Chapter 3 Resource Masters - Morgan Park High School · 2009. 12. 2. · ©Glencoe/McGraw-Hill iv...
Transcript of Chapter 3 Resource Masters - Morgan Park High School · 2009. 12. 2. · ©Glencoe/McGraw-Hill iv...
Chapter 3Resource Masters
Consumable WorkbooksMany of the worksheets contained in the Chapter Resource Masters bookletsare available as consumable workbooks in both English and Spanish.
Study Guide and Intervention Workbook 0-07-827753-1Study Guide and Intervention Workbook (Spanish) 0-07-827754-XSkills Practice Workbook 0-07-827747-7Skills Practice Workbook (Spanish) 0-07-827749-3Practice Workbook 0-07-827748-5Practice Workbook (Spanish) 0-07-827750-7
ANSWERS FOR WORKBOOKS The answers for Chapter 3 of these workbookscan be found in the back of this Chapter Resource Masters booklet.
Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Printed in the United States of America. Permission is granted to reproduce the material contained herein on the condition that such material be reproduced only for classroom use; be provided to students, teachers, and families without charge; and be used solely in conjunction with Glencoe’s Algebra 1. Any other reproduction, for use or sale, is prohibited without prior written permission of the publisher.
Send all inquiries to:The McGraw-Hill Companies8787 Orion PlaceColumbus, OH 43240-4027
ISBN: 0-07-827727-2 Algebra 1Chapter 3 Resource Masters
2 3 4 5 6 7 8 9 10 024 11 10 09 08 07 06 05 04 03
Glencoe/McGraw-Hill
© Glencoe/McGraw-Hill iii Glencoe Algebra 1
Contents
Vocabulary Builder . . . . . . . . . . . . . . . . vii
Lesson 3-1Study Guide and Intervention . . . . . . . . 137–138Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 139Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 140Reading to Learn Mathematics . . . . . . . . . . 141Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 142
Lesson 3-2Study Guide and Intervention . . . . . . . . 143–144Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 145Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 146Reading to Learn Mathematics . . . . . . . . . . 147Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 148
Lesson 3-3Study Guide and Intervention . . . . . . . . 149–150Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 151Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 152Reading to Learn Mathematics . . . . . . . . . . 153Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 154
Lesson 3-4Study Guide and Intervention . . . . . . . . 155–156Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 157Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 158Reading to Learn Mathematics . . . . . . . . . . 159Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 160
Lesson 3-5Study Guide and Intervention . . . . . . . . 161–162Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 163Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 164Reading to Learn Mathematics . . . . . . . . . . 165Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 166
Lesson 3-6Study Guide and Intervention . . . . . . . . 167–168Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 169Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 170Reading to Learn Mathematics . . . . . . . . . . 171Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 172
Lesson 3-7Study Guide and Intervention . . . . . . . . 173–174Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 175Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 176Reading to Learn Mathematics . . . . . . . . . . 177Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 178
Lesson 3-8Study Guide and Intervention . . . . . . . . 179–180Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 181Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 182Reading to Learn Mathematics . . . . . . . . . . 183Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 184
Lesson 3-9Study Guide and Intervention . . . . . . . . 185–186Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 187Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 188Reading to Learn Mathematics . . . . . . . . . . 189Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 190
Chapter 3 AssessmentChapter 3 Test, Form 1 . . . . . . . . . . . . 191–192Chapter 3 Test, Form 2A . . . . . . . . . . . 193–194Chapter 3 Test, Form 2B . . . . . . . . . . . 195–196Chapter 3 Test, Form 2C . . . . . . . . . . . 197–198Chapter 3 Test, Form 2D . . . . . . . . . . . 199–200Chapter 3 Test, Form 3 . . . . . . . . . . . . 201–202Chapter 3 Open-Ended Assessment . . . . . . 203Chapter 3 Vocabulary Test/Review . . . . . . . 204Chapter 3 Quizzes 1 & 2 . . . . . . . . . . . . . . . 205Chapter 3 Quizzes 3 & 4 . . . . . . . . . . . . . . . 206Chapter 3 Mid-Chapter Test . . . . . . . . . . . . 207Chapter 3 Cumulative Review . . . . . . . . . . . 208Chapter 3 Standardized Test Practice . . 209–210Unit 1 Test/Review (Ch. 1–3) . . . . . . . . 211–212
Standardized Test Practice Student Recording Sheet . . . . . . . . . . . . . . A1
ANSWERS . . . . . . . . . . . . . . . . . . . . . . A2–A39
© Glencoe/McGraw-Hill iv Glencoe Algebra 1
Teacher’s Guide to Using theChapter 3 Resource Masters
The Fast File Chapter Resource system allows you to conveniently file the resourcesyou use most often. The Chapter 3 Resource Masters includes the core materials neededfor Chapter 3. These materials include worksheets, extensions, and assessment options.The answers for these pages appear at the back of this booklet.
All of the materials found in this booklet are included for viewing and printing in theAlgebra 1 TeacherWorks CD-ROM.
Vocabulary Builder Pages vii–viiiinclude a student study tool that presentsup to twenty of the key vocabulary termsfrom the chapter. Students are to recorddefinitions and/or examples for each term.You may suggest that students highlight orstar the terms with which they are notfamiliar.
WHEN TO USE Give these pages tostudents before beginning Lesson 3-1.Encourage them to add these pages to theirAlgebra Study Notebook. Remind them toadd definitions and examples as theycomplete each lesson.
Study Guide and InterventionEach lesson in Algebra 1 addresses twoobjectives. There is one Study Guide andIntervention master for each objective.
WHEN TO USE Use these masters asreteaching activities for students who needadditional reinforcement. These pages canalso be used in conjunction with the StudentEdition as an instructional tool for studentswho have been absent.
Skills Practice There is one master foreach lesson. These provide computationalpractice at a basic level.
WHEN TO USE These masters can be used with students who have weakermathematics backgrounds or needadditional reinforcement.
Practice There is one master for eachlesson. These problems more closely followthe structure of the Practice and Applysection of the Student Edition exercises.These exercises are of average difficulty.
WHEN TO USE These provide additionalpractice options or may be used ashomework for second day teaching of thelesson.
Reading to Learn MathematicsOne master is included for each lesson. Thefirst section of each master asks questionsabout the opening paragraph of the lessonin the Student Edition. Additionalquestions ask students to interpret thecontext of and relationships among termsin the lesson. Finally, students are asked tosummarize what they have learned usingvarious representation techniques.
WHEN TO USE This master can be usedas a study tool when presenting the lessonor as an informal reading assessment afterpresenting the lesson. It is also a helpfultool for ELL (English Language Learner)students.
Enrichment There is one extensionmaster for each lesson. These activities mayextend the concepts in the lesson, offer anhistorical or multicultural look at theconcepts, or widen students’ perspectives onthe mathematics they are learning. Theseare not written exclusively for honorsstudents, but are accessible for use with alllevels of students.
WHEN TO USE These may be used asextra credit, short-term projects, or asactivities for days when class periods areshortened.
© Glencoe/McGraw-Hill v Glencoe Algebra 1
Assessment OptionsThe assessment masters in the Chapter 3Resources Masters offer a wide range ofassessment tools for intermediate and finalassessment. The following lists describe eachassessment master and its intended use.
Chapter Assessment CHAPTER TESTS• Form 1 contains multiple-choice questions
and is intended for use with basic levelstudents.
• Forms 2A and 2B contain multiple-choicequestions aimed at the average levelstudent. These tests are similar in formatto offer comparable testing situations.
• Forms 2C and 2D are composed of free-response questions aimed at the averagelevel student. These tests are similar informat to offer comparable testingsituations. Grids with axes are providedfor questions assessing graphing skills.
• Form 3 is an advanced level test withfree-response questions. Grids withoutaxes are provided for questions assessinggraphing skills.
All of the above tests include a free-response Bonus question.
• The Open-Ended Assessment includesperformance assessment tasks that aresuitable for all students. A scoring rubricis included for evaluation guidelines.Sample answers are provided forassessment.
• A Vocabulary Test, suitable for allstudents, includes a list of the vocabularywords in the chapter and ten questionsassessing students’ knowledge of thoseterms. This can also be used in conjunc-tion with one of the chapter tests or as areview worksheet.
Intermediate Assessment• Four free-response quizzes are included
to offer assessment at appropriateintervals in the chapter.
• A Mid-Chapter Test provides an optionto assess the first half of the chapter. It iscomposed of both multiple-choice andfree-response questions.
Continuing Assessment• The Cumulative Review provides
students an opportunity to reinforce andretain skills as they proceed throughtheir study of Algebra 1. It can also beused as a test. This master includes free-response questions.
• The Standardized Test Practice offerscontinuing review of algebra concepts invarious formats, which may appear onthe standardized tests that they mayencounter. This practice includes multiple-choice, grid-in, and quantitative-comparison questions. Bubble-in andgrid-in answer sections are provided onthe master.
Answers• Page A1 is an answer sheet for the
Standardized Test Practice questionsthat appear in the Student Edition onpages 186–187. This improves students’familiarity with the answer formats theymay encounter in test taking.
• The answers for the lesson-by-lessonmasters are provided as reduced pageswith answers appearing in red.
• Full-size answer keys are provided forthe assessment masters in this booklet.
Reading to Learn MathematicsVocabulary Builder
NAME ______________________________________________ DATE ____________ PERIOD _____
33
© Glencoe/McGraw-Hill vii Glencoe Algebra 1
Voca
bula
ry B
uild
erThis is an alphabetical list of the key vocabulary terms you will learn in Chapter 3.As you study the chapter, complete each term’s definition or description.Remember to add the page number where you found the term. Add these pages toyour Algebra Study Notebook to review vocabulary at the end of the chapter.
Vocabulary Term Found on Page Definition/Description/Example
consecutive integers
kuhn-SEH-kyuh-tihv
defining a variable
dimensional analysis
duh·MEHNCH·nuhl
equivalent equation
ih·KWIHV·luhnt
extremes
formula
identity
means
multi-step equations
(continued on the next page)
© Glencoe/McGraw-Hill viii Glencoe Algebra 1
Vocabulary Term Found on Page Definition/Description/Example
number theory
percent of change
percent of decrease
percent of increase
proportion
pruh·POHR·shun
ratio
rate
scale
solve an equation
weighted average
work backward
Reading to Learn MathematicsVocabulary Builder (continued)
NAME ______________________________________________ DATE ____________ PERIOD _____
33
Study Guide and InterventionWriting Equations
NAME ______________________________________________ DATE ____________ PERIOD _____
3-13-1
© Glencoe/McGraw-Hill 137 Glencoe Algebra 1
Less
on
3-1
Write Equations Writing equations is one strategy for solving problems. You can use avariable to represent an unspecified number or measure referred to in a problem. Then youcan write a verbal expression as an algebraic expression.
Translate eachsentence into an equation or aformula.
a. Ten times a number x is equal to2.8 times the difference y minus z.10 � x � 2.8 � ( y � z)The equation is 10x � 2.8( y � z).
b. A number m minus 8 is the sameas a number n divided by 2.m � 8 � n � 2The equation is m � 8 � .
c. The area of a rectangle equals thelength times the width. Translatethis sentence into a formula.Let A � area, � � length, and w � width.Formula: Area equals length timeswidth.A � � � wThe formula for the area of arectangle is A � �w.
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Use the Four-Step Problem-Solving Plan.The population of the United States in 2001was about 284,000,000, and the land area ofthe United States is about 3,500,000 squaremiles. Find the average number of peopleper square mile in the United States.Source: www.census.gov
Step 1 Explore You know that there are284,000,000 people. You want to knowthe number of people per square mile.
Step 2 Plan Write an equation to represent thesituation. Let p represent the number ofpeople per square mile.3,500,000 � p � 284,000,000
Step 3 Solve 3,500,000 � p � 284,000,000.3,500,000p � 284,000,000 Divide each side by
p � 81.14 3,500,000.
There about 81 people per square mile.Step 4 Examine If there are 81 people per
square mile and there are 3,500,000square miles, 81 � 3,500,000 �283,500,000, or about 284,000,000 people.The answer makes sense.
Example 1Example 1 Example 2Example 2
ExercisesExercises
Translate each sentence into an equation or formula.
