Questions: The manager of a 90-unit apartment complex knows from experience that at a rent of 750 per month, all units will be rented. However, for each increase of 15 in rent, he can expect one unit to be vacated. Let x represent the number of 15 increases over 750. Complete parts (a) through (e) below. The number of apartments that will be rented if x increases of 15 are made is.

Solution Steps

To determine the number of apartments that will be rented if \( x \) increases of \$15 are made, we need to understand the relationship between the rent increase and the number of units rented. Initially, all 90 units are rented at \$750. For each \$15 increase, one unit becomes vacant. Therefore, the number of rented units decreases by \( x \) for \( x \) increases.

1. Start with the total number of units, which is 90.
2. Subtract \( x \) from 90 to account for the units that become vacant with each \$15 increase.

The manager knows that at a rent of \$750 per month, all 90 units will be rented. This is our starting point.

For each increase of \$15 in rent, one unit becomes vacant. Let \( x \) represent the number of \$15 increases.

The number of rented units can be calculated by subtracting \( x \) from the initial 90 units: \[ \text{Rented Units} = 90 - x \]

Given \( x = 3 \): \[ \text{Rented Units} = 90 - 3 = 87 \]

Final Answer