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

  • algebra -

    S = # of seats per row
    R = # of rows
    S = R - 16
    S*R = R * (R-16) = 1161
    R^2 - 16R - 1161 = 0
    1161 is the product of 43 and 27. The equation factors to
    (R - 43)(R + 27) = 0
    R = 43 is the only positive answer for the number of rows. There are
    S = R - 16 = 27 seats per row.

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