, SOLUTION MANUAL FOR Data Discovering
Mathematics A Quantitative Reasoning Approach
2nd Edition by Richard N. Aufmann
Notes
1- The file is chapter after chapter.
2- We have shown you few pages sample.
3- The file contains all Appendix and Excel sheet
if it exists.
4- We have all what you need, we make update
at every time. There are many new editions
waiting you.
5- If you think you purchased the wrong file You
can contact us at every time, we can replace it
with true one.
Our email:
, Solution and Answer Guide: Aufmann, Discovering Mathematics: A Quantitative Approach, 2e, 9780357760031;
Chapter 1: Introduction To Problem Solving
Solution and Answer Guide
AUFMANN, DISCOVERING MATHEMATICS: A QUANTITATIVE APPROACH, 2e, 9780357760031;
CHAPTER 1: INTRODUCTION TO PROBLEM SOLVING
TABLE OF CONTENTS
Chapter 1: Introduction to Problem Solving.............................................................................1
Think About It 1.1.......................................................................................................................1
Section 1.1 Exercise Solutions .................................................................................................. 1
Think About It 1.2.......................................................................................................................5
Section 1.2 Exercise Solutions .................................................................................................. 6
Think About It 1.3.......................................................................................................................8
Section 1.3 Exercise Solutions .................................................................................................. 8
Think About It 1.4.....................................................................................................................12
Section 1.4 Exercise Solutions ................................................................................................ 12
Chapter 1 Review Exercises.....................................................................................................31
CHAPTER 1: INTRODUCTION TO PROBLEM SOLVING
THINK ABOUT IT 1.1
1. Inductive
2. Specific
3. One example is 5, which is an odd number.
SECTION 1.1 EXERCISE SOLUTIONS
1. 64. The numbers are the squares of consecutive integers. 82 = 64.
2. 35. Subtract 1 less than the integer subtracted from the previous integer.
3. Add 2 to the numerator and denominator.
4. Add 1 to the numerator and denominator.
5. –13. Use the pattern of adding 5, then subtracting 10 to obtain the next pair of numbers.
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accessible website, in whole or in part.
, Solution and Answer Guide: Aufmann, Discovering Mathematics: A Quantitative Approach, 2e, 9780357760031;
Chapter 1: Introduction To Problem Solving
6. 21. Subtract 8 from 5, add 12 to –3, subtract 16 from 9, add 20 to –7, etc., increasing the
amount by 4 each time while alternating between adding and subtracting.
7. Each image has a smaller square inside a larger square. The smaller square moves to a new
position in a counterclockwise direction. The next figure is shown.
8. Each image has a smaller square inside a larger square. The smaller square moves to a new
position in a counterclockwise direction. The next figure is shown.
9. Each image has a smaller square and a circle inside a larger square. The smaller square moves
to a new position in a corner in a counterclockwise direction. The circle moves to a new position in
a counterclockwise direction. The next figure is shown.
10. Each image has a smaller square and a circle inside a larger square. The smaller square
moves to a new position in a corner in a counterclockwise direction. The circle moves to a
new position in a clockwise direction. The next figure is shown.
11. Each figure is a circle with a polygon, alternating positions inside and outside. The first figure
is a triangle (3 sides) with a circle inside. The second is a circle with a square (4 sides) inside.
The next figure is shown.
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accessible website, in whole or in part.
, Solution and Answer Guide: Aufmann, Discovering Mathematics: A Quantitative Approach, 2e, 9780357760031;
Chapter 1: Introduction To Problem Solving
12. Each figure is a polygon within a polygon, alternating blue and yellow interiors. The first figure
is a 7-sided figure inside an 8-sided figure. The second figure is a 6-sided figure inside a 7-
sided figure. The next figure is shown.
13. The amount is decreasing by $1000 per month. Thus, the amount in year 6 will be $5000.
14. a. Greater since the temperature is increasing.
b. No. Fall and winter would come and the temperature would decrease.
