Question 129645: The manager of an 80 unit apartment complex is trying to deceide what rent to charge. Experience has shown that at a rent of $200.00 all the units will be full but with one additional unit will remain vacant f0r each $20.00increase. Find the # of occupied unit if the total revenue is $20,020.
This is the problem I am trying to solve, however I am not clear on how or where to start it. If you could possibly show me the steps I would greatly appericate it. Thank you
1 solutions
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Answer 94355 by solver91311(860) on 2008-02-25 20:07:28:
You can put this solution on YOUR website!
Let x be the number of occupied units. Then 80 - x is the number of unoccupied units.
The rental fee is 200 plus 20 times the number of unoccupied units, so:
, which simplifies to:
This is the amount charged per apartment, and there are x occupied apartments, so the total revenue is:
and that is equal to $20,020.
So:
Divide by -20:
You can factor this (the prime factors of 1001 are 7, 11, and 13), or use the quadratic formula, whichever you prefer, but the roots come out to be and ,
So, if the rental fee is 200 + 20(3) = 260 (3 unoccupied units), then the total revenue is 77 * 260 = 20020.
But if the rental fee is 200 + 20(67) = 1540, then the total revenue is 13 * 1540, also = 20020.
The second root presumes that the relationship of rent to unoccupied units is linear across the entire range of possibilities, which I suspect is not the case in real life.
***************This the help that I received and I understand it up to here,however how do you compute this into a quadratic equation? That is what I don't understand. Thank you for your time........................................
Found 2 solutions by josmiceli, stanbon:
Answer by josmiceli(19441)   (Show Source):
Answer by stanbon(75887)  (Show Source):
You can put this solution on YOUR website! The manager of an 80 unit apartment complex is trying to deceide what rent to charge.
Experience has shown that at a rent of $200.00 all the units will be full but one additional unit will remain vacant f0r each $20.00 increase.
Find the # of occupied units if the total revenue is $20,020.
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Let "x" be the number of $20 increases.
Price per unit will be (200+20x)
# of units occupied will be (80-x)
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EQUATION:
Revenue = price per unit * # of units occupied:
20,020 = (200+20x)(80-x)
-20x^2 +1600x-200x + 16000 = 20,020
-20x^2+1400x -4020 = 0
Divide thru by -20 to get:
x^2-70s+201=0
Factor to get:
(x-67)(x+3)=0
Positive answer:
x = 67 (The number of $20 raises)
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Cheers,
Stan H.
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