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  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.