15. More than. The increase in average annual salary increases from $7763 to $8927 to $10,266.
Thus the increase from 20 years to 25 years will be more than $10,266, giving an average
annual salary for a teacher having 25 years of experience of greater than $78,705 + $10,266
= $88,971, which is greater than $88,000.
16. Fewer. From the bar graph, it appears that as the price of cell phones increases, the number
of cell phones sold decreases. Assuming the same trend, if the price of the cell phone is
$700, the company will sell fewer than 333,000 cell phones.
17. For every 10 seconds, the distance is increasing by 300 feet. Therefore, after 70 seconds,
the athlete will run a distance of 2100 feet.
18. For every 2 hours, the distance is decreasing by 100 miles. Therefore, after 6 hours, the trip
will have 200 miles remaining.
19. From the table, as the depth increases, the temperature decreases. Since the last entry of
the table is 40 m and 11°C, then for 45 m, the temperature should be less than 11°C.
20. Each year the car depreciates by a smaller amount: $5336, $5191, $2930, and $2878. The
value of the car at year 5 is $11,743. After year 6, the value of the car will be less than
$11,000.
21. From the table, the distance (in feet) is equal to the time (in seconds) squared. So at 7
seconds the distance is 49 feet, and at 8 seconds the distance is 64 feet.
22. The pattern from 0 seconds to 7 seconds, repeats again starting at 8 seconds. So at 14
seconds, the distance will be the same as at 6 seconds, which is 0 inches.
23. Answers will vary. For instance,
24. Answers will vary. For instance, 5 – (–3) = 8.
25. A diamond shape can have four equal sides and is not a square.
26. Answers will vary. For instance, 20.
27. Whales are mammals and do not have legs.
28. A penguin is a bird that does not fly.
29. a. Deductive
© 2023 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 3
accessible website, in whole or in part.
, Solution and Answer Guide: Aufmann, Discovering Mathematics: A Quantitative Approach, 2e, 9780357760031;
Chapter 1: Introduction To Problem Solving
b. Inductive
30. a. Inductive
b. Deductive
31. Place 4 coins in the left balance pan, 4 coins in the right balance pan, and set 4 coins aside.
There are three possibilities. The right side goes down, the left side goes down, or the scale
balances (the heavier coin is set aside). Take the 4 coins that include the heavier coin and place 2
on the left balance pan and 2 on the right balance pan.
From the 2 coins on the heavier pan, place one coin on each balance pan to determine the
heavier coin.
32. Label the coins 1, 2, 3, … 8. Set coins 5, 6, 7, and 8 aside.
Weighing 1: Place coins 1 and 2 on one balance and coins 3 and 4 on the other.
If the scale is balanced, the heavier or lighter coin is 5, 6, 7, or 8. Coins 1, 2, 3, or 4 are of
equal weight.
If the scale is unbalanced, the heavier or lighter coin is 1, 2, 3, or 4. Coins 5, 6, 7, or 8 are
of equal weight.
Weighing 2: From the four coins that contain the heavier or lighter coin, choose two coins,
placing one coin on each balance, and set the other two coins aside. Suppose that coins 5, 6,
7, or 8 are not of equal weight. Choose coins 5 and 6 and place one on each side of the
balance.
If the scale is balanced, then coins 5 and 6 are of equal weight and the coin that is
heavier or lighter is either coin 7 or 8.
If the scale is unbalanced, then coins 7 and 8 are of equal weight and the coin that is
heavier or lighter is either coin 5 or 6.
Weighing 3: Suppose the coin that is heavier or lighter is either coin 7 or 8. Place coin 7 on
one balance and coin 1 (or any one of coins 2 to 6, since they are of equal weight), on the
other balance.
If the scale is balanced, then coin 8 is the coin that is heavier or lighter.
If the scale is unbalanced, then coin 7 is the coin that is heavier or lighter.
