Find the number of seats in each row

A rectangular auditorium seats 2709 people. The number of seats in each row exceeds the number of rows by 20. Find the number of seats in each row.

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x = the number of rows
x + 20 = the number of seats in each row {“number of seats in each row exceeds the number of rows by 20”}

If you multiply the number of rows by the number of seats in each row, that equals the total number of seats.

x(x + 20) = 2709 {multiplied number of rows by number of seats in each row and set equal to total seats}
x² + 20x = 2709 {used distributive property}
x² + 20x - 2709 = 0 {subtracted 2709 from each side}
(x + 63)(x - 43) = 0 {factored left side into two binomials}
x + 63 = 0 or x - 43 = 0 {set each factor equal to zero}
x = -63 or x = 43 {solved each equation for x}

The number of rows cannot be negative. Therefore x cannot equal -63.

x = 43
x + 20 = 63 {substituted 43, in for x, into x + 20}

43 rows
63 seats in each row

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