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

Answer:

The rent should be $ 390 or $ 410.

Step-by-step 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,

$x=\frac{200\pm \sqrt{(-200)^2-4\times 20\times 480}}{40}$

$x=\frac{200\pm \sqrt{1600}}{40}$

$x=\frac{200\pm 40}{40}$

$\implies x=\frac{200+40}{40}\text{ or }x=\frac{200-40}{40}$

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

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

While, if x = 4, is $ 390