33. Label each stack of coins as 1, 2, 3, … 10. From each stack select the same amount of coins
as the labels, so select 1 coin from stack 1, 2 coins from stack 2, and so on to 10 coins from
stack 10. Weigh the selected coins. Since the counterfeit coins each weigh 0.1 g more, the
multiple of 0.1 g over the weight expected will determine which stack contains the counterfeit
coins.
34. Label each stack of coins as 0, 1, 2, 3, … 10. Note that there are 11 stacks. From each stack
select the same amount of coins as the labels, so select 0 coins from stack 0, 1 coin from
stack 1, 2 coins from stack 2, and so on to 10 coins from stack 10. Weigh the selected coins.
Since the counterfeit coins each weigh 0.1 g more, the multiple of 0.1 g over the weight
expected will determine which stack contains the counterfeit coins. Note that if the weight is
not more than expected, the counterfeit coins are in stack 0.
35.
Util Auto Tech Oil
A X1 X1 X3
T X1 X1 X3
© 2023 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 4
accessible website, in whole or in part.
, Solution and Answer Guide: Aufmann, Discovering Mathematics: A Quantitative Approach, 2e, 9780357760031;
Chapter 1: Introduction To Problem Solving
M X2 X3 X3
J X2 X2 X2
Maria: the utility stock; Jose: the automotive stock; Anita: the technology stock; Tony: the oil
stock
36.
Soup Entree Salad Dessert
C X2 X3 X2
S X2 X3 X2
O X1 X2 X2
G X2 X2 X2
Changs: entrée; Steinbergs: salad; Ontkeans: dessert; Gonzaleses: soup
37.
Coin Stamp Comic Baseball
A X3 X3 X4
C X2 X4 X1
P X3 X3 X2
S X2 X3 X3
Atlanta: stamps; Chicago: baseball cards; Philadelphia: coins; San Diego: comic books
38. a. Yes. Change the color of Iowa to yellow and Oklahoma to blue.
b. No. One possible explanation: Oklahoma, Arkansas, and Louisiana must each have a
different color than the color of Texas and they cannot all be the same color. Thus, the
map cannot be colored using only two colors.
THINK ABOUT IT 1.2
1. a. Estimate
b. Estimate
c. Exact
d. Estimate
e. Exact
f. Exact
2. 5.32 × 10–6 = 0.00000532
The answer is b, greater than 0 but less than 1.
3. True
4. False;
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accessible website, in whole or in part.
, Solution and Answer Guide: Aufmann, Discovering Mathematics: A Quantitative Approach, 2e, 9780357760031;
Chapter 1: Introduction To Problem Solving
5. Yes
SECTION 1.2 EXERCISE SOLUTIONS
1. 1487 miles ≈ 1500 miles
2. 11 children ≈ 10 children; 3 slices ≈ 4 slices
4 pizzas is conservative; 5 pizzas should be plenty.
3. 2(25) + 30 = 80
So, 25°C ≈ 80°F.
4. 238 square feet ≈ 240 square feet
$0.28 ≈ $0.30
240 × $0.30 = $72
The cost will be approximately $72.
5. 400 × 20 = 8000 square feet
6. Since 1 gallon of paint covers 350 square feet, and the room has 400 square feet of wall
space, including windows and doors, you should purchase 2 gallons of paint.
7. Answers will vary depending on the grid. Using a 3 by 5 grid, we count 30 cars. Multiply 30 by
the number of sections, 15, to get 450. So our estimate is 450 cars.
8. Answers will vary depending on the grid. Using a 3 by 5 grid, we count 28 flowers. Multiply 24
by the number of sections, 15, to get 360. So our estimate is 360 flowers.
9. Answers will vary depending on the grid. Using a 3 by 5 grid, we count 18 cadets. Multiply 15
by the number of sections, 15, to get 225. So our estimate is 225 cadets.
10. Answers will vary depending on the grid. Using a 4 by 5 grid, we count 9 marchers. Multiply 9 by
the number of sections, 20, to get 180. So our estimate is 180 marchers.
