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March 28, 2017

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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?

I have no idea how to solve this problem. Please help if you can! Thank you! :-)

  • Algebra (please help!) - ,

    n rows
    (n-16) seats/row
    n * (n-16) = 1161
    n^2 - 16 n - 1161 = 0
    well, I want factors of 1161 that differ by 16. I know sqrt 1161 = 34.07... so I geuss that around 27 would be a good guess and 27+16 = 43 and sure enough 43*27 = 1161
    so
    (n-43)(n+27) = 0
    n = 43
    and the number of seats per row = n-16 = 27

  • Algebra (please help!) - ,

    Let R = the number of rows.
    Let Sb = the number of seats in each row

    The seats in the theater are arranged in parallel rows that form a rectangular region.

    Then, from "The number of seats in each row of the theater is 16 fewer than the number of rows" or Sb = R - 16.

    The total number of seats is given by {Sr(R) = 1161

    Therefore, Sr = R - 16 = 1161/R.

    I leave the hard part for you.

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