Foundations of Mathematical Reasoning
Student Assignment 3.3.CD
Assignment 3.3 Part CD
Questions
1) In planning a Thanksgiving vacation, you want to rent a car for a week and travel the
Pacific Highway from San Francisco to San Diego. You want to return to San
Francisco via Las Vegas, Death Valley, and Yosemite National Park. This trip covers
approximately 1,500 miles. You plan to return the car with a full tank of gasoline.
You are considering two options advertised by Hertz:
a) Toyota Camry, 33 mpg highway, costs $465.59 plus taxes and fees, totaling
$553.28.
b) Toyota Prius Hybrid, 48 mpg highway, costs $634.49 plus taxes and fees, totaling
$804.61.
In both cases, you must purchase gasoline, which costs approximately $3.80 per
gallon in California.
2) In planning a Thanksgiving vacation, you want to rent a car for a week and travel the
Pacific Highway from San Francisco to San Diego. You want to return to San
Francisco via Las Vegas, Death Valley, and Yosemite National Park. This trip covers
approximately 1,500 miles. You plan to return the car with a full tank of gasoline.
You are considering two options advertised by Hertz:
a) Toyota Camry, 33 mpg highway, costs $465.59 plus taxes and fees, totaling $553.28.
b) Toyota Prius Hybrid, 48 mpg highway, costs $634.49 plus taxes and fees, totaling
$804.61.
Additional Information: The advertised mpg for new cars is based on a speed of 55
mph. As speed increases above 55 mph, the efficiency reduces dramatically. 1


3% less efficient at 60 mph
17% less efficient at 70 mph
Part A: Compare the efficiency of a Toyota Camry (33 mpg highway) versus a Toyota
Prius (48 mpg highway) at speeds of 55 mph, 60 mph, and 70 mph. Round to the
nearest tenth.
1
Retrieved from www.mpgforspeed.com
The Charles A. Dana Center at
The University of Texas at Austin
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Foundations of Mathematical Reasoning
Student Assignment 3.3.CD
55
mph
60
mph
70
mph
Camry
33
mpg
[A]
[B]
Prius
48
mpg
[C]
[D]
Part B: If gasoline now costs $3.67 per gallon, how much money would you save by
going 60 mph versus 70 mph on the trip of 1,500 miles in the Camry?
Part C: If gasoline now costs $3.67 per gallon, how much money would you save by
going 60 mph versus 70 mph on the trip of 1,500 miles in the Prius?
Part D: How much longer, to the nearest minute, would it take to travel 300 miles at
60 mph versus 70 mph?
3) Create a formula to calculate the total fuel cost for the trip.
4) The National Center for Children in Poverty (NCCP) posted the following information
in 2013:
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The University of Texas at Austin
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Foundations of Mathematical Reasoning
Student Assignment 3.3.CD
Nearly 16 million children in the United States—22% of all
children—live in families with incomes below the federal poverty
level ($23,021 a year for a family of four). Research shows that, on
average, families need an income of about twice that level to cover
basic expenses. Using this standard, 45% of children live in lowincome families.2
The graph below can be used to illustrate the statement from the NCCP. Identify
what each section and the full circle represent in terms of the context and the
percentage. Section 1 is the darker section.
The full circle represents __________A______________ and is ___B____%.
Section 1 represents ______________C__________ and is ___D____%.
Section 2 represents ___________E_____________ and is ___F____%.
Answer choices for A, C, and E:
All children in the U.S.
U.S. children living below federal poverty level ($23,021)
2
Retrieved from www.nccp.org/topics/childpoverty.html
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The University of Texas at Austin
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Foundations of Mathematical Reasoning
Student Assignment 3.3.CD
U.S. children living below basic expenses level ($44,700)
U.S. children living above federal poverty level ($23,021)
U.S. children living above basic expenses level ($44,700)
Answer choices for B, D, and F:
16
22
45
55
78
84
100
5)
The National Center for Children in Poverty (NCCP) posted the following information in
2013:
Nearly 16 million children in the United States—22% of all
children—live in families with incomes below the federal poverty
level ($23,021 a year for a family of four). Research shows that, on
average, families need an income of about twice that level to cover
basic expenses. Using this standard, 45% of children live in lowincome families.3
Part A: Can the statement from the NCCP be restated to say that 21% of people below
the federal poverty level in the United States are children? Select the best answer.
3
Retrieved from www.nccp.org/topics/childpoverty.html
The Charles A. Dana Center at
The University of Texas at Austin
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Foundations of Mathematical Reasoning
Student Assignment 3.3.CD
Answer choices:
a) Yes, because the reference value in both statements is the children in the
United States.
b) Yes, because both statements are about children living in poverty so the
percentages are the same. The reference values do not matter.
c) No, because the percentage of children is really much higher because
families really need much more money than the federal poverty level.
d) No, because the reference value in the first statement is the total number of
children. The reference value in the second statement is the total number of
people below the poverty level.
Answer:
No, because the reference value in the first statement is the total number of
children. The reference value in the second statement is the total number of
people below the poverty level.
Part B: Based on the information in the paragraph, which of the following is the best
estimate for the number of children in the United States?
Answer choices:
a) 30 million
b) 75 million
c) 100 million
d) There is not enough information to make an estimate.
6)
Making Connections Across the Course
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Foundations of Mathematical Reasoning
Student Assignment 3.3.CD
11) Write to Jenna, explaining how she can decide if it is better to drive her own car or
to get a rental. Your explanation should include information about what factors affect the
cost of driving and why.
7)
Making Connections Across the Course
Find the cost per year of some activity or item that you pay for at least twice a week
on average. For example, buying a cup of coffee or energy drink, downloading
music, going to a movie, paying a babysitter, riding a bus, etc. Explain your work.
HINTS (Note not every question will have a hint)
Hint #1: Refer to Resource Dimensional Analysis, if needed.
Hint #2: Refer to Resources Fractions, Decimals, and Percentages or Dimensional
Analysis, if needed.
Hint #3: Refer to Resources Fractions, Decimals, and Percentages or Dimensional
Analysis, if needed.
Hint #4: Refer to Resource Understanding Visual Displays of Information, if needed.
Hint #6: Refer to Resources Writing Principles, if needed.
Hint #7: Refer to Resource Writing Skills, if needed.
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