11. people or 1.6 million people
12. 68.3 square miles ≈ 68 square miles
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accessible website, in whole or in part.
, Solution and Answer Guide: Aufmann, Discovering Mathematics: A Quantitative Approach, 2e, 9780357760031;
Chapter 1: Introduction To Problem Solving
Approximately 680,000 people
13. If a 10-foot pole casts a shadow of 18 feet, and a telephone pole has a shadow of 72 feet,
then the telephone pole will be more than half as high as its shadow is long. The telephone
pole has height
14. If an 8-foot pole casts a shadow of 6 feet, and a building has a shadow of 94 feet, then the
building will be taller than its shadow. The building has height
15. 0.0000000000089 meter = 8.9 × 10–12 meter
16. 30,900,000,000,000,000 m = 3.09 × 1016 m
17. 35,000,000,000,000 cells = 3.5 × 1013 cells
18. 0.000000076 meter = 7.6 × 10–8 meter
19. Yes. The higher the advanced degree, the higher the bar of the lifetime earnings is.
20. Yes
21. Yes. The Dogs category is more than half of the pie graph.
22. Yes
23. a. The graph decreases in years 2018 to 2020.
b. The graph increases from 0 to 2.4 from 2015 to 2018, but from 1.4 to 7 from 2020 to
2021. The inflation rate increased more from 2020 to 2021.
24. a. From the graph, the blue line is greater than the red line for 110th, 111th, and 116th
Congress.
b. From the graph, the greatest difference between the red and blue lines is for the 111th
Congress.
c. From the graph, the least difference between the red and blue lines is for the 117th
Congress.
THINK ABOUT IT 1.3
1. Understand the problem, devise a plan, carry out the plan, review the solution
2. No. We would need to know the speed at which she ran.
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accessible website, in whole or in part.
, Solution and Answer Guide: Aufmann, Discovering Mathematics: A Quantitative Approach, 2e, 9780357760031;
Chapter 1: Introduction To Problem Solving
SECTION 1.3 EXERCISE SOLUTIONS
1. Let g be the number of first grade girls, and let b be the number of first grade boys. Then b +
g = 364 and g = b + 26. Solving gives g = 195, so there are 195 girls.
2. Let a be the length in feet of the shorter ladder and b be the length in feet of the longer
ladder. Then a + b = 31.5 and a + 6.5 = b. Solving gives a = 12.5 and b = 19, so the ladders
are 12.5 feet and 19 feet long.
3. There are 36 1 × 1 squares, 25 2 × 2 squares, 16 3 × 3 squares, 9 4 × 4 squares,
4 5 × 5 squares and 1 6 × 6 square in the figure, making a total of 91 squares.
4. The first decimal digit, like all the odd decimal digits, is a zero, and the second decimal digit,
like all the even decimal digits, is a 9. Since 44 is even, the
44th decimal digit is a 9.
5. Solving:
x = cost of the shirt
x – 30 = cost of the tie
(x – 30) + x = 50
2x – 30 = 50
2x = 80
x = 40
The shirt costs $40.
6. Using the results of example 3, 12 teams play each of 11 teams for a total of
(12 × 11) ÷ 2 = 66 games. Since each team plays each of the teams twice 2 × 66 = 132 total
games.
7. There are 14 different routes to get to Fourth Avenue and Gateway Boulevard and 4 different
routes to get to Second Avenue and Crest Boulevard. Adding gives that there are 18 different
routes altogether.
8. a. There are 2 different routes from point A to the Starbucks and 2 different routes from the
Starbucks to point B. Multiplying gives a total of 4 different routes.
b. There is only one direct route to the Subway. There are 3 different routes from the
Subway to point B, so there are 3 different routes altogether.
c. Since there is only one direct route to the Subway, starting the count there will not
change the number of routes. There is only one direct route from the Subway to
Starbucks, and there are 2 different routes from Starbucks to point B, so there are 2
different routes altogether.
