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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
- Veröffentlichungsjahr: 2022
Practice makes perfect--gain math mastery with Dummies Basic Math & Pre-Algebra: 1001 Practice Problems For Dummies gives you 1,001 opportunities to practice solving problems on all the major topics in middle-grade math and Pre-Algebra--in the book and online! Get extra practice with tricky subjects, solidify what you've already learned, and get in-depth walk-throughs for every problem with this useful book. These practice problems and detailed answer explanations will improve your mathemagic abilities, no matter what your skill level is now. Thanks to Dummies, you have a resource to help you put key concepts into practice. * Work through practice problems on all middle-grade and Pre-Algebra topics covered in class * Step through detailed solutions to build your understanding * Access practice questions online to study anywhere, any time * Improve your grade and up your study game with practice, practice, practice The material presented in Basic Math & Pre-Algebra: 1001 Practice Problems For Dummies is an excellent resource for students, as well as parents and tutors looking to help supplement clasroom instruction. Basic Math & Pre-Algebra: 1001 Practice Problems For Dummies (9781119883500) was previously published as 1,001 Basic Math & Pre-Algebra Practice Problems For Dummies (9781118446560). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product.
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Basic Math & Pre-Algebra: 1001 Practice Problems For Dummies®
Published by: John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030-5774, www.wiley.com
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Published simultaneously in Canada
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Library of Congress Control Number: 2022934797
ISBN 978-1-119-88350-0 (pbk); ISBN 978-1-119-88351-7 (ebk); ISBN 978-1-119-88352-4 (ebk)
Basic Math & Pre-Algebra: 1001 Practice Problems For Dummies®
To view this book's Cheat Sheet, simply go to www.dummies.com and search for “Basic Math & Pre-Algebra: 1001 Practice Problems For Dummies Cheat Sheet” in the Search box.
Table of Contents
Cover
Title Page
Copyright
Introduction
What You’ll Find
How This Workbook Is Organized
Beyond the Book
Where to Go from Here
Part 1: The Questions
Chapter 1: The Big Four Operations
The Problems You’ll Work On
What to Watch Out For
Rounding
Adding, Subtracting, Multiplying, and Dividing
Chapter 2: Less than Zero: Working with Negative Numbers
The Problems You’ll Work On
What to Watch Out For
Adding and Subtracting Negative Numbers
Multiplying and Dividing Negative Numbers
Working with Absolute Value
Chapter 3: You’ve Got the Power: Powers and Roots
The Problems You’ll Work On
What to Watch Out For
Multiplying a Number by Itself
Finding Square Roots
Negative and Fractional Exponents
Chapter 4: Following Orders: Order of Operations
The Problems You’ll Work On
What to Watch Out For
The Big Four Operations
Operations with Exponents
Operations with Parentheses
Operations with Square Roots
Operations with Fractions
Operations with Absolute Values
Chapter 5: Big Four Word Problems
The Problems You’ll Work On
What to Watch Out For
Basic Word Problems
Intermediate Word Problems
Advanced Word Problems
Chapter 6: Divided We Stand
The Problems You’ll Work On
What to Watch Out For
Determining Divisibility
Working with Prime and Composite Numbers
Chapter 7: Factors and Multiples
The Problems You’ll Work On
What to Watch Out For
Identifying Factors
Finding Nondistinct Prime Factors
Figuring the Greatest Common Factor
Mastering Multiples
Looking for the Least Common Multiple
Chapter 8: Word Problems about Factors and Multiples
The Problems You’ll Work On
What to Watch Out For
Basic Word Problems
Intermediate Word Problems
Advanced Word Problems
Chapter 9: Fractions
The Problems You’ll Work On
What to Watch Out For
Identifying Fractions
Converting Numbers to Fractions
Converting Fractions to Mixed Numbers
Increasing Terms
Reducing Terms
Comparing Fractions
Multiplying and Dividing Fractions
Adding and Subtracting Fractions
Adding and Subtracting Fractions Using Cross-Multiplication
