math

Number of apartments rented
The manager of an 80 unit apartment complex knows from experience that at a rent of £¤300 per unit, all the units will be full.On thw average, an additional unit will remain wacant for each £¤20 increase in rent over £¤300. Furthermore, the manager must keep at least 30 units rented due to toher financial considerations. Currently, the revenue from the complex is £¤35000. How many apartments are rented?

a) Suppose that x represents the number of £¤20 increases over £¤300. Represent the number of apartment units that will be rented in terms of x

b)Represent the rent per unit in terms of x

c)Use the answer in (a) and (b) to write an expression that defines the revenue generated when there are x £¤20 increases over £¤300.

d)According to the problem, the revenue currently generated in £¤35000. Write a quadratic equation in standard form

e)Solve the equation in (d) and answer the question in the problem

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  1. I will do the question the way I would do it.
    I will let you sort out which part becomes your a) , b) , etc

    let x be as defined above.

    number of units rented = 80 - x
    rent for each unit = 300+20x

    (80 - x)(300+20x) = 35000
    24000 +1300x - 20x^2 = 35000
    -20x^2 + 1300x -11000 = 0
    x^2 - 65x + 550 = 0
    (x - 55)(x - 10) = 0

    x = 55 or x = 10

    number of units rented
    = 80-55 = 25
    or
    = 80-10 = 70

    but it said that at least 30 must be rented, so

    there are 70 units rented

    check:
    if x=10, rent = 300+10(20) = 500
    units rented = 70
    revenue = 70 x 500 = 35000

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