1. Three times a number t minus twelve equals forty.
2. One-half of the difference of a and b is 54.
3. Three times the sum of d and 4 is 32.
4. The area A of a circle is the product of � and the radius r squared.
WEIGHT LOSS For Exercises 5–6, use the following information.
Lou wants to lose weight to audition for a part in a play. He weighs 160 pounds now. Hewants to weigh 150 pounds.
5. If p represents the number of pounds he wants to lose, write an equation to representthis situation.
6. How many pounds does he need to lose to reach his goal?
© Glencoe/McGraw-Hill 138 Glencoe Algebra 1
Write Verbal Sentences You can translate equations into verbal sentences.
Translate each equation into a verbal sentence.
a. 4n � 8 � 12.
4n � 8 � 12Four times n minus eight equals twelve.
b. a2 � b2 � c2
a2 � b2 � c2
The sum of the squares of a and b is equal to the square of c.
Translate each equation into a verbal sentence.
1. 4a � 5 � 23 2. 10 � k � 4k
3. 6xy � 24 4. x2 � y2 � 8
5. p � 3 � 2p 6. b � (h � 1)
7. 100 � 2x � 80 8. 3(g � h) � 12
9. p2 � 2p � 9 10. C � (F � 32)
11. V � Bh 12. A � hb1�2
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Study Guide and Intervention (continued)
Writing Equations
NAME ______________________________________________ DATE ____________ PERIOD _____
3-13-1
ExampleExample
ExercisesExercises
Skills PracticeWriting Equations
NAME ______________________________________________ DATE ____________ PERIOD _____
3-13-1
© Glencoe/McGraw-Hill 139 Glencoe Algebra 1
Less
on
3-1
Translate each sentence into an equation.
1. Two added to three times a number m is the same as 18.
2. Twice a increased by the cube of a equals b.
3. Seven less than the sum of p and q is as much as 6.
4. The sum of x and its square is equal to y times z.
5. Four times the sum of f and g is identical to six times g.
Translate each sentence into a formula.
6. The perimeter P of a square equals four times the length of a side s.
7. The area A of a square is the length of a side s squared.
8. The perimeter P of a triangle is equal to the sum of the lengths of sides a, b, and c.
9. The area A of a circle is pi times the radius r squared.
10. The volume V of a rectangular prism equals the product of the length �, the width w,and the height h.
Translate each equation into a verbal sentence.
11. g � 10 � 3g 12. 2p � 4q � 20
13. 4(a � b) � 9a 14. 8 � 6x � 4 � 2x
15. ( f � y) � f � 5 16. s2 � n2 � 2b
Write a problem based on the given information.
17. c � cost per pound of plain coffee beans 18. p � cost of dinnerc � 3 � cost per pound of flavored coffee beans 0.15p � cost of a 15% tip2c � (c � 3) � 21 p � 0.15p � 23
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© Glencoe/McGraw-Hill 140 Glencoe Algebra 1
Translate each sentence into an equation.
1. Fifty-three plus four times c is as much as 21.
2. The sum of five times h and twice g is equal to 23.
3. One fourth the sum of r and ten is identical to r minus 4.
4. Three plus the sum of the squares of w and x is 32.
Translate each sentence into a formula.
5. Degrees Kelvin K equals 273 plus degrees Celsius C.
6. The total cost C of gas is the price p per gallon times the number of gallons g.
7. The sum S of the measures of the angles of a polygon is equal to 180 times the differenceof the number of sides n and 2.
Translate each equation into a verbal sentence.
8. q � (4 � p) � q 9. t � 2 � t
10. 9(y2 � x) � 18 11. 2(m � n) � v � 7
Write a problem based on the given information.
12. a � cost of one adult’s ticket to zoo 13. c � regular cost of one airline ticketa � 4 � cost of one children’s ticket to zoo 0.20c � amount of 20% promotional discount2a � 4(a � 4) � 38 3(c � 0.20c) � 330
14. GEOGRAPHY About 15% of all federally-owned land in the 48 contiguous states of theUnited States is in Nevada. If F represents the area of federally-owned land in thesestates, and N represents the portion in Nevada, write an equation for this situation.
FITNESS For Exercises 15–17, use the following information.Deanna and Pietra each go for walks around a lake a few times per week. Last week,Deanna walked 7 miles more than Pietra.
15. If p represents the number of miles Pietra walked, write an equation that represents thetotal number of miles T the two girls walked.
16. If Pietra walked 9 miles during the week, how many miles did Deanna walk?
17. If Pietra walked 11 miles during the week, how many miles did the two girls walktogether?
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Practice Writing Equations
NAME ______________________________________________ DATE ____________ PERIOD _____
3-13-1
Reading to Learn MathematicsWriting Equations
NAME ______________________________________________ DATE ____________ PERIOD _____
3-13-1
© Glencoe/McGraw-Hill 141 Glencoe Algebra 1
Less
on
3-1
Pre-Activity How are equations used to describe heights?
Read the introduction to Lesson 3-1 at the top of page 120 in your textbook.
Does the equation 305 � s � 154 also represent the situation? Explain.
Reading the Lesson
1. Translate each sentence into an equation.
a. Two times the sum of x and three minus four equals four times x.
b. The difference of k and 3 is two times k divided by five.
2. A 1 oz serving of chips has 140 calories. There are about 14 servings of chips in a bag.How many calories are there in a bag of chips? Write what your solution would be as youuse each step in the Four-Step Problem-Solving Plan.
Explore What do you know?
What do you want to know?
Plan Write an equation.
Solve Solve the problem.
Examine Does your answer make sense?
Helping You Remember
3. If you cannot remember all the steps of the Four-Step Problem-Solving Plan, try toremember the first letters of the first word in each step. Write those letters here withtheir associated words.
© Glencoe/McGraw-Hill 142 Glencoe Algebra 1
Rep-TilesA rep-tile is a figure that can be subdivided into smaller copies of itself. The large figure is similar to the small ones and the small figures are allcongruent.
Show that each figure is a rep-tile by subdividing it into four smaller and similar figures.
1. 2. 3.
4. 5. 6.
Subdivide each rep-tile into nine smaller and similar figures.
7. 8.
9. 10.
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
3-13-1
Study Guide and InterventionSolving Equations by Using Addition and Subtraction
NAME ______________________________________________ DATE ____________ PERIOD _____
3-23-2
© Glencoe/McGraw-Hill 143 Glencoe Algebra 1
Less
on
3-2
Solve Using Addition If the same number is added to each side of an equation, theresulting equation is equivalent to the original one. In general if the original equationinvolves subtraction, this property will help you solve the equation.
Addition Property of Equality For any numbers a, b, and c, if a � b, then a � c � b � c.
Solve m � 32 � 18.
m � 32 � 18 Original equation
m � 32 � 32 � 18 � 32 Add 32 to each side.
m � 50 Simplify.
The solution is 50.
Solve �18 � p �12.
�18 � p �12 Original equation
�18 � 12 � p �12 � 12 Add 12 to each side.
p � �6 Simplify.
The solution is �6.
Example 1Example 1 Example 2Example 2
ExercisesExercises
Solve each equation. Then check your solution.
1. h � 3 � �2 2. m � 8 � �12 3. p � 5 � 15
4. 20 � y � 8 5. k � 0.5 � 2.3 6. w � �
7. h � 18 � �17 8. �12 � �24 � k 9. j � 0.2 � 1.8
10. b � 40 � �40 11. m � (�12) � 10 12. w � �
Write an equation for each problem. Then solve the equation and check thesolution.
13. Twelve subtracted from a number equals 25. Find the number.
14. What number decreased by 52 equals �12?
15. Fifty subtracted from a number equals eighty. Find the number.
16. What number minus one-half is equal to negative one-half ?
17. The difference of a number and eight is equal to 14. What is the number?
18. A number decreased by fourteen is equal to eighteen. What is the number?
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© Glencoe/McGraw-Hill 144 Glencoe Algebra 1
Solve Using Subtraction If the same number is subtracted from each side of anequation, the resulting equation is equivalent to the original one. In general if the originalequation involves addition, this property will help you solve the equation.
Subtraction Property of Equality For any numbers a, b, and c, if a � b, then a � c � b � c.
Solve 22 � p � �12.
22 � p � �12 Original equation
22 � p � 22 � �12 � 22 Subtract 22 from each side.
p � �34 Simplify.
The solution is �34.
Solve each equation. Then check your solution.
1. x � 12 � 6 2. z � 2 � �13 3. �17 � b � 4
4. s � (�9) � 7 5. �3.2 � � � (�0.2) 6. � � x �
7. 19 � h � �4 8. �12 � k � 24 9. j � 1.2 � 2.8
10. b � 80 � �80 11. m � (�8) � 2 12. w � �
Write an equation for each problem. Then solve the equation and check thesolution.
13. Twelve added to a number equals 18. Find the number.
14. What number increased by 20 equals �10?
15. The sum of a number and fifty equals eighty. Find the number.
16. What number plus one-half is equal to four?
17. The sum of a number and 3 is equal to �15. What is the number?
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Study Guide and Intervention (continued)
Solving Equations by Using Addition and Subtraction
NAME ______________________________________________ DATE ____________ PERIOD _____
3-23-2
ExampleExample
ExercisesExercises
Skills PracticeSolving Equations by Using Addition and Subtraction
NAME ______________________________________________ DATE ____________ PERIOD _____
3-23-2
© Glencoe/McGraw-Hill 145 Glencoe Algebra 1
Less
on
3-2
Solve each equation. Then check your solution.
1. y � 7 � 8 2. w � 14 � �8
3. p � 4 � 6 4. �13 � 5 � x
5. 98 � b � 34 6. y � 32 � �1
7. s � (�28) � 0 8. y � (�10) � 6
9. �1 � s � (�19) 10. j � (�17) � 36
11. 14 � d � (�10) 12. u � (�5) � �15
13. 11 � �16 � y 14. c � (�3) � 100
15. 47 � w � (�8) 16. x � (�74) � �22
17. 4 � (�h) � 68 18. �56 � 20 � (�e)
Write an equation for each problem. Then solve the equation and check yoursolution.
19. A number decreased by 14 is �46. Find the number.
20. Thirteen subtracted from a number is �5. Find the number.
21. The sum of a number and 67 is equal to �34. Find the number.
22. What number minus 28 equals �2?
23. A number plus �73 is equal to 27. What is the number?
24. A number plus �17 equals �1. Find the number.
25. What number less 5 is equal to �39?
© Glencoe/McGraw-Hill 146 Glencoe Algebra 1
Solve each equation. Then check your solution.
1. d � 8 � 17 2. v � 12 � �5 3. b � 2 � �11
4. �16 � s � 71 5. 29 � a � 76 6. �14 � y � �2
7. 8 � (�c) � 1 8. 78 � r � �15 9. f � (�3) � �9
10. 4.2 � n � 7.3 11. w � 1.9 � �2.5 12. 4.6 � (�b) � �0.4
13. y � (�1.5) � 0.5 14. a � 0.13 � �0.58 15. k � (�4.21) � �19
16. r � � 17. � q � 18. � h �
19. � x � � 20. y � � 21. � � (�n) � �
Write an equation for each problem. Then solve the equation and check yoursolution.
22. What number minus 9 is equal to �18?
23. A number plus 15 equals �12. What is the number?
24. The sum of a number and �3 is equal to �91. Find the number.
25. Negative seventeen equals 63 plus a number. What is the number?
26. The sum of negative 14, a number, and 6 is �5. What is the number?
27. What number plus one half is equal to three eighths?
HISTORY For Exercises 28 and 29, use the following information.
Galileo Galilei was born in 1564. Many years later, in 1642, Sir Isaac Newton was born.
28. Write an addition equation to represent the situation.
29. How many years after Galileo was born was Isaac Newton born?
HURRICANES For Exercises 30 and 31, use the following information.
The day after a hurricane, the barometric pressure in a coastal town has risen to 29.7 inches of mercury, which is 2.9 inches of mercury higher than the pressure when theeye of the hurricane passed over.
30. Write an addition equation to represent the situation.
31. What was the barometric pressure when the eye passed over?
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1�3
2�3
5�9
9�10
1�5
Practice Solving Equations by Using Addition and Subtraction
NAME ______________________________________________ DATE ____________ PERIOD _____
3-23-2
Reading to Learn MathematicsSolving Equations by Using Addition and Subtraction
NAME ______________________________________________ DATE ____________ PERIOD _____
3-23-2
© Glencoe/McGraw-Hill 147 Glencoe Algebra 1
Less
on
3-2
Pre-Activity How can equations be used to compare data?
