Question

A 4800 sq.ft. school was opened up in a small town. At the time of the school's opening, the population

density of the school was only 0.046 students/ft2. Over the years, the town has seen an increase in residents,
and now, it is time to decide if there should be a new school built or not. The principal determined that if
population density of the school reached a level greater than 0.1 students/ft2, then an additional school
would need to be built. How many students were enrolled when the school first opened? If 176 new
students have enrolled since the school was first opened, what can be said about the need for building a
new school?​

Answer 1

221 students were enrolled when the school was first opened.

Explanation:

Area of the school while opened up new = 4800 square feet

At the time of opening population density of the school was = 0.046 students per square feet.

That means total number of students at the time of opening = Area of the school × population density

= 4800 × 0.046

= 220.80

≈ 221 students

If 176 new students were enrolled then total number of students enrolled since the opening = 221 + 176 = 397 students

Now population density =
`(397)/(4800)=0.0827`

Which is less than 0.1 students per square feet.

The principal of the school determined that the new school building will be built if the population density reaches to 0.1 students per feet².

Therefore, the new building will not be required.