1. Questions

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

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
john

  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

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
    Reiny

Respond to this Question

First Name

Your Response

Similar Questions

  1. test

    A city planner is designing a new apartment complex. The complex will have several apartment buildings as well as a paved parking area for residents. In one to two sentences, describe two ways the planner can help minimize the

  2. Math Help ASAP

    A movie complex has eight different movie theaters. The manager of the complex wants to conduct a survey to determine which snacks to add to the menu. Which represents the best sample the manager could use for the survey? Survey

  3. Calculus

    The manager of a 100 unit apartment complex knows from experience that all units will be occupied if the rent is $500 per month. A market survey suggests that, on average, one additional unit will remain vacant for each $10

  4. math

    Lynbrook West, an apartment complex, has 100 two-bedroom units. The monthly profit (in dollars) realized from renting out x apartments is given by the following function. p(x)=-10x^2+1700x-43,000 To maximize the monthly rental

  1. Stats

    You want to rent an unfurnished one-bedroom apartment in Boston next year. The mean monthly rent for a random sample of 14 apartments advertised in the local newspaper is $1200. Assume that the standard deviation is $230. Find a

  2. Survey Math help

    A movie complex has eight different movie theaters. The manager of the complex wants to conduct a survey to determine which snacks to add to the menu. Which represents the best sample the manager could use for the survey? Would I

  3. Math

    You are the manager of an apartment complex with 50 units. When you set rent at $800/month, all apartments are rented. As you increase rent by $25/month, one fewer apartment is rented. Maintenance costs run $50/month for each

  4. MATH

    1. Which is equivalent to this expression? 9 – 5(4 – 2) / 3 + 5 A. -13/8 B. -1/8 C. 1 *** D. 7/4 2. There are 2 linen closets and 3 walk-in closets in each apartment in a building. The total number of closets in the building

  1. Science

    Question 12 A) Use the scenario to answer the question. A city planner is designing a new apartment complex. The complex will have several apartment buildings as well as a paved parking area for residents. In one to two sentences,

  2. managerial econ

    As manager of Citywide Racquet Club, you must determine the best price to charge for locker rentals. Assume that the (marginal) cost of providing lockers is 0. The monthly demand for lockers is estimated to be Q = 100 - 2P where P

  3. Calculus

    The manager of a large apartment complex knows from experience that 80 units will be occupied if the rent is 460 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 10

  4. Calculus

    The manager of a large apartment complex knows from experience that 80 units will be occupied if the rent is 460 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 10

View more similar questions or ask a new question.