Algebra

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.

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  1. 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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