SOLUTION: 800 persons are seated on benches of equal length. if there were 20 fewer benches it would be necessary that two persons more should sit on each bench. find the number of benches.

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Question 468272: 800 persons are seated on benches of equal length. if there were 20 fewer benches it would be necessary that two persons more should sit on each bench. find the number of benches.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
800 persons are seated on benches of equal length.
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Let original # of benches be "x".
Average persons per bench = 800/x
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If there were 20 fewer benches it would be necessary that two persons more should sit on each bench. find the number of benches.
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Average persons per bench after change:
800/(x-20)
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Equation:
New average - original average = 2
800/(x-20) - 800/x = 2
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800x-800(x-20) = 2
800*20 = 2x(x-20)
800*10 = x^2-20x
x^2-20x-8000 = 0
(x+80)(x-100) = 0
Positive solution:
x = 100 (original # of benches)
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Cheers,
Stan H.
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