An audience of 450 people is seated in an auditorium. each row contains the same number of seats and each seat in the auditorium is occupied. with three fewer seats per row, and five extra rows, the same audience could still be seated, occupying all seats. how many rows does the auditorium have?

Thank you for posting your question here at . I hope the answer will help you. Feel free to ask more questions here.

SR = 450 
S = 450/R 

(S - 3)(R + 5) = 450 
(450/R - 3)(R + 5) = 450 
(450 - 3R)(R + 5) = 450R 
450R + 2250 - 3R^2 - 15R = 450R 
3R^2 + 15R - 2250 = 0 
R^2 + 5R - 750 = 0 
R^2 + 30R - 25R - 750 = 0 
R(R + 30) - 25(R + 30) = 0 
(R + 30)(R - 25) = 0 
R ∈ {-30,25} 

Only positive numbers make sense in this context, therefore R = 25.