© 2023 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 8
accessible website, in whole or in part.
Mathematics A Quantitative Reasoning Approach
2nd Edition by Richard N. Aufmann
Notes
1- The file is chapter after chapter.
2- We have shown you few pages sample.
3- The file contains all Appendix and Excel sheet
if it exists.
4- We have all what you need, we make update
at every time. There are many new editions
waiting you.
5- If you think you purchased the wrong file You
can contact us at every time, we can replace it
with true one.
Our email:
, Solution and Answer Guide: Aufmann, Discovering Mathematics: A Quantitative Approach, 2e, 9780357760031;
Chapter 1: Introduction To Problem Solving
Solution and Answer Guide
AUFMANN, DISCOVERING MATHEMATICS: A QUANTITATIVE APPROACH, 2e, 9780357760031;
CHAPTER 1: INTRODUCTION TO PROBLEM SOLVING
TABLE OF CONTENTS
Chapter 1: Introduction to Problem Solving.............................................................................1
Think About It 1.1.......................................................................................................................1
Section 1.1 Exercise Solutions .................................................................................................. 1
Think About It 1.2.......................................................................................................................5
Section 1.2 Exercise Solutions .................................................................................................. 6
Think About It 1.3.......................................................................................................................8
Section 1.3 Exercise Solutions .................................................................................................. 8
Think About It 1.4.....................................................................................................................12
Section 1.4 Exercise Solutions ................................................................................................ 12
Chapter 1 Review Exercises.....................................................................................................31
CHAPTER 1: INTRODUCTION TO PROBLEM SOLVING
THINK ABOUT IT 1.1
1. Inductive
2. Specific
3. One example is 5, which is an odd number.
SECTION 1.1 EXERCISE SOLUTIONS
1. 64. The numbers are the squares of consecutive integers. 82 = 64.
2. 35. Subtract 1 less than the integer subtracted from the previous integer.
3. Add 2 to the numerator and denominator.
4. Add 1 to the numerator and denominator.
5. –13. Use the pattern of adding 5, then subtracting 10 to obtain the next pair of numbers.
© 2023 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 1
accessible website, in whole or in part.
, Solution and Answer Guide: Aufmann, Discovering Mathematics: A Quantitative Approach, 2e, 9780357760031;
Chapter 1: Introduction To Problem Solving
6. 21. Subtract 8 from 5, add 12 to –3, subtract 16 from 9, add 20 to –7, etc., increasing the
amount by 4 each time while alternating between adding and subtracting.
7. Each image has a smaller square inside a larger square. The smaller square moves to a new
position in a counterclockwise direction. The next figure is shown.
8. Each image has a smaller square inside a larger square. The smaller square moves to a new
position in a counterclockwise direction. The next figure is shown.
9. Each image has a smaller square and a circle inside a larger square. The smaller square moves
to a new position in a corner in a counterclockwise direction. The circle moves to a new position in
a counterclockwise direction. The next figure is shown.
10. Each image has a smaller square and a circle inside a larger square. The smaller square
moves to a new position in a corner in a counterclockwise direction. The circle moves to a
new position in a clockwise direction. The next figure is shown.
11. Each figure is a circle with a polygon, alternating positions inside and outside. The first figure
is a triangle (3 sides) with a circle inside. The second is a circle with a square (4 sides) inside.
The next figure is shown.
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accessible website, in whole or in part.
, Solution and Answer Guide: Aufmann, Discovering Mathematics: A Quantitative Approach, 2e, 9780357760031;
Chapter 1: Introduction To Problem Solving
12. Each figure is a polygon within a polygon, alternating blue and yellow interiors. The first figure
is a 7-sided figure inside an 8-sided figure. The second figure is a 6-sided figure inside a 7-
sided figure. The next figure is shown.
13. The amount is decreasing by $1000 per month. Thus, the amount in year 6 will be $5000.
14. a. Greater since the temperature is increasing.
b. No. Fall and winter would come and the temperature would decrease.