Read the introduction to Lesson 3-2 at the top of page 128 in your textbook.
In the equation m � 66 � 5, the number 5 represents
and the number 66 represents
Reading the Lesson
1. To solve x � 17 � 46 using the Subtraction Property of Equality, you would subtract from each side.
2. To solve y � 9 � �30 using the Addition Property of Equality, you would add to each side.
3. Write an equation that you could solve by subtracting 32 from each side.
4. A student used the Subtraction Property of Equality to solve an equation. Explain why itwould also be possible to use the Addition Property of Equality to solve the equation.
Helping You Remember
5. Explain how you decide whether to use the Addition Property or the SubtractionProperty of Equality to solve an equation.
© Glencoe/McGraw-Hill 148 Glencoe Algebra 1
Counting-Off Puzzles
Solve each puzzle.
1. Twenty-five people are standing in a circle.Starting with person 1, they count off from 1 to 7 and then start over with 1. Each person who says “7” drops out of the circle.Who is the last person left?
2. Forty people stand in a circle. They count off so that every third person drops out. Which two people are the last ones left?
3. Only half of the 30 students in Sharon’s class can go on a field trip. Sharon arranges the boys and girls as shown. They count off from 1 to 9 and every ninthperson drops out until only 15 people are left. Who gets to go on the field trip.
A group of people stand in a circle and count off 1, 2, 1, 2, 1 and so on. Every second person drops out. Person number 1 is the last person left.
4. Draw a diagram to show why the number of people in the circle must be even. Then, explain your answer.
5. When the count returns to person number 1 for the first time, how many people have dropped out?
6. Find the number of people in the circle if the number is between 10 and 20. Do the same if the number is between 30 and 40. What can you conclude about the original number of people?
G
GG
G
G G GG
G
GG
GGG
G B
B
B B B
BBBBBB
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B1
23
4 5 6 7 8 9 1011
12
13
14
15
1617
181920212223242526
2728
29
30
1 2 3 45
6
7
8
9
10
11
1213
1415161718
19
20
21
22
23
2425
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
3-23-2
Study Guide and InterventionSolving Equations by Using Multiplication and Division
NAME ______________________________________________ DATE ____________ PERIOD _____
3-33-3
© Glencoe/McGraw-Hill 149 Glencoe Algebra 1
Less
on
3-3
Solve Using Multiplication If each side of an equation is multiplied by the samenumber, the resulting equation is equivalent to the given one. You can use the property tosolve equations involving multiplication and division.
Multiplication Property of Equality For any numbers a, b, and c, if a � b, then ac � bc.
Solve 3 p � 1 .
3 p � 1 Original equation
p � Rewrite each mixed number as animproper fraction.
� p� � � � Multiply each side by .
p � Simplify.
The solution is .3�7
3�7
2�7
3�2
2�7
7�2
2�7
3�2
7�2
1�2
1�2
1�2
1�2
Solve � n � 16.
� n � 16 Original equation
�4�� n� � �4(16) Multiply each side by �4.
n � �64 Simplify.
The solution is �64.
1�4
1�4
1�4
Example 1Example 1 Example 2Example 2
ExercisesExercises
Solve each equation. Then check your solution.
1. � �2 2. m � 6 3. p �
4. 5 � 5. � k � �2.5 6. � �
7. �1 h � 4 8. �12 � � k 9. �
10. �3 b � 5 11. m � 10 12. � �
Write an equation for each problem. Then solve the equation.
13. One-fifth of a number equals 25. Find the number.
14. What number divided by 2 equals �18?
15. A number divided by eight equals 3. Find the number.
16. One and a half times a number equals 6. Find the number.
1�4
p�5
7�10
1�3
2�5
j�3
3�2
1�2
5�8
m�8
1�4
y�12
3�5
1�5
1�8
h�3
© Glencoe/McGraw-Hill 150 Glencoe Algebra 1
Solve Using Division To solve equations with multiplication and division, you can alsouse the Division Property of Equality. If each side of an equation is divided by the samenumber, the resulting equation is true.
Division Property of Equality For any numbers a, b, and c, with c � 0, if a � b, then � .b�c
a�c
Study Guide and Intervention (continued)
Solving Equations by Using Multiplication and Division
NAME ______________________________________________ DATE ____________ PERIOD _____
3-33-3
Solve 8n � 64.
8n � 64 Original equation
� Divide each side by 8.
n � 8 Simplify.
The solution is 8.
64�8
8n�8
Solve �5n � 60.
�5n � 60 Original equation
� Divide each side by �5.
n � �12 Simplify.
The solution is �12.
60��5
�5n��5
Example 1Example 1 Example 2Example 2
ExercisesExercises
Solve each equation. Then check your solution.
1. 3h � �42 2. 8m � 16 3. �3t � 51
4. �3r � �24 5. 8k � �64 6. �2m � 16
7. 12h � 4 8. �2.4p � 7.2 9. 0.5j � 5
10. �25 � 5m 11. 6m � 15 12. �1.5p � �75
Write an equation for each problem. Then solve the equation.
13. Four times a number equals 64. Find the number.
14. What number multiplied by �4 equals �16?
15. A number times eight equals �36. Find the number.
Skills PracticeSolving Equations by Using Multiplication and Division
NAME ______________________________________________ DATE ____________ PERIOD _____
3-33-3
© Glencoe/McGraw-Hill 151 Glencoe Algebra 1
Less
on
3-3
Solve each equation. Then check your solution.
1. 12z � 108 2. �7t � 49
3. 18e � �216 4. �22 � 11v
5. �6d � �42 6. 96 � �24a
7. � 16 8. � 9
9. �84 � 10. � � �13
11. � �13 12. 31 � � n
13. �6 � z 14. q � �4
15. p � �10 16. �
17. �0.4b � 5.2 18. 1.6m � �4
Write an equation for each problem. Then solve the equation.
19. The opposite of a number is �9. What is the number?
20. Fourteen times a number is �42. Find the number.
21. Eight times a number equals 128. What is the number?
22. Negative twelve times a number equals �132. Find the number.
23. Negative eighteen times a number is �54. What is the number?
24. One sixth of a number is �17. Find the number.
25. Negative three fifths of a number is �15. What is the number?
2�5
a�10
5�9
2�7
2�3
1�6
t�4
d�7
d�3
a�16
c�4
© Glencoe/McGraw-Hill 152 Glencoe Algebra 1
Solve each equation. Then check your solution.
1. 8j � 96 2. �13z � �39 3. �180 � 15m
4. 243 � 27c 5. � �8 6. � � �8
7. � 8. � 9. �
10. �1 � � t 11. � w � �9 12. � s � 4
13. �3x � 14. a � 15. h �
16. 5n � 17. 2.5k � 20 18. �3.4e � �3.74
19. �1.7b � 2.21 20. 0.26p � 0.104 21. 4.2q � �3.36
Write an equation for each problem. Then solve the equation.
22. Negative nine times a number equals �117. Find the number.
23. Negative one eighth of a number is � . What is the number?
24. Five sixths of a number is � . Find the number.
25. 2.7 times a number equals 8.37. What is the number?
26. One and one fourth times a number is one and one third. What is the number?
27. PUBLISHING Two units of measure used in publishing are the pica and the point. A picais one sixth of an inch. There are 12 points in a pica, so Points � 12 · Picas. How manypicas are equivalent to 108 points?
ROLLER COASTERS For Exercises 28 and 29, use the following information.
Superman the Escape in California is the fastest roller coaster in the world. Riders fall 415 feet in 7 seconds. Speeds reach a maximum of 100 miles per hour.
28. If x represents the average rate of fall of the roller coaster, write an expression torepresent the situation (Hint: Use the distance formula d � rt.)
29. What is the average rate that riders fall in feet per second?
5�9
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11�4
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Practice Solving Equations by Using Multiplication and Division
NAME ______________________________________________ DATE ____________ PERIOD _____
3-33-3
Reading to Learn MathematicsSolving Equations by Using Multiplication and Division
NAME ______________________________________________ DATE ____________ PERIOD _____
3-33-3
© Glencoe/McGraw-Hill 153 Glencoe Algebra 1
Less
on
3-3
Pre-Activity How can equations be used to find how long it takes light to reachEarth?
Read the introduction to Lesson 3-3 at the top of page 135 in your textbook.
• In the equation d � rt, shown in the introduction, what number is usedfor r? for d?
• What equation could you use to find the time it takes light to reach Earthfrom the farthest star in the Big Dipper?
Reading the Lesson
Complete the sentence after each equation to tell how you would solve theequation.
1. � 16 each side by .
2. 5x � 125 each side by , or multiply each side by .
3. �8k � 96 Divide each side by , or multiply each side by
4. Explain how rewriting 4 x � 2 as x � helps you solve the equation.
Helping You Remember
5. One way to remember something is to explain it to someone else. Write how you would
explain to a classmate how to solve the equation x � 12.2�3
17�8
13�3
1�8
1�3
x�7
© Glencoe/McGraw-Hill 154 Glencoe Algebra 1
Dissection Puzzles: Make the SquareIn a dissection puzzle, you are to cut apart one figure using onlystraight cuts and then rearrange the pieces to make a new figure.Usually the puzzle-solver must figure out where to make the givennumber of cuts. However, for these puzzles, the cut lines are shown.You must discover how to rearrange the pieces.
Cut apart each figure. Then rearrange the pieces to form a square.
1.
2.
3.
4. Hint: Cut one of the triangles into two pieces to make this square.
A AA A
A
2x 2x 2x
x
A AA A
B
2x 2x x
x
A
C
B
D
A
BB
BB
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
3-33-3
Study Guide and InterventionSolving Multi-Step Equations
NAME ______________________________________________ DATE ____________ PERIOD _____
3-43-4
© Glencoe/McGraw-Hill 155 Glencoe Algebra 1
Less
on
3-4
Work Backward Working backward is one of many problem-solving strategies thatyou can use to solve problems. To work backward, start with the result given at the end of aproblem and undo each step to arrive at the beginning number.
A number is dividedby 2, and then 8 is subtracted fromthe quotient. The result is 16. Whatis the number?
Solve the problem by working backward.The final number is 16. Undosubtracting 8 by adding 8 to get 24. Toundo dividing 24 by 2, multiply 24 by 2to get 48.The original number is 48.
A bacteria culture doubleseach half hour. After 3 hours, there are6400 bacteria. How many bacteria werethere to begin with?
Solve the problem by working backward.The bacteria have grown for 3 hours. Since thereare 2 one-half hour periods in one hour, in 3 hoursthere are 6 one-half hour periods. Since thebacteria culture has grown for 6 time periods, ithas doubled 6 times. Undo the doubling byhalving the number of bacteria 6 times.
6,400 � � � � � � � 6,400 �
� 100
There were 100 bacteria to begin with.
1�64
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1�2
1�2
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Example 1Example 1 Example 2Example 2
ExercisesExercises
Solve each problem by working backward.
1. A number is divided by 3, and then 4 is added to the quotient. The result is 8. Find thenumber.
2. A number is multiplied by 5, and then 3 is subtracted from the product. The result is 12.Find the number.
3. Eight is subtracted from a number, and then the difference is multiplied by 2. The resultis 24. Find the number.
4. Three times a number plus 3 is 24. Find the number.
5. CAR RENTAL Angela rented a car for $29.99 a day plus a one-time insurance cost of$5.00. Her bill was $124.96. For how many days did she rent the car?
6. MONEY Mike withdrew an amount of money from his bank account. He spent onefourth for gasoline and had $90 left. How much money did he withdraw?
7. TELEVISIONS In 1999, 68% of households with TV’s subscribed to cable TV. If 8,000 moresubscribers are added to the number of households with cable, the total number ofhouseholds with cable TV would be 67,600,000. How many households were there withTV in 1999? Source: World Almanac
© Glencoe/McGraw-Hill 156 Glencoe Algebra 1
Solve Multi-Step Equations To solve equations with more than one operation, oftencalled multi-step equations, undo operations by working backward. Reverse the usualorder of operations as you work.
Solve 5x � 3 � 23.
5x � 3 � 23 Original equation.
5x � 3 � 3 � 23 � 3 Subtract 3 from each side.
