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.
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 Ask Algebra House
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