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?
Answers
Answered by
0
Step-by-step explanation:
oh wow, i got it by pure luck guessing. there are originally 18 seats per row and 25 rows.
18*25=450
(18-3)(25+5)
=15*30
=450
as for the algebraic way to solve it, i'm not quite sure.
Answered by
3
Answer (please vote a brainliest):
25
Step-by-step explanation:
R=Rows. S=Seats
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}
R = 25.
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