Quantitative Literacy

Question

As of mid-2016, the world's population was about 7.4 billion people. The population of the United States was 324 million.

The area of a certain city is 302 square miles. If in mid-2016 every person in the world moved into that city, how many square feet of space would each person have?

Answer 1

• we need to put 7.4 billion people in 302 square miles

 

  this means (7.4 billion people)⁄(302 miles)

 

• the challenge with this problem is the units--use fractions and cancel the units 

 

  for example, (a/b)(b/c) = a/c

 

• we need to know that there are 5280 feet/mile

 

   recall that (m/n)² = m²/n²

 

  (5280 feet/ 1 miles)²(302 miles²/7.4 billion persons)

 

=(5280² feet²/1² miles²)(302 miles²/7,400,000,000 persons)

 

=(5280²)(302)(ft^2•miles²)/(1²)(7,400,000,000)(miles² •persons)     cancel miles²

 

=(5280²•302)/7,400,000,000 ft²/person

 

so do the arithmetic  5280•5280•302  ft²/person

                               7,400,000,000

                                              

                                             

          

                                              

 

                                             

 

 

Answer 2

(302 miles ^2)/7,400,000,000people = .00000004 sq miles/person = 4 x 10^-8 sq mile/ person

4 X 10^-8 sq miles/person x 5280 ft/ mile x 5280 ft / mile = 1.1 sq ft/ person