Adding and Subtracting Fractions by Increasing Terms
Adding and Subtracting Fractions by Finding a Common Denominator
Multiplying and Dividing Mixed Numbers
Adding and Subtracting Mixed Numbers
Simplifying Fractions
Chapter 10: Decimals
The Problems You’ll Work On
What to Watch Out For
Converting Fractions and Decimals
Adding and Subtracting Decimals
Multiplying and Dividing Decimals
Chapter 11: Percents
The Problems You’ll Work On
What to Watch Out For
Converting Decimals, Fractions, and Percents
Solving Percent Problems
Chapter 12: Ratios and Proportions
The Problems You’ll Work On
What to Watch Out For
Fractions and Ratios
Using Equations to Solve Ratios and Proportions
Chapter 13: Word Problems for Fractions, Decimals, and Percents
The Problems You’ll Work On
What to Watch Out For
Fraction Problems
Decimal Problems
Percent Problems
Chapter 14: Scientific Notation
The Problems You’ll Work On
What to Watch Out For
Converting Standard Notation and Scientific Notation
Multiplying Numbers in Scientific Notation
Chapter 15: Weights and Measures
The Problems You’ll Work On
What to Watch Out For
English Measurements
Metric Units
Temperature Conversions
Converting English and Metric Units
Chapter 16: Geometry
The Problems You’ll Work On
What to Watch Out For
Angles
Squares
Rectangles
Parallelograms and Trapezoids
Area of Triangles
The Pythagorean Theorem
Circles
Volume
Chapter 17: Graphing
The Problems You’ll Work On
What to Watch Out For
Bar Graph
Pie Chart
Line Graph
Population Pictograph
Pie Chart
Trees Pictograph
Cartesian Graph
Chapter 18: Statistics and Probability
The Problems You’ll Work On
What to Watch Out For
Finding Means
Finding Weighted Means
Medians and Modes
Independent Events
Dependent Events
Probability
Chapter 19: Set Theory
The Problems You’ll Work On
What to Watch Out For
Performing Operations on Sets
Set Relationships
Complements
Venn Diagrams
Chapter 20: Algebraic Expressions
The Problems You’ll Work On
What to Watch Out For
Evaluating
Simplifying
Factoring
Simplifying by Factoring
Chapter 21: Solving Algebraic Equations
The Problems You’ll Work On
What to Watch Out For
Simple Equations
Isolating Variables
Solving Equations with Decimals
Solving Equations with Parentheses
Solving Equations with Fractions
Factoring
Chapter 22: Solving Algebra Word Problems
The Problems You’ll Work On
What to Watch Out For
Word Problems
Part 2: The Answers
Chapter 23: Answers
Index
About the Author
Advertisement Page
Connect with Dummies
End User License Agreement
Guide
Cover
Title Page
Copyright
Table of Contents
Begin Reading
Index
About the Author
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Introduction
Are you kidding … 1,001 math problems, really?
That’s right, a thousand questions plus one to grow on, here in your hot little hands. I’ve arranged them in order, starting with beginning arithmetic and ending with basic algebra. Topics include everything from the Big Four operations (adding, subtracting, multiplying, and dividing), through negative numbers and fractions, on to geometry and probability, and finally algebra — plus lots more!
Every chapter provides tips for solving the problems in that chapter. And, of course, the back of the book includes detailed explanations of the answers to every question. It’s all here, so get to work!
What You’ll Find
This book includes 1,001 basic math and pre-algebra problems, divided into 22 chapters. Each chapter contains problems focusing on a single math topic, such as negative numbers, fractions, or geometry. Within each chapter, topics are broken into subtopics so that you can work on a specific type of math skill until you feel confident with it. Generally speaking, each section starts with easy problems, moves on to medium ones, and then finishes with hard problems.
You can jump right in anywhere you like and solve these problems in any order. You can also take on one chapter or section at a time, working from easy to medium to hard problems. Or, if you like, you can begin with Question 1 and move right through to Question 1,001.
Additionally, each chapter begins with a list of tips for answering the questions in that chapter. Every question in Part 1 is answered in Part 2, with a full explanation that walks you through how to understand, set up, and solve the problem.