5x � 20 Simplify.
� Divide each side by 5.
x � 4 Simplify.
Solve each equation. Then check your solution.
1. 5x � 2 � 27 2. 6x � 9 � 27 3. 5x � 16 � 51
4. 14n � 8 � 34 5. 0.6x � 1.5 � 1.8 6. p � 4 � 10
7. 16 � 8. 8 � � 13 9. � 3 � �13
10. � 10 11. 0.2x � 8 � �2 12. 3.2y � 1.8 � 3
13. �4 � 14. 8 � �12 � 15. 0 � 10y � 40
Write an equation and solve each problem.
16. Find three consecutive integers whose sum is 96.
17. Find two consecutive odd integers whose sum is 176.
18. Find three consecutive integers whose sum is �93.
k��4
7x � (�1)��
�8
4b � 8�
�2
g��5
3n�12
d � 12�14
7�8
20�5
5x�5
Study Guide and Intervention (continued)
Solving Multi-Step Equations
NAME ______________________________________________ DATE ____________ PERIOD _____
3-43-4
ExampleExample
ExercisesExercises
Skills PracticeSolving Multi-Step Equations
NAME ______________________________________________ DATE ____________ PERIOD _____
3-43-4
© Glencoe/McGraw-Hill 157 Glencoe Algebra 1
Less
on
3-4
Solve each problem by working backward.
1. A number is divided by 2, and then the quotient is added to 8. The result is 33. Find thenumber.
2. Two is subtracted from a number, and then the difference is divided by 3. The result is30. Find the number.
3. A number is multiplied by 2, and then the product is added to 9. The result is 49. Whatis the number?
4. ALLOWANCE After Ricardo received his allowance for the week, he went to the mallwith some friends. He spent half of his allowance on a new paperback book. Then hebought himself a snack for $1.25. When he arrived home, he had $5.00 left. How muchwas his allowance?
Solve each equation. Then check your solution.
5. 5x � 3 � 23 6. 4 � 3a � 14 7. 2y � 5 � 19
8. 6 � 5c � �29 9. 8 � 5w � �37 10. 18 � 4v � 42
11. � 8 � �2 12. 5 � � 1 13. � � 4 � 13
14. � � 12 � �7 15. � 2 � 9 16. � 3 � �1
17. q � 7 � 8 18. g � 6 � �12 19. z � 8 � �3
20. m � 2 � 6 21. � 3 22. � 2
Write an equation and solve each problem.
23. Twice a number plus four equals 6. What is the number?
24. Sixteen is seven plus three times a number. Find the number.
25. Find two consecutive integers whose sum is 35.
26. Find three consecutive integers whose sum is 36.
b � 1�3
c � 5�4
4�5
5�2
2�3
3�4
w�7
a�5
d�6
h�3
x�4
n�3
© Glencoe/McGraw-Hill 158 Glencoe Algebra 1
Solve each problem by working backward.
1. Three is added to a number, and then the sum is multiplied by 4. The result is 16. Findthe number.
2. A number is divided by 4, and the quotient is added to 3. The result is 24. What is thenumber?
3. Two is subtracted from a number, and then the difference is multiplied by 5. The resultis 30. Find the number.
4. BIRD WATCHING While Michelle sat observing birds at a bird feeder, one fourth of thebirds flew away when they were startled by a noise. Two birds left the feeder to go toanother stationed a few feet away. Three more birds flew into the branches of a nearbytree. Four birds remained at the feeder. How many birds were at the feeder initially?
Solve each equation. Then check your solution.
5. �12n � 19 � 77 6. 17 � 3f � 14 7. 15t � 4 � 49
8. � 6 � 2 9. � 3 � 15 10. � 6 � �2
11. y � � 12. �32 � f � �17 13. 8 � k � �4
14. � 1 15. � �9 16. � 16
17. � 0.5 � 2.5 18. 2.5g � 0.45 � 0.95 19. 0.4m � 0.7 � 0.22
Write an equation and solve each problem.
20. Seven less than four times a number equals 13. What is the number?
21. Find two consecutive odd integers whose sum is 116.
22. Find two consecutive even integers whose sum is 126.
23. Find three consecutive odd integers whose sum is 117.
24. COIN COLLECTING Jung has a total of 92 coins in his coin collection. This is 8 morethan three times the number of quarters in the collection. How many quarters does Junghave in his collection?
x�7
3k � 7�5
15 � a�3
r � 13�12
3�8
3�5
7�8
1�8
1�2
b�3
d��4
u�5
Practice Solving Multi-Step Equations
NAME ______________________________________________ DATE ____________ PERIOD _____
3-43-4
Reading to Learn MathematicsSolving Multi-Step Equations
NAME ______________________________________________ DATE ____________ PERIOD _____
3-43-4
© Glencoe/McGraw-Hill 159 Glencoe Algebra 1
Less
on
3-4
Pre-Activity How can equations be used to estimate the age of an animal?
Read the introduction to Lesson 3-4 at the top of page 142 in your textbook.
• Write the equation 8 � 12a � 124 in words.
• How many operations are involved in the equation?
Reading the Lesson
1. What does the phrase undo the operations mean to you? Give an example.
2. a. If we undo operations in reverse of the order of operations, what operations do we dofirst?
b. What operations do we do last?
3. Suppose you want to solve � 6.
a. What is the grouping symbol in the equation � 6?
b. What is the first step in solving the equation?
c. What is the next step in solving the equation?
4. Write an equation for the problem below.
Seven times k minus five equals negative forty-seven
Helping You Remember
5. Explain why working backward is a useful strategy for solving equations.
x � 3�5
x � 3�5
© Glencoe/McGraw-Hill 160 Glencoe Algebra 1
Consecutive Integer ProblemsMany types of problems and puzzles involve the idea of consecutiveintegers. Knowing how to represent these integers algebraically canhelp to solve the problem.
Find four consecutive odd integers whose sum is �80.
An odd integer can be written as 2n � 1, where n is any integer.If 2n + 1 is the first odd integer, then add 2 to get the next largest oddinteger, and so on.Now write an equation to solve this problem.(2n � 1) � (2n � 3) � (2n � 5) � (2n � 7) � �80
Write an equation for each problem. Then solve.
1. Complete the solution to the problem in the example.
2. Find three consecutive even integers whose sum is 132.
3. Find two consecutive integers whose sum is 19.
4. Find two consecutive integers whose sum is 100.
5. The lesser of two consecutive even integers is 10 more than one-half the greater. Find the integers.
6. The greater of two consecutive even integers is 6 less than three times the lesser. Find the integers.
7. Find four consecutive integers such that twice the sum of the two greater integers exceeds three times the first by 91.
8. Find a set of four consecutive positive integers such that the greatest integer in the set is twice the least integer in the set.
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
3-43-4
ExampleExample
ExercisesExercises
Study Guide and InterventionSolving Equations with the Variable on Each Side
NAME ______________________________________________ DATE ____________ PERIOD _____
3-53-5
© Glencoe/McGraw-Hill 161 Glencoe Algebra 1
Less
on
3-5
Variables on Each Side To solve an equation with the same variable on each side,first use the Addition or the Subtraction Property of Equality to write an equivalentequation that has the variable on just one side of the equation. Then solve the equation.
Solve 5y � 8 � 3y � 12.
5y � 8 � 3y � 125y � 8 � 3y � 3y � 12 � 3y
2y � 8 � 122y � 8 � 8 � 12 � 8
2y � 20
�
y � 10
The solution is 10.
20�2
2y�2
Solve �11 � 3y � 8y � 1.
�11 � 3y � 8y � 1�11 � 3y � 3y � 8y � 1 � 3y
�11 � 11y � 1�11 � 1 � 11y � 1 � 1
�12 � 11y
�
�1 � y
The solution is �1 .1�11
1�11
11y�11
�12�11
Example 1Example 1 Example 2Example 2
ExercisesExercises
Solve each equation. Then check your solution.
1. 6 � b � 5b � 30 2. 5y � 2y � 3y � 2 3. 5x � 2 � 2x � 10
4. 4n � 8 � 3n � 2 5. 1.2x � 4.3 � 2.1 � x 6. 4.4s � 6.2 � 8.8s � 1.8
7. b � 4 � b � 88 8. k � 5 � k � 1 9. 8 � 5p � 4p � 1
10. 4b � 8 � 10 � 2b 11. 0.2x � 8 � �2 � x 12. 3y � 1.8 � 3y � 1.8
13. �4 � 3x � 7x � 6 14. 8 � 4k � �10 � k 15. 20 � a � 10a � 2
16. n � 8 � n � 2 17. y � 8 � 9 � y 18. �4r � 5 � 5 � 4r
19. �4 � 3x � 6x � 6 20. 18 � 4k � �10 �4k 21. 12 � 2y � 10y � 12
3�5
2�5
1�2
2�3
1�4
3�4
1�8
1�2
© Glencoe/McGraw-Hill 162 Glencoe Algebra 1
Grouping Symbols When solving equations that contain grouping symbols, first usethe Distributive Property to eliminate grouping symbols. Then solve.
Solve 4(2a � 1) � �10(a � 5).
4(2a � 1) � �10(a � 5) Original equation
8a � 4 � �10a � 50 Distributive Property
8a � 4 � 10a � �10a � 50 � 10a Add 10a to each side.
18a � 4 � 50 Simplify.
18a � 4 � 4 � 50 � 4 Add 4 to each side.
18a � 54 Simplify.
� Divide each side by 18.
a � 3 Simplify.
The solution is 3.
Solve each equation. Then check your solution.
1. �3(x � 5) � 3(x � 1) 2. 2(7 � 3t) � �t 3. 3(a � 1) � 5 � 3a � 2
4. 75 � 9g � 5(�4 � 2g) 5. 5(f � 2) � 2(3 � f ) 6. 4(p � 3) � 36
7. 18 � 3(2c � 2) 8. 3(d � 8) � 3d 9. 5(p � 3) � 9 � 3(p � 2) � 6
10. 4(b � 2) � 2(5 � b) 11. 1.2(x � 2) � 2 � x 12. �
13. � 14. 2(4 � 2k) � 10 � k 15. 2(w � 1) � 4 � 4(w � 1)
16. 6(n � 1) � 2(2n � 4) 17. 2[2 � 3( y � 1)] � 22 18. �4(r � 2) � 4(2 � 4r)
19. �3(x � 8) � 24 20. 4(4 � 4k) � �10 �16k 21. 6(2 � 2y) � 5(2y � 2)
2a � 5�3
a � 8�12
�y �8
3 � y�4
54�18
18a�18
Study Guide and Intervention (continued)
Solving Equations with the Variable on Each Side
NAME ______________________________________________ DATE ____________ PERIOD _____
3-53-5
ExampleExample
ExercisesExercises
Skills PracticeSolving Equations with the Variable on Each Side
NAME ______________________________________________ DATE ____________ PERIOD _____
3-53-5
© Glencoe/McGraw-Hill 163 Glencoe Algebra 1
Less
on
3-5
Justify each step.
1. 4k � 3 � 2k � 54k � 3 � 2k � 2k � 5 � 2k a.
2k � 3 � 5 b.
2k � 3 � 3 � 5 � 3 c.
2k � 8 d.
� e.
k � 4 f.
2. 2(8u � 2) � 3(2u � 7)16u � 4 � 6u � 21 a.
16u � 4 � 6u � 6u � 21 � 6u b.
10u � 4 � �21 c.
10u � 4 � 4 � �21 � 4 d.
10u � �25 e.
� f.
u � �2.5 g.
Solve each equation. Then check your solution.
3. 2m � 12 � 3m � 31 4. 2h � 8 � h � 17
5. 7a � 3 � 3 � 2a 6. 4n � 12 � 12 � 4n
7. 4x � 9 � 7x � 12 8. �6y � 3 � 3 � 6y
9. 5 � 3r � 5r � 19 10. �9 � 8k � 7 � 4k
11. 8q � 12 � 4(3 � 2q) 12. 3(5j � 2) � 2(3j � 6)
13. 6(�3v � 1) � 5(�2v � 2) 14. �7(2b � 4) � 5(�2b � 6)
15. 3(8 � 3t) � 5(2 � t) 16. 2(3u � 7) � �4(3 � 2u)
17. 8(2f � 2) � 7(3f � 2) 18. 5(�6 � 3d) � 3(8 � 7d)
19. 6(w � 1) � 3(3w � 5) 20. 7(�3y � 2) � 8(3y � 2)
21. v � 6 � 6 � v 22. � x � x �7�2
7�8
5�8
1�2
2�3
2�3
�25�10
10u�10
8�2
2k�2
© Glencoe/McGraw-Hill 164 Glencoe Algebra 1
Solve each equation. Then check your solution.
