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26 August, 16:50

A rectangular auditorium seats 1833 people. The number of seats in each row exceeds the number of rows by 8. Find the number of seats in each row.

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  1. 26 August, 18:45
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    Let x be the no. of seats in each row and y be the no. of seats in each row.

    we have,

    Total no. of people in the auditorium = 1833

    => xy = 1833

    => y = 1833/x - - - (1)

    From the given condition, we get,

    y = x+8

    => 1833/x = x+8 [from equation (1) ]

    => (1833/x) - x = 8

    => (1833-x^2/x) = 8

    => 1833-x^2 = 8x

    => - x^2 - 8x + 1833 = 0

    => x^2 + 8x - 1833 = 0

    => x^2 + 47x - 39x - 1833 = 0

    => x (x+47) - 39 (x+47) = 0

    => (x-39) (x+47) = 0

    i. e, either x-39 = 0

    => x = 39

    or x+47=0

    =>x=-47 [but no. of seats cannot be negative]

    therefore x = 39

    Hence there are 39 seats in each row.
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