How This Workbook Is Organized
This workbook includes 1,001 questions in Part 1, and answers to all of these questions in Part 2.
Part 1: Questions
Here are the topics covered by the 1,001 questions in this book:
Basic arithmetic:
In
Chapters 1
through
5
, you find dozens of basic arithmetic problems.
Chapter 1
begins with rounding numbers and then moves on to basic calculating with addition, subtraction, multiplication, and division. Then, in
Chapter 2
, you tackle negative numbers, and in
Chapter 3
, you move on to working with powers and square roots.
Chapter 4
gives you plenty of practice in solving arithmetic problems using the order of operations. You may remember this using the mnemonic PEMDAS —
P
arentheses,
E
xponents,
M
ultiplication and
D
ivision,
A
ddition and
S
ubtraction. Finally, in
Chapter 5
, you put all of this information together to answer arithmetic word problems, from easy to challenging.
Divisibility, factors, and multiples:
Chapters 6
,
7
, and
8
cover a set of topics related to divisibility. In
Chapter 6
, you discover a variety of divisibility tricks, which allow you to find out whether a number is divisible by another number without actually doing the division. You also work on division with remainders and discover the distinction between prime and composite numbers.
Chapter 7
focuses on factors and multiples. You discover how to generate all the factors and prime factors of a number and calculate the greatest common factor (GCF) for a set of two or more numbers.
Chapter 8
wraps up the section with word problems that sharpen and extend your skills at working with factors, multiples, remainders, and prime numbers.
Fractions, decimals, percents, and ratios:Chapters 9 through 13 focus on four distinct ways to represent parts of a whole — fractions, decimals, percents, and ratios. In Chapter 9, you work with fractions, including increasing the terms of fractions and reducing them to lowest terms. You change improper fractions to mixed numbers, and vice versa. You add, subtract, multiply, and divide fractions, including mixed numbers. You also simplify complex fractions.
In Chapter 10, you convert fractions to decimals, and vice versa. You add, subtract, multiply, and divide decimals, and you also find out how to work with repeating decimals. Chapter 11 focuses on percents. You convert fractions and multiples to percents, and vice versa. You discover a few tricks for calculating simple percents. You also work on more difficult percent problems by creating word equations, which can then be translated into equations and solved.
Chapter 12 presents a variety of problems, including word problems, that use ratios and proportions. And in Chapter 13, you tackle even more word problems where you apply your skills working with fractions, decimals, and percents.
Scientific notation, weights and measures, geometry, graphs, statistics and probability, and sets:
In
Chapters 14
through
19
, you take a great stride forward as you begin working with a wide variety of intermediate math skills. In
Chapter 14
, the topic is scientific notation, which is used to represent very large and very small numbers.
Chapter 15
introduces you to weights and measures, focusing on the English and metric systems, and conversions between the two systems.
Chapter 16
gives you a huge number of geometry problems of every description, including both plane and solid geometry. In
Chapter 17
, you work with a variety of graphs, including bar graphs, pie charts, line graphs, pictographs, and the
xy
-graph that is used so much in algebra and later math.
Chapter 18
gives you an introduction to basic statistics, including the mean, median, and mode. It also provides problems in probability and gives you an introduction to counting both independent and dependent events.
Chapter 19
gives you some problems in basic set theory, including finding the union, intersection, relative complement, and complement. You also use Venn diagrams to solve word problems.
Algebraic expressions and equations:
To finish up,
Chapters 20
,
21
, and
22
give you a taste of the work you’ll be doing in your first algebra class.
Chapter 20
shows you the basics of working with algebraic expressions, including evaluating, simplifying, and factoring. In
Chapter 21
, you solve basic algebraic equations. And in
Chapter 22
, you put these skills to use, solving a set of word problems with basic algebra.
Part 2: Answers
In this part, you find answers to all 1,001 questions that appear in Part 1. Each answer contains a complete step-by-step explanation of how to solve the problem from beginning to end.
Beyond the Book
In addition to what you’re reading right now, this book comes with a free, access-anywhere Cheat Sheet that includes tips and other goodies you may want to have at your fingertips. To get this Cheat Sheet, simply go to www.dummies.com and type Basic Math & Pre-Algebra 1001 Dummies Cheat Sheet into the Search box.