1. 5x � 3 � 13 � 3x 2. �4c � 11 � 4c � 21
3. 1 � s � 6 � 6s 4. 14 � 5n � �4n � 17
5. k � 3 � 2 � k 6. (6 � z) � z
7. 3(�2 � 3x) � �9x � 4 8. 4(4 � w) � 3(2w � 2)
9. 9(4b � 1) � 2(9b � 3) 10. 3(6 � 5y) � 2(�5 � 4y)
11. �5x � 10 � 2 � (x � 4) 12. 6 � 2(3j � 2) � 4(1 � j)
13. t � t � 3 � t 14. 1.4f � 1.1 � 8.3 � f
15. x � � x � 16. 2 � z � z � 9
17. (3g � 2) � 18. (c � 1) � (3c � 5)
19. (5 � 2h) � 20. (2m � 16) � (2m � 4)
21. 3(d � 8) � 5 � 9(d � 2) � 1 22. 2(a � 8) � 7 � 5(a � 2) � 3a � 19
23. Two thirds of a number reduced by 11 is equal to 4 more than the number. Find thenumber.
24. Five times the sum of a number and 3 is the same as 3 multiplied by 1 less than twicethe number. What is the number?
25. NUMBER THEORY Tripling the greater of two consecutive even integers gives the sameresult as subtracting 10 from the lesser even integer. What are the integers?
26. GEOMETRY The formula for the perimeter of a rectangle is P � 2� � 2w, where � isthe length and w is the width. A rectangle has a perimeter of 24 inches. Find itsdimensions if its length is 3 inches greater than its width.
1�3
1�9
h�2
1�4
1�6
1�3
g�6
1�2
1�8
3�4
5�6
1�2
1�6
2�3
3�2
5�2
1�2
3�4
1�2
Practice Solving Equations with the Variable on Each Side
NAME ______________________________________________ DATE ____________ PERIOD _____
3-53-5
Reading to Learn MathematicsSolving Equations with the Variable on Each Side
NAME ______________________________________________ DATE ____________ PERIOD _____
3-53-5
© Glencoe/McGraw-Hill 165 Glencoe Algebra 1
Less
on
3-5
Pre-Activity How can an equation be used to determine when two populationsare equal?
Read the introduction to Lesson 3-5 at the top of page 149 in your textbook.
In the equation 12 � 7.6x � 6 � 8x, what do 7.6x and 8x represent?
Reading the Lesson
1. Suppose you want to help a friend solve 6k � 7 � 3k � 8. What would you advise her todo first? Why?
2. When solving 2(3x � 4)� 3(x � 5), why is it helpful first to use the Distributive Propertyto remove the grouping symbols?
3. On a quiz, Jason solved three equations. His teacher said all the work was correct, butshe asked him to write short sentences to tell what the solutions were. In what follows,you see the last equation in his work for each equation. Write sentences to describe thesolutions.
a. x � �4
b. 6m � 6m
c. 12 � 37
4. In Question 3, one of the equations Jason solved was an identity. Which equation was it?Explain how you know.
Helping You Remember
5. An equation with variables is an identity when the equation is always true. In otherwords, the expressions on the left and right sides always have the same value. Look upthe word identity in the dictionary. Write all the definitions that are similar to themathematical definition.
© Glencoe/McGraw-Hill 166 Glencoe Algebra 1
IdentitiesAn equation that is true for every value of the variable is called anidentity. When you try to solve an identity, you end up with astatement that is always true. Here is an example.
Solve 8 � (5 � 6x) � 3(1 � 2x).
8 � (5 � 6x) � 3(1 � 2x)
8 � 5 � (�6x) � 3(1 � 2x)
8 � 5 � 6x � 3 � 6x
3 � 6x � 3 � 6x
State whether each equation is an identity. If it is not, find its solution.
1. 2(2 � 3x) � 3(3 � x) � 4 2. 5(m � 1) � 6 � 3(4 � m) � (2m � 1)
3. (5t � 9) � (3t � 13) � 2(11 � t) 4. 14 � (6 � 3c) � 4c � c
5. 3y � 2( y � 19) � 9y � 3(9 � y) 6. 3(3h � 1) � 4(h � 3)
7. Use the true equation 3x � 2 � 3x � 2 to create an identity of your own.
8. Use the false equation 1 � 2 to create an equation with no solution.
9. Create an equation whose solution is x � 3.
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
3-53-5
ExampleExample
ExercisesExercises
Study Guide and InterventionRatios and Proportions
NAME ______________________________________________ DATE ____________ PERIOD _____
3-63-6
© Glencoe/McGraw-Hill 167 Glencoe Algebra 1
Less
on
3-6
Ratios and Proportions A ratio is a comparison of two numbers by division. The ratio
of x to y can be expressed as x to y, x:y or . Ratios are usually expressed in simplest form.
An equation stating that two ratios are equal is called a proportion. To determine whethertwo ratios form a proportion, express both ratios in simplest form or check cross products.
x�y
Determine whether the
ratios and form a proportion.
� when expressed in simplest form.
� when expressed in simplest form.
The ratios and form a proportion
because they are equal when expressed insimplest form.
12�18
24�36
2�3
12�18
2�3
24�36
12�18
24�36
Use cross products to
determine whether and form aproportion.
� Write the proportion.
10(45) � 18(25) Cross products
450 � 450 Simplify.
The cross products are equal, so � .
Since the ratios are equal, they form aproportion.
25�45
10�18
25�45
10�18
25�45
10�18
Example 1Example 1 Example 2Example 2
ExercisesExercises
Use cross products to determine whether each pair of ratios forms a proportion.
1. , 2. , 3. ,
4. , 5. , 6. ,
7. , 8. , 9. ,
10. 2:3, 20:30 11. 5 to 9, 25 to 45 12. ,
13. 5:5, 30:20 14. 18 to 24, 50 to 75 15. 100:75, 44:33
16. , 17. , 18. , 0.45�0.9
0.1�0.2
6�8
1.5�2
1�20
0.05�1
9�8
72�64
20�30
14�21
9�12
15�20
5�100
0.1�2
12�27
4�9
3�16
12�32
15�20
25�36
25�49
10�20
10�15
5�8
16�32
1�2
© Glencoe/McGraw-Hill 168 Glencoe Algebra 1
Solve Proportions If a proportion involves a variable, you can use cross products to solve
the proportion. In the proportion � , x and 13 are called extremes and 5 and 10 are
called means. In a proportion, the product of the extremes is equal to the product of the means.
Means-Extremes Property of Proportions For any numbers a, b, c, and d, if � , then ad � bc.
Solve � .
� Original proportion
13(x) � 5(10) Cross products
13x � 50 Simplify.
� Divide each side by 13.
x � 3 Simplify.
The solution is 3 .
Solve each proportion.
1. � 2. � 3. �
4. � 5. � 6. �
7. � 8. � 9. �
10. � 11. � 12. �
13. � 14. � 15. �
Use a proportion to solve each problem.
16. MODELS To make a model of the Guadeloupe River bed, Hermie used 1 inch of clay for5 miles of the river’s actual length. His model river was 50 inches long. How long is theGuadeloupe River?
17. EDUCATION Josh finished 24 math problems in one hour. At that rate, how manyhours will it take him to complete 72 problems?
12�9
2 � w�6
24�k
12�k
15�3
a � 8�12
�y�8
3 � y�4
12�x
1.5�x
4�12
4�b � 2
p�24
5�8
18�3
3�d
18�54
9�y � 1
3�63
x�21
8�x
4�6
3�4
x � 1�4
0.5�x
0.1�2
5�3
1�t
2�8
�3�x
11�13
11�13
50�13
13x�13
10�13
x�5
10�13
x�5
c�d
a�b
10�13
x�5
Study Guide and Intervention (continued)
Ratios and Proportions
NAME ______________________________________________ DATE ____________ PERIOD _____
3-63-6
ExampleExample
ExercisesExercises
Skills PracticeRatios and Proportions
NAME ______________________________________________ DATE ____________ PERIOD _____
3-63-6
© Glencoe/McGraw-Hill 169 Glencoe Algebra 1
Less
on
3-6
Use cross products to determine whether each pair of ratios forms a proportion.Write yes or no.
1. , 2. ,
3. , 4. ,
5. , 6. ,
7. , 8. ,
Solve each proportion. If necessary, round to the nearest hundredth.
9. � 10. �
11. � 12. �
13. � 14. �
15. � 16. �
17. � 18. �
19. � 20. �
21. � 22. �
23. � 24. �
25. BOATING Hue’s boat used 5 gallons of gasoline in 4 hours. At this rate, how manygallons of gasoline will the boat use in 10 hours?
11�30
22�x
s�84
4�21
20�g
5�12
27�39
9�c
n�60
11�15
30�m
10�14
1�9
7�b
6�f
42�56
y�69
6�23
36�s
12�7
35�21
5�e
3�5
6�z
1�6
3�a
15�10
9�g
3�9
5�b
2�14
1�a
50�85
12�17
21�98
3�14
26�38
13�19
42�90
7�16
72�81
8�9
24�28
6�7
7�11
5�9
20�25
4�5
© Glencoe/McGraw-Hill 170 Glencoe Algebra 1
Use cross products to determine whether each pair of ratios forms a proportion.Write yes or no.
1. , 2. , 3. ,
4. , 5. , 6. ,
7. , 8. , 9. ,
Solve each proportion. If necessary, round to the nearest hundredth.
10. � 11. � 12. �
13. � 14. � 15. �
16. � 17. � 18. �
19. � 20. � 21. �
22. � 23. � 24. �
25. � 26. � 27. �
28. � 29. � 30. �
31. � 32. � 33. �
34. PAINTING Ysidra paints a room that has 400 square feet of wall space in 2 hours. At
this rate, how long will it take her to paint a room that has 720 square feet of wallspace?
35. VACATION PLANS Walker is planning a summer vacation. He wants to visit PetrifiedNational Forest and Meteor Crater, Arizona, the 50,000-year-old impact site of a largemeteor. On a map with a scale where 2 inches equals 75 miles, the two areas are about
1 inches apart. What is the distance between Petrified National Forest and Meteor
Crater?
1�2
1�2
x � 2�6
3�7
5�7
r � 2�7
x � 1�4
5�12
2�4
m � 1�8
2�y � 6
3�12
14�6
7�a � 4
3�0.51
6�n
12�b
3�0.72
7�1.61
v�0.23
5�8
m�6
5�6
3�q
8�c
7�9
2�a
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6�4
g�16
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6�61
z�17
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35�x
5�11
10�60
2�y
48�9
y�3
27�162
3�u
4�w
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k�7
40�56
34�23
v�46
30�54
5�a
3.9�0.9
7.6�1.8
2.9�2.4
1.7�1.2
7.14�10.92
3.4�5.2
1�6
1.5�9
72�81
8�9
108�99
12�11
36�48
18�24
15�66
3�11
52�48
7�6
Practice Ratios and Proportions
NAME ______________________________________________ DATE ____________ PERIOD _____
3-63-6
Reading to Learn MathematicsRatios and Proportions
NAME ______________________________________________ DATE ____________ PERIOD _____
3-63-6
© Glencoe/McGraw-Hill 171 Glencoe Algebra 1
Less
on
3-6
Pre-Activity How are ratios used in recipes?
Read the introduction to Lesson 3-6 at the top of page 155 in your textbook.
• How many servings of honey frozen yogurt are made by this recipe?
• How many recipes would be needed to make enough honey frozen yogurtfor all the students in your class?
Reading the Lesson
1. Complete the following sentence.
A ratio is a comparison of two numbers by .
2. Describe two ways to decide whether the sentence � is a proportion.
3. For each proportion, tell what the extremes are and what the means are.
a. � Extremes: Means:
b. � Extremes: Means:
4. A jet flying at a steady speed traveled 825 miles in 2 hours. If you solved the proportion
� , what would the answer tell you about the jet?
