SOLUTION: An 150-unit apartment complex currently collects $90,000 per month in rent. Rent on each apartment is $600. The new management company wants to increase revenues to $113,400. But f
Question 1154160: An 150-unit apartment complex currently collects $90,000 per month in rent. Rent on each apartment is $600. The new management company wants to increase revenues to $113,400. But for each $25 increase, two tenants will move out. How many rent increases will be needed to produce revenue of $113,400? Found 2 solutions by ikleyn, josmiceli:Answer by ikleyn(52754) (Show Source):
From the condition, when the rent price is 600 + 25i, where i is the number of the 25-dollar increments,
the number of units occupied is
N(i) = 150 - 2i.
So, the revenue is R(i) = (600+25i)*N(i) = (600+25i)*(150-2i).
We want to find " i " in a way to get R(i) = 113400.
It gives you an equation
(600+25i)*(150-2i) = 113400.
Simplify and solve for " i "
90000 + 3750i - 1200i - 50i^2 = 113400
50i^2 - 2550i + 23400 = 0
i^2 - 51i + 468 = 0
= = .
Case 1. i = = 12.
It means 12 increments by 25 dollars each; so, the new price is 600+12*25 = 900 dollars.
Case 2. i = = 39.
It means 39 increments by 25 dollars each; so, the new price is 600+39*25 = 1575 dollars.
ANSWER. There are two answers, 900 dollars and 1575 dollars.
You can put this solution on YOUR website! Let = the number of $25 increases in rent
I assume that 1 tenant moving out means 1 apartment
becoming vacant
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[ total monthly rent ] = [ rent/apt + increase ] x [ decreased number of apps ]
divide both sides by
The other answer is:
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and
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Either 12 or 39 rent increases will produce
a revenue of $113,400
( depends of whether they want empty apts
or empty apts )
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Get a 2nd opinion if needed