15. More than. The increase in average annual salary increases from $7763 to $8927 to $10,266.
Thus the increase from 20 years to 25 years will be more than $10,266, giving an average
annual salary for a teacher having 25 years of experience of greater than $78,705 + $10,266
= $88,971, which is greater than $88,000.
16. Fewer. From the bar graph, it appears that as the price of cell phones increases, the number
of cell phones sold decreases. Assuming the same trend, if the price of the cell phone is
$700, the company will sell fewer than 333,000 cell phones.
17. For every 10 seconds, the distance is increasing by 300 feet. Therefore, after 70 seconds,
the athlete will run a distance of 2100 feet.
18. For every 2 hours, the distance is decreasing by 100 miles. Therefore, after 6 hours, the trip
will have 200 miles remaining.
19. From the table, as the depth increases, the temperature decreases. Since the last entry of
the table is 40 m and 11°C, then for 45 m, the temperature should be less than 11°C.
20. Each year the car depreciates by a smaller amount: $5336, $5191, $2930, and $2878. The
value of the car at year 5 is $11,743. After year 6, the value of the car will be less than
$11,000.
21. From the table, the distance (in feet) is equal to the time (in seconds) squared. So at 7
seconds the distance is 49 feet, and at 8 seconds the distance is 64 feet.
22. The pattern from 0 seconds to 7 seconds, repeats again starting at 8 seconds. So at 14
seconds, the distance will be the same as at 6 seconds, which is 0 inches.
23. Answers will vary. For instance,
24. Answers will vary. For instance, 5 – (–3) = 8.
25. A diamond shape can have four equal sides and is not a square.
26. Answers will vary. For instance, 20.
27. Whales are mammals and do not have legs.
28. A penguin is a bird that does not fly.
29. a. Deductive
© 2023 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 3
accessible website, in whole or in part.
, Solution and Answer Guide: Aufmann, Discovering Mathematics: A Quantitative Approach, 2e, 9780357760031;
Chapter 1: Introduction To Problem Solving
b. Inductive
30. a. Inductive
b. Deductive
31. Place 4 coins in the left balance pan, 4 coins in the right balance pan, and set 4 coins aside.
There are three possibilities. The right side goes down, the left side goes down, or the scale
balances (the heavier coin is set aside). Take the 4 coins that include the heavier coin and place 2
on the left balance pan and 2 on the right balance pan.
From the 2 coins on the heavier pan, place one coin on each balance pan to determine the
heavier coin.
32. Label the coins 1, 2, 3, … 8. Set coins 5, 6, 7, and 8 aside.
Weighing 1: Place coins 1 and 2 on one balance and coins 3 and 4 on the other.
If the scale is balanced, the heavier or lighter coin is 5, 6, 7, or 8. Coins 1, 2, 3, or 4 are of
equal weight.
If the scale is unbalanced, the heavier or lighter coin is 1, 2, 3, or 4. Coins 5, 6, 7, or 8 are
of equal weight.
Weighing 2: From the four coins that contain the heavier or lighter coin, choose two coins,
placing one coin on each balance, and set the other two coins aside. Suppose that coins 5, 6,
7, or 8 are not of equal weight. Choose coins 5 and 6 and place one on each side of the
balance.
If the scale is balanced, then coins 5 and 6 are of equal weight and the coin that is
heavier or lighter is either coin 7 or 8.
If the scale is unbalanced, then coins 7 and 8 are of equal weight and the coin that is
heavier or lighter is either coin 5 or 6.
Weighing 3: Suppose the coin that is heavier or lighter is either coin 7 or 8. Place coin 7 on
one balance and coin 1 (or any one of coins 2 to 6, since they are of equal weight), on the
other balance.
If the scale is balanced, then coin 8 is the coin that is heavier or lighter.
If the scale is unbalanced, then coin 7 is the coin that is heavier or lighter.