Helping You Remember
5. Write how you would explain solving a proportion to a friend who missed Lesson 3-6.
x�1.5
825�2
12�16
6�8
6�15
14�35
8�20
2�5
© Glencoe/McGraw-Hill 172 Glencoe Algebra 1
Angles of a TriangleIn geometry, many statements about physical space are proven to betrue. Such statements are called theorems. Here are two examples ofgeometric theorems.
a. The sum of the measures of the angles of a triangle is 180°.b. If two sides of a triangle have equal measure, then the two angles
opposite those sides also have equal measure.
For each of the triangles, write an equation and then solve for x. (A tick mark ontwo or more sides of a triangle indicates that the sides have equal measure.)
1. 2.
3. 4.
5. 6.
7. 8.
9. 10.
11. Two angles of a triangle have the same 12. The measure of one angle of a triangle is measure. The sum of the measures of twice the measure of a second angle. The these angles is one-half the measure of measure of the third angle is 12 less than the third angle. Find the measures of the sum of the other two. Find the the angles of the triangle. measures of the angles of the triangle.
x2x
30°
x
40°
x
x � 15°
3x
x � 30°
90°
4x
5x
5x
2x x
x � 30°
x5x � 10°
90° x
90° 45°
x70°
50°x
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
3-63-6
Study Guide and InterventionPercent of Change
NAME ______________________________________________ DATE ____________ PERIOD _____
3-73-7
© Glencoe/McGraw-Hill 173 Glencoe Algebra 1
Less
on
3-7
Percent of Change When an increase or decrease in an amount is expressed as apercent, the percent is called the percent of change. If the new number is greater than theoriginal number, the percent of change is a percent of increase. If the new number is lessthan the original number, the percent of change is the percent of decrease.
Find the percent of increase.original: 48new: 60
First, subtract to find the amount ofincrease. The amount of increase is 60 � 48 � 12.Then find the percent of increase by usingthe original number, 48, as the base.
� Percent proportion
12(100) � 48(r) Cross products
1200 � 48r Simplify.
� Divide each side by 48.
25 � r Simplify.
The percent of increase is 25%.
48r�48
1200�48
r�100
12�48
Find the percent of decrease.original: 30new: 22
First, subtract to find the amount ofdecrease. The amount of decrease is 30 � 22 � 8.Then find the percent of decrease by usingthe original number, 30, as the base.
� Percent proportion
8(100) � 30(r) Cross products
800 � 30r Simplify.
� Divide each side by 30.
26 � r Simplify.
The percent of decrease is 26 %, or about27%.
2�3
2�3
30r�30
800�30
r�100
8�30
Example 1Example 1 Example 2Example 2
ExercisesExercises
State whether each percent of change is a percent of increase or a percent ofdecrease. Then find each percent of change. Round to the nearest whole percent.
1. original: 50 2. original: 90 3. original: 45new: 80 new: 100 new: 20
4. original: 77.5 5. original: 140 6. original: 135new: 62 new: 150 new: 90
7. original: 120 8. original: 90 9. original: 27.5new: 180 new: 270 new: 25
10. original: 84 11. original: 12.5 12. original: 250new: 98 new: 10 new: 500
© Glencoe/McGraw-Hill 174 Glencoe Algebra 1
Solve Problems Discounted prices and prices including tax are applications of percentof change. Discount is the amount by which the regular price of an item is reduced. Thus,the discounted price is an example of percent of decrease. Sales tax is amount that is addedto the cost of an item, so the price including tax is an example of percent of increase.
A coat is on sale for 25% off the original price. If the original priceof the coat is $75, what is the discounted price?
The discount is 25% of the original price.
25% of $75 � 0.25 � 75 25% � 0.25
� 18.75 Use a calculator.
Subtract $18.75 from the original price.$75 � $18.75 � $56.25
The discounted price of the coat is $56.25.
Find the final price of each item. When a discount and a sales tax are listed,compute the discount price before computing the tax.
1. Compact disc: $16 2. Two concert tickets: $28 3. Airline ticket: $248.00Discount: 15% Student discount: 28% Superair discount: 33%
4. Shirt: $24.00 5. CD player: $142.00 6. Celebrity calendar: $10.95Sales tax: 4% Sales tax: 5.5% Sales tax: 7.5%
7. Class ring: $89.00 8. Software: $44.00 9. Video recorder: $110.95Group discount: 17% Discount: 21% Discount: 20%Sales tax: 5% Sales tax: 6% Sales tax: 5%
10. VIDEOS The original selling price of a new sports video was $65.00. Due to the demandthe price was increased to $87.75. What was the percent of increase over the originalprice?
11. SCHOOL A high school paper increased its sales by 75% when it ran an issue featuringa contest to win a class party. Before the contest issue, 10% of the school’s 800 studentsbought the paper. How many students bought the contest issue?
12. BASEBALL Baseball tickets cost $15 for general admission or $20 for box seats. Thesales tax on each ticket is 8%, and the municipal tax on each ticket is an additional 10%of the base price. What is the final cost of each type of ticket?
Study Guide and Intervention (continued)
Percent of Change
NAME ______________________________________________ DATE ____________ PERIOD _____
3-73-7
ExampleExample
ExercisesExercises
Skills PracticePercent of Change
NAME ______________________________________________ DATE ____________ PERIOD _____
3-73-7
© Glencoe/McGraw-Hill 175 Glencoe Algebra 1
Less
on
3-7
State whether each percent of change is a percent of increase or a percent ofdecrease. Then find each percent of change. Round to the nearest whole percent.
1. original: 25 2. original: 50new: 10 new: 75
3. original: 55 4. original: 25new: 50 new: 28
5. original: 50 6. original: 90new: 30 new: 95
7. original: 48 8. original: 60new: 60 new: 45
Find the total price of each item.
9. dress: $69.00 10. binder: $14.50tax: 5% tax: 7%
11. hardcover book: $28.95 12. groceries: $47.52tax: 6% tax: 3%
13. filler paper: $6.00 14. shoes: $65.00tax: 6.5% tax: 4%
15. basketball: $17.00 16. concert tickets: $48.00tax: 6% tax: 7.5%
Find the discounted price of each item.
17. backpack: $56.25 18. monitor: $150.00discount: 20% discount: 50%
19. CD: $15.99 20. shirt: $25.50discount: 20% discount: 40%
21. sleeping bag: $125 22. coffee maker: $102.00discount: 25% discount: 45%
© Glencoe/McGraw-Hill 176 Glencoe Algebra 1
State whether each percent of change is a percent of increase or a percent ofdecrease. Then find each percent of change. Round to the nearest whole percent.
1. original: 18 2. original: 140 3. original: 200new: 10 new: 160 new: 320
4. original: 10 5. original: 76 6. original: 128new: 25 new: 60 new: 120
7. original: 15 8. original: 98.6 9. original: 58.8new: 35.5 new: 64 new: 65.7
Find the total price of each item.
10. concrete blocks: $95.00 11. crib: $240.00 12. jacket: $125.00tax: 6% tax: 6.5% tax: 5.5%
13. class ring: $325.00 14. blanket: $24.99 15. kite: $18.90tax: 6% tax: 7% tax: 5%
Find the discounted price of each item.
16. dry cleaning: $25.00 17. computer game: $49.99 18. luggage: $185.00discount: 15% discount: 25% discount: 30%
19. stationery: $12.95 20. prescription glasses: $149 21. pair of shorts: $24.99 discount: 10% discount: 20% discount: 45%
Find the final price of each item.
22. television: $375.00 23. DVD player: $269.00 24. printer: $255.00discount: 25% discount: 20% discount: 30%tax: 6% tax: 7% tax: 5.5%
25. INVESTMENTS The price per share of an internet-related stock decreased from $90 pershare to $36 per share early in 2001. By what percent did the price of the stockdecrease?
26. HEATING COSTS Customers of a utility company received notices in their monthly billsthat heating costs for the average customer had increased 125% over last year becauseof an unusually severe winter. In January of last year, the Garcia’s paid $120 for heating.What should they expect to pay this January if their bill increased by 125%?
Practice Percent of Change
NAME ______________________________________________ DATE ____________ PERIOD _____
3-73-7
Reading to Learn MathematicsPercent of Change
NAME ______________________________________________ DATE ____________ PERIOD _____
3-73-7
© Glencoe/McGraw-Hill 177 Glencoe Algebra 1
Less
on
3-7
Pre-Activity How can percents describe growth over time?
Read the introduction to Lesson 3-7 at the top of page 160 in your textbook.
• How many area codes were in use in 1947?
• How many more area codes were in use in 1999?
Reading the Lesson
1. If you use (original amount) — (new amount) to find the change for a percent of change problem, then the problem involves a percent of (increase/decrease).
2. If you use (new amount) — (original amount) to find the change for a percent of change problem, then the problem involves a percent of (increase/decrease).
Complete the chart.
Original New Percent Increase or Amount Amount
Percent ProportionPercent Decrease?
3. 10 13
4. 10 7
5. 50 42
6. 50 58
7. When you find a discount price, do you add to or subtract from the original price?
Helping You Remember
8. If you remember only two things about the ratio used for finding percent of change, whatshould they be?
© Glencoe/McGraw-Hill 178 Glencoe Algebra 1
Using PercentUse what you have learned about percent to solve each problem.
A TV movie had a “rating” of 15 and a 25 “share.” The rating is the percentageof the nation’s total TV households that were tuned in to this show. The shareis the percentage of homes with TVs turned on that were tuned to the movie.How many TV households had their TVs turned off at this time?To find out, let T � the number of TV households
and x � the number of TV households with the TV off.Then T � x � the number of TV households with the TV on.
Since 0.15T and 0.25(T � x) both represent the number of households tunedto the movie,
0.15T � 0.25(T � x)0.15T � 0.25T � 0.25x.
Solve for x. 0.25x � 0.10T
x � � 0.40T
Forty percent of the TV households had their TVs off when the movie was aired.
Answer each question.
1. During that same week, a sports broadcast had a rating of 22.1 and a 43 share.Show that the percent of TV households with their TVs off was about 48.6%.0.221T � 0.43T � 0.43x
x �
� 0.486T2. Find the percent of TV households with their TVs turned off during a show
with a rating of 18.9 and a 29 share. 34.8%
3. Show that if T is the number of TV households, r is the rating, and s is the
share, then the number of TV households with the TV off is .Solve rT � s(T � x) for x.
4. If the fraction of TV households with no TV on is then show that the
fraction of TV households with TVs on is .
5. Find the percent of TV households with TVs on during the most watched serial program in history: the last episode of M*A*S*H, which had a 60.3 rating and a 77 share. � 78.3%
6. A local station now has a 2 share. Each share is worth $50,000 in advertising revenue per month. The station is thinking of going commercial free for the three months of summer to gain more listeners. What would its new share have to be for the last 4 months of the year to make more money for the year than it would have made had it not gone commercial free? greater than 3.5
60.3�77
r�s
s – r�s
(s � r)T�s
0.221T � 0.43T��
�0.43
0.10T�0.25
Enrichment
NAME ______________________________________________ DATE______________ PERIOD _____
3-73-7
1 � � r�s
s � r�
s
Study Guide and InterventionSolving Equations and Formulas
NAME ______________________________________________ DATE ____________ PERIOD _____
3-83-8
© Glencoe/McGraw-Hill 179 Glencoe Algebra 1
Less
on
3-8
Solve for Variables Sometimes you may want to solve an equation such as V � �wh forone of its variables. For example, if you know the values of V, w, and h, then the equation
� � is more useful for finding the value of �. If an equation that contains more than one
variable is to be solved for a specific variable, use the properties of equality to isolate thespecified variable on one side of the equation.
V�wh
Solve 2x � 4y � 8 for y.
2x � 4y � 82x � 4y � 2x � 8 � 2x
�4y � 8 � 2x
�
y � or
The value of y is .2x � 8�4
2x � 8�4
8 � 2x�
�4
8 � 2x�
�4�4y��4
Solve 3m � n � km � 8 for m.
3m � n � km � 83m � n � km � km � 8 � km3m � n � km � � 8
3m � n � km � n � � 8 � n3m � km � �8 � nm(3 � k) � �8 � n
�
m � , or
The value of m is . Since division by 0 is
undefined, 3 � k � 0, or k � 3.
n � 8�3 � k
n � 8�3 � k
�8 � n�3 � k
�8 � n�3 � k
m(3 � k)��3 � k
Example 1Example 1 Example 2Example 2
ExercisesExercises
Solve each equation or formula for the variable specified.
