Question

A real estate firm owns the Kasumba Garden Apartments which consists of 90 apartments. At $350 per month every apartment can be rented. However, for each $10 per month increase there will be two vacancies with no possibility of filling them. The firm wants to receive $31 980 per month from rents. What rent should be charged for each apartment?

Answer 1

The rent should be $ 390 or $ 410.

Explanation:

Given,

The original monthly rent of an apartment = $350,

Also, the original number of apartment that could be filled = 90,

Let the rent is increased by x times of $ 10,

That is, the new monthly rent of an apartment =( 350 + 10x ) dollars

Since, for each $10 per month increase there will be two vacancies with no possibility of filling them.

Thus, the new number of filled apartments = 90 - 2x,

Hence, the total revenue of the firm = ( 90 - 2x )(350 + 10x ) dollars,

According to the question,

( 90 - 2x )(350 + 10x ) = 31,980

`90(350)+90(10x)-2x(350)-2x(10x)=31980`

`31500+900x-700x-20x^2=31980`

`-20x^2+200x+31500-31980=0`

`20x^2-200x+480=0`

By the quadratic formula,

`x=(200\pm √((-200)^2-4* 20* 480))/(40)`

`x=(200\pm √(1600))/(40)`

`x=(200\pm 40)/(40)`

`\implies x=(200+40)/(40)\text{ or }x=(200-40)/(40)`

`\implies x=6\text{ or } x =4`

Hence, the new rent of each apartment, if x = 6, is $ 410,

While, if x = 4, is $ 390