33. Label each stack of coins as 1, 2, 3, … 10. From each stack select the same amount of coins
as the labels, so select 1 coin from stack 1, 2 coins from stack 2, and so on to 10 coins from
stack 10. Weigh the selected coins. Since the counterfeit coins each weigh 0.1 g more, the
multiple of 0.1 g over the weight expected will determine which stack contains the counterfeit
coins.
34. Label each stack of coins as 0, 1, 2, 3, … 10. Note that there are 11 stacks. From each stack
select the same amount of coins as the labels, so select 0 coins from stack 0, 1 coin from
stack 1, 2 coins from stack 2, and so on to 10 coins from stack 10. Weigh the selected coins.
Since the counterfeit coins each weigh 0.1 g more, the multiple of 0.1 g over the weight
expected will determine which stack contains the counterfeit coins. Note that if the weight is
not more than expected, the counterfeit coins are in stack 0.
35.
Util Auto Tech Oil
A X1 X1 X3
T X1 X1 X3
© 2023 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 4
accessible website, in whole or in part.
, Solution and Answer Guide: Aufmann, Discovering Mathematics: A Quantitative Approach, 2e, 9780357760031;
Chapter 1: Introduction To Problem Solving
M X2 X3 X3
J X2 X2 X2
Maria: the utility stock; Jose: the automotive stock; Anita: the technology stock; Tony: the oil
stock
36.
Soup Entree Salad Dessert
C X2 X3 X2
S X2 X3 X2
O X1 X2 X2
G X2 X2 X2
Changs: entrée; Steinbergs: salad; Ontkeans: dessert; Gonzaleses: soup
37.
Coin Stamp Comic Baseball
A X3 X3 X4
C X2 X4 X1
P X3 X3 X2
S X2 X3 X3
Atlanta: stamps; Chicago: baseball cards; Philadelphia: coins; San Diego: comic books
38. a. Yes. Change the color of Iowa to yellow and Oklahoma to blue.
b. No. One possible explanation: Oklahoma, Arkansas, and Louisiana must each have a
different color than the color of Texas and they cannot all be the same color. Thus, the
map cannot be colored using only two colors.
THINK ABOUT IT 1.2
1. a. Estimate
b. Estimate
c. Exact
d. Estimate
e. Exact
f. Exact
2. 5.32 × 10–6 = 0.00000532
The answer is b, greater than 0 but less than 1.
3. True
4. False;
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accessible website, in whole or in part.
, Solution and Answer Guide: Aufmann, Discovering Mathematics: A Quantitative Approach, 2e, 9780357760031;
Chapter 1: Introduction To Problem Solving
5. Yes
SECTION 1.2 EXERCISE SOLUTIONS
1. 1487 miles ≈ 1500 miles
2. 11 children ≈ 10 children; 3 slices ≈ 4 slices
4 pizzas is conservative; 5 pizzas should be plenty.
3. 2(25) + 30 = 80
So, 25°C ≈ 80°F.
4. 238 square feet ≈ 240 square feet
$0.28 ≈ $0.30
240 × $0.30 = $72
The cost will be approximately $72.
5. 400 × 20 = 8000 square feet
6. Since 1 gallon of paint covers 350 square feet, and the room has 400 square feet of wall
space, including windows and doors, you should purchase 2 gallons of paint.
7. Answers will vary depending on the grid. Using a 3 by 5 grid, we count 30 cars. Multiply 30 by
the number of sections, 15, to get 450. So our estimate is 450 cars.
8. Answers will vary depending on the grid. Using a 3 by 5 grid, we count 28 flowers. Multiply 24
by the number of sections, 15, to get 360. So our estimate is 360 flowers.
9. Answers will vary depending on the grid. Using a 3 by 5 grid, we count 18 cadets. Multiply 15
by the number of sections, 15, to get 225. So our estimate is 225 cadets.
10. Answers will vary depending on the grid. Using a 4 by 5 grid, we count 9 marchers. Multiply 9 by
the number of sections, 20, to get 180. So our estimate is 180 marchers.
