A company handles an apartment building with 50 units. Experience has shown that if the rent for each of the units is $380 per month, then all of the units will be filled; however, one unit will become vacant for each $30 increase in the monthly rate. If x represents the number of $30 increases, express the revenue R from the building as a function of x.
A) R(x) = 380+30x
B) R(x) = (380+30x)(50-x)
C) R(x) = 50(380+30x)
D) R(x) = 30(380-30x)(50-x)
E) R(x) = 50(380-30x)

Question

A company handles an apartment building with 50 units. Experience has shown that if the rent for each of the units is $380 per month, then all of the units will be filled; however, one unit will become vacant for each $30 increase in the monthly rate. If x represents the number of $30 increases, express the revenue R from the building as a function of x. ​
A) ​R(x) = 380+30x
B) R(x) = (380+30x)(50-x)
C) R(x) = 50(380+30x)
D) R(x) = 30(380-30x)(50-x)
E) R(x) = 50(380-30x)

Quizplus · Accepted Answer

The revenue R from the building is calculated by multiplying the rent per unit by the number of units rented. If the rent is increased by $30x, the new rent per unit is $380 + $30x. However, for each $30 increase, one unit becomes vacant, so the number of units rented is 50 - x. Therefore, the revenue function is R(x) = (380 + 30x)(50 - x).

A Company Handles an Apartment Building with 50 Units