Question

I NEED A MATH WIZ!

An apartment complex currently houses 280 people who are spread out across 4 buildings standing on 200,000 square feet of land. The owner of the complex is planning to expand by purchasing an additional square plot of land measuring 200 ft by 200 ft and constructing one more apartment building on this plot. Assuming that the new building will house as many people as each of the other 4 buildings, which statement provides the best estimate of the effect this expansion will have in terms of the square feet of land per person living in the complex?

the square footage of land per person will decrease by about 140 ft2
the square footage of land per person will decrease by about 30 ft2
the square footage of land per person will not change
the square footage of land per person will increase by about 140 ft2

Answer 1

Answer:it would decrease by 140 square ft

Explanation:

Answer 2

So each of these statements are talking about the square footage of land per person. Let's go and find it!

First off, let's find the number in each building of the original complex:
280 people / 4 buildings

Each building has an equal number of residents. So just divide:
280/4 = 70.

So 70 residents per building

Now consider the fact that once a new building is built, another 70 people will move in.
280 + 70= 350

350 people total.

Then lets look at the plot of land
Originally, there are 200,000 square feet of land for the 4 buildings. Then after the expansion, the plot of land will be:
200,000 + 200*200
= 200,400

Go back to the question. What's the effect of the expansion in terms of square feet of land per person?
Divide!
200,400 / 350
Approximately = 572.57 square feet

Then since it's being compared to the amount each resident had before the expansion, do the same thing with the corresponding numbers:
200,000 / 280
Approximately = 714.29

So how much will each person's land decrease?
714.29 - 572.57 approximately = 141.72 square feet.

The answer is the first choice!

Hope this helps