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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.
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.
Answer with Step-by-step explanation:
Let there be r rows and s seats in every row.
An audience of 450 people is seated in an auditorium and each seat is occupied.
i.e. rs=450
or s=450/r
With three fewer seats per row, and five extra rows, the same audience could still be seated, occupying all seats.
i.e. (s-3)(r+5)=450
s(r+5)-3(r+5)=450
rs+5s-3r-15=450
450+5s-3r-15=450
Subtracting both sides by 450,we get
5s-3r-15=0
i.e. 5s-3r=15
5(450/r)-3r=15
Dividing both sides by 3 and multiplying by r, we get
750-r²=5r
r²+5r-750=0
r² + 30r - 25r - 750 = 0
r(r + 30) - 25(r + 30) = 0
(r + 30)(r - 25) = 0
either r+30=0 or r-25=0
either r= -30 or r=25
r can't be negative
Hence, number of rows in auditorium are:
25