The online practice that comes free with this book offers you the same 1,001 questions and answers that are available here, presented in a multiple-choice format. The beauty of the online problems is that you can customize your online practice to focus on the topic areas that give you trouble. If you’re short on time and want to maximize your study, you can specify the quantity of problems you want to practice, pick your topics, and go. You can practice a few hundred problems in one sitting or just a couple dozen, and you can focus on a few types of problems or a mix of several types. Regardless of the combination you create, the online program keeps track of the questions you get right and wrong so you can monitor your progress and spend time studying exactly what you need to.
To gain access to the online practice, you simply have to register. Just follow these steps:
Register your book or ebook at Dummies.com to get your PIN. Go to
www.dummies.com/go/getaccess
Select your product from the drop-down list on that page.
Follow the prompts to validate your product, and then check your email for a confirmation message that includes your PIN and instructions for logging in.
If you don’t receive this email within two hours, please check your spam folder before contacting us through our Technical Support website at http://support.wiley.com or by phone at 877-762-2974.
Now you’re ready to go! You can come back to the practice material as often as you want — simply log in with the username and password you created during your initial login. No need to enter the access code a second time.
Your registration is good for one year from the day you activate your PIN.
Where to Go from Here
Every chapter in this book opens with tips for solving the problems in that chapter. And, of course, if you get stuck on any question, you can flip to the answer section and try to work through the solution provided. However, if you feel that you need a bit more basic math information than this book provides, I highly recommend my earlier book Basic Math & Pre-Algebra For Dummies. This book gives you a ton of useful information for solving every type of problem included here.
Additionally, you can also check out my Basic Math & Pre-Algebra Workbook For Dummies. It contains a nice mix of short explanations for how to do various types of problems, followed by practice. And, for a quick take on the most important basic math concepts, have a look at Basic Math & Pre-Algebra Essentials For Dummies. Yep, I wrote that one, too — how’s that for shameless plugs?
Part 1
The Questions
IN THIS PART …
One thousand and one math problems. That’s one problem for every night in the Arabian Nights stories. That’s almost ten problems for every floor in the Empire State Building. In short, that’s a lot of problems — plenty of practice to help you attain the math skills you need to do well in your current math class. Here’s an overview of the types of questions provided:
Basic arithmetic, including absolute value, negative numbers, powers, and square roots (
Chapters 1
–
5
)
Divisibility, factors, and multiples (
Chapters 6
–
8
)
Fractions, decimals, percents, and ratios (
Chapters 9
–
13
)
Scientific notation, measures, geometry, graphs, statistics, probability, and sets (
Chapters 14
–
19
)
Algebraic expressions and equations (
Chapters 20
–
22
)
Chapter 1
The Big Four Operations
The Big Four operations (adding, subtracting, multiplying, and dividing) are the basis for all of arithmetic. In this chapter, you get plenty of practice working with these important operations.
The Problems You’ll Work On
Here are the types of problems you find in this chapter:
Rounding numbers to the nearest ten, hundred, thousand, or million
Adding columns of figures, including addition with carrying
Subtracting one number from another, including subtraction with borrowing
Multiplying one number by another
Division, including division with a remainder
What to Watch Out For
Here’s a quick tip for rounding numbers to help you in this chapter: When rounding a number, check the number to the right of the place you’re rounding to. If that number is from 0 to 4, round down by changing that number to 0. If that number is from 5 to 9, round up by changing that number to 0 and adding 1 to the number to its left.
For example, to round 7,654 to the nearest hundred, check the number to the right of the hundreds place. That number is 5, so change it to 0 and add 1 to the 6 that’s to the left of it. Thus, 7,654 becomes 7,700.
