Question

your development company recently purchased 12.5 acres of land. according to local regulations, each housing lot must be at least 54,450 square feet. in addition, $\frac{1}{7}$ of the purchased land must be left undeveloped. what is the maximum number of housing lots that you can develop on the land?

o a 8
o b. 10
o c 11
o d. 13
o e 18

Explanation:

Step1: Convert acres to square - feet

1 acre = 43560 square - feet. So, 12.5 acres of land is \(12.5\times43560 = 544500\) square - feet.

Step2: Calculate the developable land area

Since \(\frac{1}{7}\) of the land must be left undeveloped, the fraction of land that can be developed is \(1-\frac{1}{7}=\frac{6}{7}\). The developable land area is \(\frac{6}{7}\times544500=\frac{3267000}{7}\approx466714.29\) square - feet.

Step3: Calculate the number of housing lots

To find the number of housing lots, divide the developable land area by the area of each housing lot. Let \(n\) be the number of housing lots. \(n=\frac{\frac{6}{7}\times544500}{54450}\). Since \(\frac{544500}{54450} = 10\), then \(n=\frac{6}{7}\times10=\frac{60}{7}\approx8.57\). Since the number of lots must be an integer, the maximum number of housing lots is 8.

Answer:

A. 8