1. ax � b � c for x 2. 15x � 1 � y for x 3. (x � f) � 2 � j for x
4. xy � z � 9 for y 5. x(4 � k) � p for k 6. 7x � 3y � m for y
7. 4(c � 3) � t for c 8. 2x � b � c for x 9. x(1 � y) � z for x
10. 16z � 4x � y for x 11. d � rt for r 12. A � for h
13. C� (F � 32) for F 14. P � 2� � 2w for w 15. A � �w for �5�9
h(a � b)��2
© Glencoe/McGraw-Hill 180 Glencoe Algebra 1
Use Formulas Many real-world problems require the use of formulas. Sometimes solvinga formula for a specified variable will help solve the problem.
The formula C � �d represents the circumference of a circle, or thedistance around the circle, where d is the diameter. If an airplane could fly aroundEarth at the equator without stopping, it would have traveled about 24,900 miles.Find the diameter of Earth.
C � �d Given formula
d � Solve for d.
d � Use � � 3.14.
d � 7930 Simplify.
The diameter of Earth is about 7930 miles.
1. GEOMETRY The volume of a cylinder V is given by the formula V � �r2h, where r isthe radius and h is the height.
a. Solve the formula for h.
b. Find the height of a cylinder with volume 2500� feet and radius 10 feet.
2. WATER PRESSURE The water pressure on a submerged object is given by P � 64d,where P is the pressure in pounds per square foot, and d is the depth of the object in feet.
a. Solve the formula for d.
b. Find the depth of a submerged object if the pressure is 672 pounds per square foot.
3. GRAPHS The equation of a line containing the points (a, 0) and (0, b) is given by the
formula � � 1.
a. Solve the equation for y.
b. Suppose the line contains the points (4, 0), and (0, �2). If x � 3, find y.
4. GEOMETRY The surface area of a rectangular solid is given by the formula S � 2�w � 2�h � 2wh, where � � length, w � width, and h � height.
a. Solve the formula for h.
b. The surface area of a rectangular solid with length 6 centimeters and width 3 centimeters is 72 square centimeters. Find the height.
y�b
x�a
24,900�3.14
C��
Study Guide and Intervention (continued)
Solving Equations and Formulas
NAME ______________________________________________ DATE ____________ PERIOD _____
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ExampleExample
ExercisesExercises
Skills PracticeSolving Equations and Formulas
NAME ______________________________________________ DATE ____________ PERIOD _____
3-83-8
© Glencoe/McGraw-Hill 181 Glencoe Algebra 1
Less
on
3-8
Solve each equation or formula for the variable specified.
1. 7t � x, for t 2. e � wp, for p
3. q � r � r, for r 4. 4m � n � m, for m
5. 7a � b � 15a, for a 6. �5c � d � 2c, for c
7. x � 2y � 1, for y 8. m � 3n � 1, for n
9. 7f � g � 5, for f 10. ax � c � b, for x
11. rt � 2n � y, for t 12. bc � 3g � 2k, for c
13. kn � 4f � 9v, for n 14. 8c � 6j � 5p, for c
15. � d, for x 16. � d, for c
17. � q, for p 18. � a, for b
Write an equation and solve for the variable specified.
19. Five more than a number g is six less than twice a number h. Solve for g.
20. One fourth of a number q is three more than three times a number w. Solve for q.
21. Eight less than a number s is three more than four times a number t. Solve for s.
b � 4z�7
p � 9�5
x � c�2
x � c�2
© Glencoe/McGraw-Hill 182 Glencoe Algebra 1
Solve each equation or formula for the variable specified.
1. d � rt, for r 2. 6w � y � 2z, for w
3. mx � 4y � 3c, for x 4. 9s � 5g � �4u, for s
5. ab � 3c � 2d, for b 6. 2p � kx � q, for x
7. m � a � a � c, for m 8. h � g � d, for h
9. y � v � s, for y 10. a � q � k, for a
11. � h, for x 12. � c, for b
13. 2w � y � 7w � 2, for w 14. 3� � y � 5 � 5�, for �
Write an equation and solve for the variable specified.
15. Three times a number s plus 4 times a number y is 1 more than 6 times the number s.Solve for s.
16. Five times a number k minus 9 is two thirds of a number j. Solve for j.
ELECTRICITY For Exercises 17 and 18, use the following information.
The formula for Ohm’s Law is E � IR, where E represents voltage measured in volts,I represents current measured in amperes, and R represents resistance measured in ohms.
17. Solve the formula for R.
18. Suppose a current of 0.25 ampere flows through a resistor connected to a 12-volt battery.What is the resistance in the circuit?
MOTION For Exercises 19 and 20, use the following information.
In uniform circular motion, the speed v of a point on the edge of a spinning disk is v � r,
where r is the radius of the disk and T is the time it takes the point to travel once aroundthe circle.
19. Solve the formula for r.
20. Suppose a merry-go-round is spinning once every 3 seconds. If a point on the outsideedge has a speed of 12.56 feet per second, what is the radius of the merry-go-round? (Use 3.14 for �.)
2��T
3b � 4�2
rx � 9�5
3�4
2�3
2�5
2�3
Practice Solving Equations and Formulas
NAME ______________________________________________ DATE ____________ PERIOD _____
3-83-8
Reading to Learn MathematicsSolving Equations and Formulas
NAME ______________________________________________ DATE______________ PERIOD _____
3-83-8
© Glencoe/McGraw-Hill 183 Glencoe Algebra 1
Less
on
3-8
Pre-Activity How are equations used to design roller coasters?
Read the introduction to Lesson 3-8 at the top of page 166 in your textbook.
The equation g(195 � h) � v2 contains several variables. What
number values do you know for these variables in this situation?
32 for g and 49 for v
Reading the Lesson
1. Suppose you have an equation with several variables. You want to solve for a particularvariable. How does the procedure compare with that for solving an equation with justone variable? How does the solution compare with the solution for an equation with onevariable?
Sample answer: The procedure is basically the same. You use propertiesof operations and equality to isolate the variable in which you areinterested. The solution will probably contain variables instead of just anumber.
2. Describe what dimensional analysis involves.
Sample answer: You use the units along with number values as you docalculations. You treat the units pretty much the same way you wouldvariables. For example, you can divide them and use exponents with them.
3. What do you have to be careful about when you use variables in denominators offractions?
You have to be sure that you do not use values that would make thedenominator 0.
Helping You Remember
4. When you give the dimensions of a rectangle, you have to tell how many units long it isand how many units wide it is. How can this help you remember what dimensionalanalysis involves.
Sample answer: Keep the words dimension and unit in mind. Indimensional analysis, you include units for dimensions in calculations.
1�2
© Glencoe/McGraw-Hill 184 Glencoe Algebra 1
Dr. Bernardo Houssay Even though researchers have been studying the disease diabetesmellitus for hundreds of years, scientists have only recently discoveredthe cause of the disease and developed methods for reducing itsseverity. Dr. Bernardo Houssay, an Argentine physiologist, was one ofthe pioneers of this more modern research. He studied the relationshipbetween diabetes and the pituitary gland, and in 1947 became the firstLatin American to win the Nobel Prize in Medicine and Physiology.
Though there is no cure for diabetes, specific diets and exercise can helppeople control the disease. The American Diabetes Association (ADA)has helped establish flexible dietary guidelines for consumers to follow.These guidelines include some of the following general nutrition rules.
• Fat intake should be equal to or less than 30% of daily calories.
• Saturated fat intake should be equal to or less than 10% of dailycalories.
• Protein should be limited to 10% to 20% of daily calories. Personsshowing the initial signs of diabetes-induced kidney disease shouldlimit protein to 10% of daily calories.
• Cholesterol intake should be 300 milligrams or less daily.
Refer to the information above for Exercises 1–4.
1. Robert consumed 2100 calories on Tuesday. His fat intake totaled70 grams, and of that 70 grams, 14 were saturated.
a. What percentage of his calorie consumption was fat, and whatpercentage of that fat was saturated? (To find the percentage ofcalories from fat, multiply the number of fat grams by 9 beforedividing by the number of calories.) 30%; 20%
b. Did Robert stay within the recommended allowance of fats? yes
2. Anna's cholesterol intake was 330 milligrams on Sunday. By whatpercentage does she need to reduce her cholesterol consumption toremain within the guidelines? 10%
3. What number of fat grams is 30% of 240 calories? 8
4. Sharon follows a diet that provides about 50 grams of protein eachday. Sharon's doctor has just told her to reduce her daily proteinintake by 30%. About how much protein will be in her reducedprotein diet? 35 grams
Enrichment
NAME ______________________________________________ DATE______________ PERIOD _____
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Study Guide and InterventionWeighted Averages
NAME ______________________________________________ DATE ____________ PERIOD _____
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© Glencoe/McGraw-Hill 185 Glencoe Algebra 1
Less
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3-9
Mixture Problems
Weighted AverageThe weighted average M of a set of data is the sum of the product of each number in the set and its weight divided by the sum of all the weights.
Mixture Problems are problems where two or more parts are combined into a whole. Theyinvolve weighted averages. In a mixture problem, the weight is usually a price or a percentof something.
Delectable Cookie Company sells chocolate chip cookies for $6.95per pound and white chocolate cookies for $5.95 per pound. How many pounds ofchocolate chip cookies should be mixed with 4 pounds of white chocolate cookiesto obtain a mixture that sells for $6.75 per pound.
Let w � the number of pounds of chocolate chip cookies
Number of Pounds Price per Pound Total Price
Chocolate Chip w 6.95 6.95w
White Chocolate 4 5.95 4(5.95)
Mixture w � 4 6.75 6.75(w � 4)
Equation: 6.95w � 4(5.95) � 6.75(w � 4)Solve the equation.
6.95w � 4(5.95) � 6.75(w � 4) Original equation
6.95w � 23.80 � 6.75w � 27 Simplify.
6.95w � 23.80 � 6.75w � 6.75w � 27 � 6.75w Subtract 6.75w from each side.
0.2w � 23.80 � 27 Simplify.
0.2w � 23.80 � 23.80 � 27 � 23.80 Subtract 23.80 from each side.
0.2w � 3.2 Simplify.
w � 16 Simplify.
16 pounds of chocolate chip cookies should be mixed with 4 pounds of white chocolate cookies.
1. SOLUTIONS How many grams of sugar must be added to 60 grams of a solution that is32% sugar to obtain a solution that is 50% sugar?
2. NUTS The Quik Mart has two kinds of nuts. Pecans sell for $1.55 per pound andwalnuts sell for $1.95 per pound. How many pounds of walnuts must be added to 15pounds of pecans to make a mixture that sells for $1.75 per pound?
3. INVESTMENTS Alice Gleason invested a portion of $32,000 at 9% interest and thebalance at 11% interest. How much did she invest at each rate if her total income fromboth investments was $3,200.
4. MILK Whole milk is 4% butterfat. How much skim milk with 0% butterfat should beadded to 32 ounces of whole milk to obtain a mixture that is 2.5% butterfat?
ExampleExample
ExercisesExercises
© Glencoe/McGraw-Hill 186 Glencoe Algebra 1
Uniform Motion Problems Motion problems are another application of weightedaverages. Uniform motion problems are problems where an object moves at a certainspeed, or rate. Use the formula d � rt to solve these problems, where d is the distance, r isthe rate, and t is the time.
Bill Gutierrez drove at a speed of 65 miles per hour on anexpressway for 2 hours. He then drove for 1.5 hours at a speed of 45 miles perhour on a state highway. What was his average speed?
M � Definition of weighted average
� 56.4 Simplify.
Bill drove at an average speed of about 56.4 miles per hour.
1. TRAVEL Mr. Anders and Ms. Rich each drove home from a business meeting. Mr. Anderstraveled east at 100 kilometers per hour and Ms. Rich traveled west at 80 kilometers perhours. In how many hours were they 100 kilometers apart.
2. AIRPLANES An airplane flies 750 miles due west in 1 hours and 750 miles due south
in 2 hours. What is the average speed of the airplane?
