Respuesta :
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
[tex]90(350)+90(10x)-2x(350)-2x(10x)=31980[/tex]
[tex]31500+900x-700x-20x^2=31980[/tex]
[tex]-20x^2+200x+31500-31980=0[/tex]
[tex]20x^2-200x+480=0[/tex]
By the quadratic formula,
[tex]x=\frac{200\pm \sqrt{(-200)^2-4\times 20\times 480}}{40}[/tex]
[tex]x=\frac{200\pm \sqrt{1600}}{40}[/tex]
[tex]x=\frac{200\pm 40}{40}[/tex]
[tex]\implies x=\frac{200+40}{40}\text{ or }x=\frac{200-40}{40}[/tex]
[tex]\implies x=6\text{ or } x =4[/tex]
Hence, the new rent of each apartment, if x = 6, is $ 410,
While, if x = 4, is $ 390
