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.
26 August, 18:45
Let x be the no. of seats in each row and y be the no. of seats in each row.
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
=>x=-47 [but no. of seats cannot be negative]
therefore x = 39
Hence there are 39 seats in each row.
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» 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.