Number of apartments rented

Question

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

Answer 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