A company handles an apartment building with 50 units. Experience has shown that if the rent for each of the units is $370 per month, then all of the units will be filled; however, one unit will become vacant for each $10 increase in the monthly rate. If x represents the number of $10 increases, express the revenue R from the building as a function of x.
A)R(x) = 370+10x
B)R(x) = (370+10x)(50-x)
C)R(x) = 50(370+10x)
D)R(x) = 10(370-10x)(50-x)
E)R(x) = 50(370-10x)

Question

A company handles an apartment building with 50 units. Experience has shown that if the rent for each of the units is $370 per month, then all of the units will be filled; however, one unit will become vacant for each $10 increase in the monthly rate. If x represents the number of $10 increases, express the revenue R from the building as a function of x. ​
A)​R(x) = 370+10x
B)R(x) = (370+10x)(50-x)
C)R(x) = 50(370+10x)
D)R(x) = 10(370-10x)(50-x)
E)R(x) = 50(370-10x)

Quizplus · Accepted Answer

At the initial rent of $370, all units are filled so the initial revenue is:

R(0) = $370 x 50 = $18,500

For each $10 increase, one unit becomes vacant. This means that the number of filled units decreases by x, so the revenue decreases by (370 + 10x) for each x increase. Thus, the revenue can be modeled by:

R(x) = (370 + 10x) (50 - x)

where (370 + 10x) is the rent per filled unit and (50 - x) is the number of filled units.

Therefore, the best choice is B.

A Company Handles an Apartment Building with 50 Units