (R+36)(R-25)

    Therefore, you must have 25 rows with 36 seats in each row. We can't use -36 rows because it does not give us a realistic answer.

  • Algebra II -

    Essentially we've created a quadratic equation and we're solving it using factoring. If you don't understand how I solved this question, I can expand on my thinking. Let me know if it makes sense.

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