Rounding
1–6
1. Round the number 136 to the nearest ten.
2. Round the number 224 to the nearest ten.
3. Round the number 2,492 to the nearest hundred.
4. Round the number 909,090 to the nearest hundred.
5. Round the number 9,099 to the nearest thousand.
6. Round the number 234,567,890 to the nearest million.
Adding, Subtracting, Multiplying, and Dividing
7–30
7. Add
8. Add
9. Add
10. Add
11. Add
12. Add
13. Subtract
14. Subtract
15. Subtract
16. Subtract
17. Subtract
18. Subtract
19. Multiply
20. Multiply
21. Multiply
Chapter 2
Less than Zero: Working with Negative Numbers
Negative numbers can be a cause of negativity for some students. The rules for working with negative numbers can be a little tricky. In this chapter, you practice applying the Big Four operations to negative numbers. You also strengthen your skills evaluating absolute value.
The Problems You’ll Work On
This chapter shows you how to work with the following types of problems:
Subtracting a smaller number minus a larger number
Adding and subtracting with negative numbers
Multiplying and dividing with negative numbers
Evaluating absolute value
What to Watch Out For
Here are a few things to keep an eye out for when you’re working with negative numbers:
To subtract a smaller number minus a larger number, reverse and negate:
Reverse
by subtracting the larger number minus the smaller one, and then
negate
by attaching a minus sign (−) in front of the result. For example,
.
To subtract a negative number minus a positive number, add and negate:
Add
the two numbers as if they were positive, then
negate
by attaching a minus sign in front of the result. For example,
.
To add a positive number and a negative number (in either order), subtract the larger number minus the smaller number; then attach the same sign to the result as the number that is farther from 0. For example,
and
Adding and Subtracting Negative Numbers
31–41
31. Evaluate each of the following.
32. Evaluate each of the following.
33. Evaluate each of the following.
34. Evaluate each of the following.
35. Evaluate each of the following.
36.
37.
38.
39.
40.
41.
Multiplying and Dividing Negative Numbers
42–53
42. Evaluate each of the following.
43.
44.
45.
46.
47.
48.
49.
Chapter 3
You’ve Got the Power: Powers and Roots
Powers provide a shorthand notation for multiplication using a base number and an exponent. Roots — also called radicals — reverse the process of powers. In this chapter, you practice taking powers and roots of positive integers as well as fractions and negative integers.
The Problems You’ll Work On
This chapter deals with the following types of problems:
Using powers to multiply a number by itself
Applying exponents to negative numbers and fractions
Understanding square roots
Knowing how to evaluate negative exponents and fractional exponents
What to Watch Out For
Following are some tips for working with powers and roots:
When you find the power of a number, multiply the base by itself as many times as indicated by the exponent. For example,
.
When the base is a negative number, use the standard rules of multiplication for negative numbers (see
Chapter 2
). For example,
.
When the base is a fraction, use the standard rules of multiplication for fractions (see
Chapter 9
). For example,
.
To find the square root of a square number, find the number that, when multiplied by itself, results in the number you started with. For example,
, because
.
To simplify the square root of a number that’s not a square number, if possible, factor out a square number and then evaluate it. For example,
.
Evaluate an exponent of
as the square root of the base. For example,
.
Evaluate an exponent of –1 as the reciprocal of the base. For example,
.
To evaluate an exponent of a negative number, make the exponent positive and evaluate its reciprocal. For example,
.
Multiplying a Number by Itself
58–72
58. Evaluate each of the following.
59.
60.
61.
62.
63.
64.
65. Evaluate each of the following.
66.
67.
68.
69. Evaluate each of the following.
70.
71.
72.
Finding Square Roots
73–79
73. Simplify each of the following as a whole number by finding the square root.
74. Simplify each of the following as a whole number by finding the square root and then multiplying.
75.
76.
77.
78.
79.
Negative and Fractional Exponents
80–90
80. Express each of the following as a square root and then simplify as a positive whole number.
81.
82.
83.
84.
85. Simplify each of the following as a fraction.
86.
87.
Chapter 4
Following Orders: Order of Operations
The order of operations (also called the order of precedence) provides a clear way to evaluate complex expressions so you always get the right answer. The mnemonic PEMDAS helps you to remember to evaluate parentheses first; then move on to exponents; then multiplication and division; and finally addition and subtraction.
