A real-state firm owns the PArklane Garden Apartments, which consists of 96 apartments. At $550 per month, every apartment can be rented. However, for each $25 per month increase, there will be three vacancies with no possibility of filling them. The firm wants to receive $54,600 per month from rents. What rent should be charged for each apartment?

Attempt:
I treated this like a maximum/minimum problem.
$54,600 is the wanted revenue.

Let 'x' represent a $25 month increase.
(96 - 3x) is the bracket that represents the number of occupied apartments.
(550 + 25x) is the bracket that represents..

Question

A real-state firm owns the PArklane Garden Apartments, which consists of 96 apartments. At $550 per month, every apartment can be rented. However, for each $25 per month increase, there will be three vacancies with no possibility of filling them. The firm wants to receive $54,600 per month from rents. What rent should be charged for each apartment?

Attempt:
I treated this like a maximum/minimum problem.
$54,600 is the wanted revenue.

Let 'x' represent a $25 month increase.
(96 - 3x) is the bracket that represents the number of occupied apartments.
(550 + 25x) is the bracket that represents..

anonymous · Answer

(550 + 25x) is the bracket that represents the price per apartment.
So then my equation turns out to be:
54600 = (96-3x)(550+25x)
Is this the correct equation? If so, then can someone explain as to why the RHS is written out in the form of ( )*( ). I have been taught to format it like this, but I didn't really get a sense as to why it is done like this.

anonymous · Answer

because it's a quadratic equation.. if you expand you'll see y=Ax^2 + Bx + C

that's what i think..

anonymous · Answer

when you graph it, you get a maximum, and that's your answer