11. people or 1.6 million people
12. 68.3 square miles ≈ 68 square miles
© 2023 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 6
accessible website, in whole or in part.
, Solution and Answer Guide: Aufmann, Discovering Mathematics: A Quantitative Approach, 2e, 9780357760031;
Chapter 1: Introduction To Problem Solving
Approximately 680,000 people
13. If a 10-foot pole casts a shadow of 18 feet, and a telephone pole has a shadow of 72 feet,
then the telephone pole will be more than half as high as its shadow is long. The telephone
pole has height
14. If an 8-foot pole casts a shadow of 6 feet, and a building has a shadow of 94 feet, then the
building will be taller than its shadow. The building has height
15. 0.0000000000089 meter = 8.9 × 10–12 meter
16. 30,900,000,000,000,000 m = 3.09 × 1016 m
17. 35,000,000,000,000 cells = 3.5 × 1013 cells
18. 0.000000076 meter = 7.6 × 10–8 meter
19. Yes. The higher the advanced degree, the higher the bar of the lifetime earnings is.
20. Yes
21. Yes. The Dogs category is more than half of the pie graph.
22. Yes
23. a. The graph decreases in years 2018 to 2020.
b. The graph increases from 0 to 2.4 from 2015 to 2018, but from 1.4 to 7 from 2020 to
2021. The inflation rate increased more from 2020 to 2021.
24. a. From the graph, the blue line is greater than the red line for 110th, 111th, and 116th
Congress.
b. From the graph, the greatest difference between the red and blue lines is for the 111th
Congress.
c. From the graph, the least difference between the red and blue lines is for the 117th
Congress.
THINK ABOUT IT 1.3
1. Understand the problem, devise a plan, carry out the plan, review the solution
2. No. We would need to know the speed at which she ran.
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, Solution and Answer Guide: Aufmann, Discovering Mathematics: A Quantitative Approach, 2e, 9780357760031;
Chapter 1: Introduction To Problem Solving
SECTION 1.3 EXERCISE SOLUTIONS
1. Let g be the number of first grade girls, and let b be the number of first grade boys. Then b +
g = 364 and g = b + 26. Solving gives g = 195, so there are 195 girls.
2. Let a be the length in feet of the shorter ladder and b be the length in feet of the longer
ladder. Then a + b = 31.5 and a + 6.5 = b. Solving gives a = 12.5 and b = 19, so the ladders
are 12.5 feet and 19 feet long.
3. There are 36 1 × 1 squares, 25 2 × 2 squares, 16 3 × 3 squares, 9 4 × 4 squares,
4 5 × 5 squares and 1 6 × 6 square in the figure, making a total of 91 squares.
4. The first decimal digit, like all the odd decimal digits, is a zero, and the second decimal digit,
like all the even decimal digits, is a 9. Since 44 is even, the
44th decimal digit is a 9.
5. Solving:
x = cost of the shirt
x – 30 = cost of the tie
(x – 30) + x = 50
2x – 30 = 50
2x = 80
x = 40
The shirt costs $40.
6. Using the results of example 3, 12 teams play each of 11 teams for a total of
(12 × 11) ÷ 2 = 66 games. Since each team plays each of the teams twice 2 × 66 = 132 total
games.
7. There are 14 different routes to get to Fourth Avenue and Gateway Boulevard and 4 different
routes to get to Second Avenue and Crest Boulevard. Adding gives that there are 18 different
routes altogether.
8. a. There are 2 different routes from point A to the Starbucks and 2 different routes from the
Starbucks to point B. Multiplying gives a total of 4 different routes.
b. There is only one direct route to the Subway. There are 3 different routes from the
Subway to point B, so there are 3 different routes altogether.
c. Since there is only one direct route to the Subway, starting the count there will not
change the number of routes. There is only one direct route from the Subway to
Starbucks, and there are 2 different routes from Starbucks to point B, so there are 2
different routes altogether.
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