Problema Solution
A real estate office handles an apartment complex with 50 units. When the rent is $600 per month, all 50 units are occupied. However, when the rent is $645, the average number of occupied units drops to 47. Assume that the relationship between the monthly rent p and the demand x is linear. Predict the number of units occupied if the rent is raised to $660.
Answer provided by our tutors
for p = $600 the demand x = 50 units
for p = $645 the demand x = 47 units
we need to find x if p = $660
the relationship between the monthly rent p and the demand x is linear means:
x = ap + b, where a and b are constants
plug p = 600, x = 50 and we have 50 = 600a + b
plug p = 645, x = 47 and we have 47 = 645a + b
by solving the system of equations:
600a + b = 50
645a + b = 47
we find
a = -1/15
b = 90
click here to see the step by step solution of the system of equations:
x = (-1/15)p + 90
if the rent is p = $660 we find for x:
x = (-1/15)*660 + 90
x = 46 units
if the rent is $660 the number of occupied units will be 46.