Question

A real estate office handles an apartment complex with 50 units. When the rent per unit is $580 per month, all 50 units are occupied. However, when the rent is $625 per month, the average number of occupied units drops to 47. Assume that the relationship between the monthly rent p and the demand x is linear.
(a) Write the equation of the line giving the demand x in terms of the rent p.
x =
(b) Use a graphing utility to graph the demand equation and use the trace feature to estimate the number of units occupied when the rent is $655. Verify your answer algebraically.
____________ units
(c) Use the demand equation to predict the number of units occupied when the rent is lowered to $610. Verify your answer graphically.
____________ units

Answer 1

Answer:

a. $x=\frac{1330-y}{15}$

b. $x=\frac{1330-655}{15}$

$x=\frac{655}{15} = 45$

c. $x=\frac{1330-610}{15}$

$x=\frac{720}{15} = 48$

Explanation:

a.

using the point-slope form we have that:

y= mx + b

m being the slope which has the next equation:

y is the rent price

x is the units of the apartment complex rented

$m=\frac{y1-y2}{x1-x2}$

$m=\frac{580-625}{50-47}=\frac{-45}{3} = -15$

Now we find the Y intercept (b):

580=-15(50)+b

580=-750+b

b=580+750 = 1330

We have the equation:

y=-15x + 1330

Now we have tu put in terms of the rent p (y)

y=-15x + 1330

15x = 1330 - y

$x=\frac{1330-y}{15}$

b.

The first graph attached corresponds to the equation showed in point a.

The second graph attached corresponds to the equation if the rent is $655

Using the trace feature it is estimated that for a rent price of $655 the units occupied are 45.

$x=\frac{1330-655}{15}$

$x=\frac{655}{15} = 45$

c. The third graph attached corresponds to the equation if the rent is $610

Using the trace feature it is estimated that for a rent price of $610 the units occupied are 48.

$x=\frac{1330-610}{15}$

$x=\frac{720}{15} = 48$