The Problems You’ll Work On
This chapter includes these types of problems:
Evaluating expressions that contain the Big Four operations (addition, subtraction, multiplication, and division)
Evaluating expressions that include exponents
Evaluating expressions that include parentheses, including nested parentheses
Evaluating expressions that include parenthetical expressions, such as square roots and absolute value
Evaluating expressions that include fractions with expressions in the numerator and/or denominator
What to Watch Out For
Keep the following tips in mind as you work with the problems in this chapter:
When an expression has only addition and subtraction, evaluate it from left to right. For example,
.
When an expression has only multiplication and division, evaluate it from left to right. For example,
.
When an expression has any combination of the Big Four operations, first evaluate all multiplication and division from left to right; then evaluate addition and subtraction from left to right. For example,
.
When an expression includes powers, evaluate them
first
, and
then
evaluate Big Four operations. For example,
.
The Big Four Operations
91–102
91.
92.
93.
94.
95.
96.
97.
98.
99.
100.
101.
102.
Operations with Exponents
103–112
103.
104.
105.
106.
107.
108.
109.
110.
111.
112.
Operations with Parentheses
113–124
113.
114.
115.
116.
117.
118.
119.
120.
121.
122.
Chapter 5
Big Four Word Problems
Word problems provide an opportunity for you to apply your math skills to real-world situations. In this chapter, all the problems can be solved using the Big Four operations (adding, subtracting, multiplying, and dividing).
The Problems You’ll Work On
The problems in this chapter fall into three basic categories, based on their difficulty:
Basic word problems where you need to perform a single operation
Intermediate word problems where you need to use two different operations
Tricky word problems that require several different operations and more difficult calculations
What to Watch Out For
Here are a few tips for getting the right answer to word problems:
Read each problem carefully to make sure you understand what it’s asking.
Use scratch paper to gather and organize information from the problem.
Think about which Big Four operation (adding, subtracting, multiplying, or dividing) will be most helpful for solving the problem.
Perform calculations carefully to avoid mistakes.
Ask yourself whether the answer you got makes sense.
Check your work to make sure you’re right.
Basic Word Problems
145–154
145. A horror movie triple-feature included Zombies Are Forever, which was 80 minutes long, An American Werewolf in Bermuda, which ran for 95 minutes, and Late Night Snack of the Vampire, which was 115 minutes from start to finish. What was the total length of the three movies?
146. At a height of 2,717 feet, the tallest building in the world is the Burj Khalifa in Dubai. It’s 1,263 feet taller than the Empire State Building in New York City. What is the height of the Empire State Building?
147. Janey’s six children are making colored eggs for Easter. She bought a total of five dozen eggs for all of the children to use. Assuming each child gets the same number of eggs, how many eggs does each child receive?
148. Arturo worked a 40-hour week at $12 per hour. He then received a raise of $1 per hour and worked a 30-hour week. How much more money did he receive for the first week of work than the second?
149. A restaurant has 5 tables that seat 8 people each, 16 tables with room for 6 people each, and 11 tables with room for 4 people each. What is the total capacity of all the tables at the restaurant?
150. The word pint originally comes from the word pound because a pint of water weighs 1 pound. If a gallon contains 8 pints, how many pounds does 40 gallons of water weigh?
151. Antonia purchased a sweater normally priced at $86, including tax. When she brought it to the cash register, she found that it was selling for half off. Additionally, she used a $20 gift card to help pay for the purchase. How much money did she have to spend to buy the sweater?
152. A large notebook costs $1.50 more than a small notebook. Karan bought two large notebooks and four small notebooks, while Almonte bought five large notebooks and one small notebook. How much more did Almonte spend than Karan?
153. A company invests $7,000,000 in the development of a product. Once the product is on the market, each sale returns $35 on the investment. If the product sells at a steady rate of 25,000 per month, how long will it take for the company to break even on its initial investment?
154. Jessica wants to buy 40 pens. A pack of 8 pens costs $7, but a pack of 10 pens costs $8. How much does she save by buying packs of 10 pens instead of packs of 8 pens?
Intermediate Word Problems
155–171
155. Jim bought four boxes of cereal on sale. One box weighed 10 ounces and the remaining boxes weighed 16 ounces each. How many ounces of cereal did he buy altogether?
