A rectangular auditorium seats 1302 people. The number of seats in each row exceeds the number of rows by 11. Find the number of seats in each row

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06-02-2021
Mathematics

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A rectangular auditorium seats 1302 people. The number of seats in each row exceeds the number of rows by 11. Find the number of seats in each row

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Angstar4idn Angstar4idn · Answer 1 · 2021-02-06T20:25:14-05:00

Angstar4idn Angstar4idn

06-02-2021

Number of seats = 42

Seats per row x row = 1302
s x r = 1302

rows + 11 = seats per row
r + 11 = s

s x r = 1302
(r + 11) x r = 1302
r^2 + 11r = 1302
r^2 + 11r - 1302 = 0
(r + 42) x (r - 31) = 0
r = -43 or 31

Cannot have negative rows so the number of rows is 31, and the number of seats per row is 31 + 11 = 42

Check: 31 x 42 = 1302 :)

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