Download Foundations of Mathematical Reasoning Student Assignment 3.1.B

Foundations of Mathematical Reasoning
Student Assignment 3.1.B
Assignment 3.1 Part B
Questions/Hints
Question 1: Refer to the table shown below.
Population
Land Area (sq. miles)
United States
309,975,000
3,717,000
China
1,339,190,000
3,705,000
1) In India, about 1,184,639,000 people live on 1,269,000 square miles of land. Which
of the following statements is false?
Answer Choices:
The population density of India is approximately three times that of China.
The population density of India is approximately 11 times larger than the population
density of the United States.
The population densities of these three countries ranked from smallest to largest are
United States, India, and China.
The population density of the United States is approximately 83.4 people per square
mile. That is smaller than the population densities for China and India.
2) Which of the following population densities are equivalent to a density of 20 people/mi2?
There may be more than one correct answer.
Answer Choices:
a)
b)
c)
d)
e)
1 person/0.2 mi2
1 person/0.05 mi2
1 person/0.5 mi2
200 people/2 mi2
100 people/5 mi2
3) Typically, about 15,000 people are needed to support a fire station. How many fire stations
would you expect in a city of 1 million people? Round to the nearest whole fire station.
The Charles A. Dana Center at
The University of Texas at Austin
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Foundations of Mathematical Reasoning
Student Assignment 3.1.B
4) A chain of popular coffee shops has about 6 shops per 100,000 people in California. In
Texas, the chain has about 3 shops per 100,000 people. A city of 1.5 million in California would
be expected to have about __[A]__ locations of the chain, while a city the same size in Texas
would be expected to have about __[B]__ locations.
5) In the lesson, you used ratios in the form of population densities. A population density is a
ratio because it is a comparison of two measures: Number of people per number of square
miles. Which of the following are ratios? There may be more than one correct answer.
Answer Choices:
a)
b)
c)
d)
e)
252 miles
67 hours
10 miles/hour
5 lb/$3
$98
6) Calculate the gas mileage of a car that drives 283 miles on 12.3 gallons of gas. Round to the
nearest tenth of a mile/gallon. Remember to label your answer.
The gas mileage of a car that drives 283 miles on 12.3 gallons of gas is ____________.
7) The population of Nebraska is 1,826,341, and its population density is 23.8 people per mi2.
The population of New Hampshire is 1,316,470, and its population density is 146.8 people per
mi2. Which of the following statements is a valid interpretation of this information?
Answer Choices:
Nebraska is approximately six times more densely populated than New Hampshire.
The population of Nebraska is approximately 72% of the population of New
Hampshire.
New Hampshire is approximately six times more densely populated than Nebraska.
The population of New Hampshire is approximately 139% of the population of
Nebraska.
The Charles A. Dana Center at
The University of Texas at Austin
Unedited Draft
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Foundations of Mathematical Reasoning
Student Assignment 3.1.B
Hints (Please note: not all questions have hints)
Hint #1: It might be helpful to calculate the population densities for the three countries
mentioned and then compare them.
Hint #3: It might be helpful to write out a proportion so you have an equation that shows two
ratios that are equal. Refer to Resource Rounding and Estimation, if needed.
Hint #4: It might be helpful to write out a proportion so you have an equation that shows two
ratios that are equal.
Hint #6: Refer to Resource Rounding and Estimation, if needed.
The Charles A. Dana Center at
The University of Texas at Austin
Unedited Draft
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