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.

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) (Show Source): You can put this solution on YOUR website!
800 persons are seated on benches of equal length.
---
Let original # of benches be "x".
Average persons per bench = 800/x
---------------------------------------------
If there were 20 fewer benches it would be necessary that two persons more should sit on each bench. find the number of benches.
----
Average persons per bench after change:
800/(x-20)
-----------------
Equation:
New average - original average = 2
800/(x-20) - 800/x = 2
---
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)
===========
Cheers,
Stan H.
=============

RELATED QUESTIONS
If 8 students are seated on each bench ,3 benches are left over .If 5 students are seated (answered by KMST)

There are 21 total benches sold. $32 per stained and $20 per unstained. The total money... (answered by TimothyLamb)

if 8 students are seated on each bench, 3 benches are left over. if 5 students are seated (answered by josmiceli)

I need help figuring out what the equation should be for this word problem. This is the... (answered by Theo,ikleyn)

f 5 pupils are seated on each bench in a classroom, 4 will be left without a place. If 6... (answered by ewatrrr)

An audience of 530 persons is seated in rows having the same number of persons in each... (answered by richwmiller)

Benches are placed 4.5 m apart along a straight path, including one at the start and one... (answered by Boyen)

There are benches in a class room if 4 students sit on each bench , three benches are... (answered by Theo)

There are benches in a classroom. If 4 students sit on each bench, three benches are left (answered by solver91311,advanced_Learner)