Areal 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?

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

By the quadratic formula,

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

While, if x = 4, is $ 390

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