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SOLUTIONS
MANUAL
(All Chapters) For
A PROBLEM SOLVING APPROACH
TO MATHEMATICS
FOR ELEMENTAR Y SCHOOL TEACHERS
THIRTEENTH EDITION
Rick Billstein Barbara Boschmans Shlomo Libeskind Johnny W. Lott 1 / 4
iii Contents Chapter 1 An Introduction to Problem Solving 1 Chapter 2 Introduction to Logic and Sets 21 Chapter 3 Numeration Systems and Whole Number Operations 45 Chapter 4 Number Theory 87 Chapter 5 Integers 105 Chapter 6 Rational Numbers and Proportional Reasoning 127 Chapter 7 Decimals, Percents, and Real Numbers 155 Chapter 8 Algebraic Thinking 189 Chapter 9 Probability 217
Chapter 10 Data Analysis/Statistics: An Introduction 245
Chapter 11 Introductory Geometry 273 Chapter 12 Congruence and Similarity with Constructions 297 Chapter 13 Area, Pythagorean Theorem, and Volume 323 Chapter 14 Transformations 361 2 / 4
Copyright © 2020 Pearson Education, Inc.1
CHAPTER 1
AN INTRODUCTION TO PROBLEM SOLVING
Assessment 1-1A: Mathematics and
Problem Solving
1. (a) <> List the numb ers:
12 9899
99 982 1
100 100100 100
+++ + +++ + +++ + There are 99 sums of 100. Thus the total can be found by computing
99 100
2 .⋅ =4950 (Another way of looking at this problem is to realize there are 99 2 49.5= pairs of sums, each of 100; thus 49.5
100 = 4950.)
(b)The number of terms in any sequence of numbers may be found by subtracting the first term from the last, dividing the result by the common difference between terms, and then adding 1 (because both ends must be accounted for). Thus
1001 1
2 1501 - += terms.
List the numbers:
1 3999 1001
1001 9993 1
1002 1002 1002 1002
+++ + +++ + +++ + There are 501 sums of 1002. Thus the total can be found by computing
501 1002
2 .⋅
=251,001
(c)The number of terms in any sequence of numbers may be found by subtracting the first term from the last, dividing the result by the common difference between terms, and then adding 1 (because both ends must be accounted for). Thus 300 3 3 1100 - += terms.
List the numbers:
3 6 297 300
300 2976 3
303 303 303 303
++++ ++++ ++++ There are 100 sums of 303. Thus the total can be found by computing
100 303
2
.15,150
⋅ = (d)The number of terms in any sequence ofnumbers may be found by subtracting the first term from the last, dividing the result by the common difference between terms, and then adding 1 (because both ends must be accounted for). Thus 400 4 4
- 100
- += terms.
List the numbers:
4 8396 400
400 3968 4
404 404 404 404
+++ + +++ + +++ + There are 100 sums of 404. Thus the total can be found by computing
100 404
2
.20, 200
⋅ =
- (a)
(b) 3 / 4
2 Chapter 1: An Introduction to Problem Solving
Copyright © 2020 Pearson Education, Inc.When the stack in (a) and a stack of the same size is placed differently next to the original stack in (a), a rectangle containing 100 (101) blocks is created. Since each block is represented twice, the desired sum is 100(101) 2 .=5050 While the above represents a specific example, the same thinking can be used for any natural number n to arrive at a formula (1)2.nn
- There are
147 36
1 1112 - += terms.
List the numbers:
36 37 146 147
147 146 37 36
183 183 183 183
++++
++++ ++++
There are 112 sums of 183. Thus the total can be found by computing
112 183
2 .⋅
=10, 248
- (a) Make a table as follows; there are 9 rows
- 2 0
- 1 2
- 0 4
- 5 0
- 4 2
- 3 4
- 2 6
- 1 8
so there are 9 different ways.6-cookie packages 2-cookie packages single-cookie packages
0 0 10
(b) Make a table as follows; there are 12 rows so there are 12 different ways.
6-cookie 2-cookie single-cookie packages packages packages 20 0 13 0 12 2 11 4 10 6 06 0 05 2 04 4 03 6 02 8 01 10 00 12
- If each layer of boxes has 7 more than the
previous layer we can add powers of 7:
7
= 1 (red box) 7 1 = 7 (blue boxes) 7 2 = 49 (black boxes) 7 3 = 343 (yellow boxes) 7 4 = 2401 (gold boxes)
- + 7 + 49 + 343 + 2401 = 2801 boxes
- Using strategies from Poyla’s problem solving
altogether.
list identify subgoals (solve simpler problems) and make diagrams to solve the original problem.
- triangle; name this the “unit” triangle.
This triangle is made of 4 unit triangles.Counting the large triangle there are
- triangles
- / 4
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