A real estate office handles an apartment complex with 50 units.When the rent is $700 per month,all 50 units are occupied.However,when the rent is $745,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 $790.
A)41 units
B)56 units
C)59 units
D)47 units
E)44 units

Question

A real estate office handles an apartment complex with 50 units.When the rent is $700 per month,all 50 units are occupied.However,when the rent is $745,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 $790. ​
A)41 units
B)56 units
C)59 units
D)47 units
E)44 units

Quizplus · Accepted Answer

First, we find the slope of the line that represents the relationship between the rent (p) and the number of units occupied (x). Using the two points given, (700, 50) and (745, 47), the slope (m) is (47 - 50) / (745 - 700) = -3 / 45 = -1/15. The equation of the line can be written as x = mp + b. Substituting one point into the equation allows us to solve for b: 50 = (-1/15)*700 + b, which gives b = 50 + 700/15 = 96.6667. Thus, the equation is x = -1/15*p + 96.6667. Substituting p = 790 into the equation gives x = -1/15*790 + 96.6667 ≈ 44 units.

A Real Estate Office Handles an Apartment Complex with 50