156. Mina took a long walk on the beach each day of her eight-day vacation. On half of the days, she walked 3 miles and on the other half she walked 5 miles. How many miles did she walk altogether?
157. A three-day bike-a-thon requires riders to travel 100 miles on the first day and 20 miles fewer on the second day. If the total trip is 250 miles, how many miles do they travel on the third day?
158. If six T-shirts sell for $42, what is the cost of nine T-shirts at the same rate?
159. Kenny did 25 pushups. His older brother, Sal, did twice as many pushups as Kenny. Then, their oldest sister, Natalie, did 10 more pushups than Sal. How many pushups did the three children do altogether?
160. A candy bar usually sells at two for 90 cents. This week, it is specially packaged at three for $1.05. How much can you save on a single candy bar by buying a package of three rather than two?
161. Simon noticed a pair of square numbers that add up to 130. He then noticed that when you subtract one of these square numbers from the other, the result is 32. What is the smaller of these two square numbers?
162. If Donna took 20 minutes to read 60 pages of a 288-page graphic novel, how long did she take to read the whole novel, assuming that she read it all at the same rate?
163. Kendra sold 50 boxes of cookies in 20 days. Her older sister, Alicia, sold twice as many boxes in half as many days. If the two girls continued at the same sales rates, how many total boxes would both girls have sold if they had both sold cookies for 40 days?
164. A group of 70 third graders has exactly three girls for every four boys. When the teacher asks the children to pair up for an exercise, six boy-girl pairs are formed, and the rest of the children pair up with another child of the same sex. How many more boy-boy pairs are there than girl-girl pairs?
165. Together, a book and a newspaper cost $11.00. The book costs $10.00 more than the newspaper. How many newspapers could you buy for the same price as the book?
166. Yianni just purchased a house priced at $385,000 with a mortgage from the bank. His monthly mortgage payment to cover the principal and interest will be $1,800 per month for 30 years. When he has finished paying off the house, how much over and above the cost of the house will Yianni have paid in interest?
167. The distance from New York to San Diego is approximately 2,700 miles. Because of prevailing winds, when flying east-to-west, the flight usually takes one hour longer than when flying west-to-east. If a plane from San Diego to New York travels at a forward speed of 540 miles per hour, what is the forward speed of a plane traveling from New York to San Diego under the same conditions?
168. Arlo went to an all-night poker game hosted by friends. By 11:00, he was down $65 from where he had started. Between 11:00 and 2:00, he won $120. Then, in the next three hours, he lost another $45. In the final hour of the game, he won $30. How much did Arlo win or lose during the game?
169. Clarissa bought a diamond for $1,000 and then sold it to Andre for $1,100. A month later, Andre needed money, so he sold the diamond back to Clarissa for $900. But a few months later, he had a windfall and bought the diamond back from Clarissa for $1,200. How much profit did Clarissa make as a result of the total transactions?
170. Angela and Basil both work at a cafeteria making sandwiches. At top speed, Angela can make four sandwiches in three minutes and Basil can make three sandwiches in four minutes. Working together, how long will they take to make 200 sandwiches?
171. All 16 children in Ms. Morrow’s preschool have either two or three siblings. Altogether, the children have a total of 41 siblings. How many of the children have three siblings?
Advanced Word Problems
172–180
172. What is the sum of all the numbers from 1 to 100?
173. Louise works in retail and has a $1,200-per-day sales quota. On Monday, she exceeded this quota by $450. On Tuesday, she exceeded it by $650. On Wednesday and Thursday, she made her quota exactly. Friday was a slow day, so Louise sold $250 less than her quota. What were her total sales for the five days?
174. A sign posted over a large swimming pool reminds swimmers that 40 lengths of the pool equals 1 mile. Jordy swam 1 length of the pool at a rate of 3 miles per hour. How long did he take to swim 1 length of the pool?
175. In a group of two people, only one pair can shake hands. But in a group of three people, three different pairings of people can shake hands. How many different pairings of people can shake hands in a group of ten people?
176.