3. TRACK Sprinter A runs 100 meters in 15 seconds, while sprinter B starts 1.5 secondslater and runs 100 meters in 14 seconds. If each of them runs at a constant rate, who isfurther in 10 seconds after the start of the race? Explain.
4. TRAINS An express train travels 90 kilometers per hour from Smallville to Megatown.A local train takes 2.5 hours longer to travel the same distance at 50 kilometers perhour. How far apart are Smallville and Megatown?
5. CYCLING Two cyclists begin traveling in the same direction on the same bike path. Onetravels at 15 miles per hour, and the other travels at 12 miles per hour. When will thecyclists be 10 miles apart?
6. TRAINS Two trains leave Chicago, one traveling east at 30 miles per hour and onetraveling west at 40 miles per hour. When will the trains be 210 miles apart?
1�2
65 2 � 45 1.5��2 � 1.5
Study Guide and Intervention (continued)
Weighted Averages
NAME ______________________________________________ DATE ____________ PERIOD _____
3-93-9
ExampleExample
ExercisesExercises
Skills PracticeWeighted Averages
NAME ______________________________________________ DATE ____________ PERIOD _____
3-93-9
© Glencoe/McGraw-Hill 187 Glencoe Algebra 1
Less
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SEASONING For Exercises 1–4, use the following information.
A health food store sells seasoning blends in bulk. One blend contains 20% basil. Sheilawants to add pure basil to some 20% blend to make 16 ounces of her own 30% blend. Let brepresent the amount of basil Sheila should add to the 20% blend.
1. Complete the table representing the problem.
Ounces Amount of Basil
20% Basil Blend
100% Basil
30% Basil Blend
2. Write an equation to represent the problem.
3. How many ounces of basil should Sheila use to make the 30% blend?
4. How many ounces of the 20% blend should she use?
HIKING For Exercises 5–7, use the following information.
At 7:00 A.M., two groups of hikers begin 21 miles apart and head toward each other. The firstgroup, hiking at an average rate of 1.5 miles per hour, carries tents, sleeping bags, andcooking equipment. The second group, hiking at an average rate of 2 miles per hour, carriesfood and water. Let t represent the hiking time.
5. Copy and complete the table representing the problem.
r t d � rt
First group of hikers
Second group of hikers
6. Write an equation using t that describes the distances traveled.
7. How long will it be until the two groups of hikers meet?
SALES For Exercises 8 and 9, use the following information.
Sergio sells a mixture of Virginia peanuts and Spanish peanuts for $3.40 per pound. Tomake the mixture, he uses Virginia peanuts that cost $3.50 per pound and Spanish peanutsthat cost $3.00 per pound. He mixes 10 pounds at a time.
8. How many pounds of Virginia peanuts does Sergio use?
9. How many pounds of Spanish peanuts does Sergio use?
© Glencoe/McGraw-Hill 188 Glencoe Algebra 1
GRASS SEED For Exercises 1–4, use the following information.
A nursery sells Kentucky Blue Grass seed for $5.75 per pound and Tall Fescue seed for$4.50 per pound. The nursery sells a mixture of the two kinds of seed for $5.25 per pound.Let k represent the amount of Kentucky Blue Grass seed the nursery uses in 5 pounds ofthe mixture.
1. Complete the table representing the problem.
Number of Pounds Price per Pound Cost
Kentucky Blue Grass
Tall Fescue
Mixture
2. Write an equation to represent the problem.
3. How much Kentucky Blue Grass does the nursery use in 5 pounds of the mixture?
4. How much Tall Fescue does the nursery use in 5 pounds of the mixture?
TRAVEL For Exercises 5–7, use the following information.
Two commuter trains carry passengers between two cities, one traveling east, and the otherwest, on different tracks. Their respective stations are 150 miles apart. Both trains leave atthe same time, one traveling at an average speed of 55 miles per hour and the other at anaverage speed of 65 miles per hour. Let t represent the time until the trains pass each other.
5. Copy and complete the table representing the problem.
r t d � rt
First Train
Second Train
6. Write an equation using t that describes the distances traveled.
7. How long after departing will the trains pass each other?
8. TRAVEL Two trains leave Raleigh at the same time, one traveling north, and the othersouth. The first train travels at 50 miles per hour and the second at 60 miles per hour.In how many hours will the trains be 275 miles apart?
9. JUICE A pineapple drink contains 15% pineapple juice. How much pure pineapple juiceshould be added to 8 quarts of the drink to obtain a mixture containing 50% pineapplejuice?
Practice Weighted Averages
NAME ______________________________________________ DATE ____________ PERIOD _____
3-93-9
Reading to Learn MathematicsWeighted Averages
NAME ______________________________________________ DATE ____________ PERIOD _____
3-93-9
© Glencoe/McGraw-Hill 189 Glencoe Algebra 1
Less
on
3-9
Pre-Activity How are scores calculated in a figure skating competition?
Read the introduction to Lesson 3-9 at the top of page 171 in your textbook.
Why is the sum of Ilia Kulik’s scores divided by 3?
Reading the Lesson
1. Read the definition of weighted average on page 171 of your textbook. What is meant bythe weight of a number in a set of data?
2. Linda’s quiz scores in science are 90, 85, 85, 75, 85, and 90. What is the weight of thescore 85?
3. Suppose Clint drives at 50 miles per hour for 2 hours. Then he drives at 60 miles perhour for 3 hours.
a. Write his speed for each hour of the trip.
Speed
Hour 1 2 3 4 5
b. What is the weight of each of the two speeds?
Helping You Remember
4. Making a table can be helpful in solving mixture problems. In your own words, explainhow you use a table to solve mixture problems.
© Glencoe/McGraw-Hill 190 Glencoe Algebra 1
Diophantine EquationsThe first great algebraist, Diophantus of Alexandria (about A.D. 300),devoted much of his work to the solving of indeterminate equations.An indeterminate equation has more than one variable and anunlimited number of solutions. An example is x � 2y � 4.
When the coefficients of an indeterminate equation are integers andyou are asked to find solutions that must be integers, the equation iscalled diophantine. Such equations can be quite difficult to solve,often involving trial and error—and some luck!
Solve each diophantine equation by finding at least one pair of positive integers that makes the equation true. Some hints are given to help you.
1. 2x � 5y � 32
a. First solve the equation for x.
b. Why must y be an even number?
c. Find at least one solution.
2. 5x � 2y � 42
a. First solve the equation for x.
b. Rewrite your answer in the form x � 8 � some expression.
c. Why must (2 � 2y) be a multiple of 5?
d. Find at least one solution.
3. 2x � 7y � 29 4. 7x � 5y � 118
5. 8x � 13y � 100 6. 3x � 4y � 22
7. 5x � 14y � 11 8. 7x � 3y � 40
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
3-93-9
Chapter 3 Test, Form 1
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 191 Glencoe Algebra 1
Ass
essm
ent
Write the letter for the correct answer in the blank at the right of each question.
1. Solve x � 19 � 5.A. 24 B. 14 C. �24 D. �14 1.
2. Solve y � 18 � �3.A. �21 B. 21 C. �15 D. 15 2.
3. Solve 5n � 35.A. 30 B. 7 C. 40 D. 165 3.
4. Solve �3c
� � 6.
A. 3 B. 9 C. 2 D. 18 4.
5. Solve �35�x � 15.
A. 9 B. 5 C. 25 D. 75 5.
6. Solve 2t � 1 � 3.A. 1 B. �1 C. 2 D. �2 6.
7. Translate the following sentence into an equation.Twice a number m minus three equals the sum of m and five.A. 2(m � 3) � m � 5 B. 2m � 3 � m � 5C. 2m � 3 � 5m D. 2(m � 3) � 5m 7.
8. Translate the following equation into a verbal sentence.x � 5 � 2(7 � x)A. The quotient of x and five is two times seven plus x.B. The number x plus five is two times the sum of seven and x.C. The number x plus five is two times seven plus x.D. The product of x and five is the sum of two times seven and x. 8.
9. A number is added to 9. The result is then multiplied by 4 to give a new result of 120. What is the number?A. 21 B. 39 C. 489 D. 4(n � 9) � 120 9.
10. Which ratio forms a proportion with �174�
?
A. �49� B. �1
52�
C. �25� D. �
36� 10.
33
© Glencoe/McGraw-Hill 192 Glencoe Algebra 1
Chapter 3 Test, Form 1 (continued)
11. Solve the proportion �27� � �4
x2�
.
A. �12� B. 12 C. �
27� D. 6 11.
12. Solve 3t � 6 � t �2.A. �2 B. �4 C. 2 D. 1 12.
13. Solve 4(t � 1) � 6t � 1.A. 2�
12� B. 1 C. 0 D. 1�
12� 13.
14. Solve 5(g � 2) � g � 6(g � 4).A. all numbers B. 0 C. 2 D. no solution 14.
15. Solve ax � 5 � b for a.
A. x(b � 5) B. �b�
x5
� C. �b �
x5
� D. x(b � 5) 15.
16. Find the percent of change. original: 10 new: 12A. 12% B. 25% C. 20% D. 18% 16.
17. A baseball costs $4.00. If the sales tax is 5%, what is the total price?A. $3.80 B. $4.20 C. $4.05 D. $4.50 17.
18. How many liters of pure acid must be added to 3 liters of a 50% acid solution to obtain a 75% acid solution?A. 1 L B. 4.5 L C. 1.5 L D. 3 L 18.
19. Joe and Janna leave home at the same time, traveling in opposite directions. Joe drives 45 miles per hour and Janna drives 40 miles per hour. In how many hours will they be 510 miles apart?A. 7 hours B. 6 hours C. 5 hours D. 4 hours 19.
20. TEMPERATURE In Death Valley, California, the highest ground temperature recorded was 94�C on July 15, 1972. In the formula
C � �59�(F � 32), C represents the temperature in degrees Celsius and F
represents the temperature in degrees Fahrenheit. To the nearest degree,what is the highest ground temperature in Death Valley in Fahrenheit?A. 201�F B. 84�F C. 34�F D. 137�F 20.
Bonus A concrete mixture is made with 3 parts water and B:5 parts cement. If 27 parts of water are being used in the current batch of concrete, how many parts of cement are being used?
NAME DATE PERIOD
33
Chapter 3 Test, Form 2A
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 193 Glencoe Algebra 1
Ass
essm
ent
Write the letter for the correct answer in the blank at the right of each question.
1. Solve m � (�4) � 7.A. 11 B. 3 C. �3 D. �11 1.
2. Solve m � 13 � 8.A. 21 B. �21 C. 5 D. �5 2.
3. Solve 5w � �75.A. 15 B. �80 C. �15 D. 80 3.
4. Solve ��n4� � �12.
A. 3 B. 48 C. �8 D. �16 4.
5. Solve ��38�y � �24.
A. �9 B. 9 C. �64 D. 64 5.
6. Solve 5x � 3 � 23.
A. 4 B. 5�12� C. 25 D. 15 6.
7. Translate the following sentence into an equation.The sum of twice a number x and 13 is two less than three times x.A. 2(x � 13) � 3x � 2 B. 2x � 13 � 2 � 3xC. 2x � 13 � 3x � 2 D. 2x � 13 � 3(x � 2) 7.
8. Translate the following equation into a verbal sentence.3x � y � 5(y � 2x)A. Three times the difference of x and y equals five times the sum of y and
two times x.B. Three times x less than y is five times y plus two times x.C. The sum of three times x and y is five times y plus two times x.D. Three times x minus y is five times the sum of y and two times x. 8.
9. Six is subtracted from a number. The result is divided by four. This result is added to 10 to give 30. What is the number?A. 4 B. 80 C. 86 D. 16 9.
10. Which ratio forms a proportion with �2355�
?
A. �35� B. �
1251�
C. �2344�
D. �150�
10.
33
33
© Glencoe/McGraw-Hill 194 Glencoe Algebra 1
11. Solve the proportion �35c�
� �16�.
A. 2 B. 10 C. 30 D. �131� 11.
12. Solve 2x � 7 � 5x � 16.
A. �3 B. �23� C. �7�
23� D. 3 12.
13. Solve �23�(6x � 30) � x � 5(x � 4) � 2x.
A. 6 B. 0 C. all numbers D. no solution 13.
14. Solve �3(h � 6) � 5(2h � 3).
A. ��133�
B. �133�
C. ��193�
D. �193�
14.
15. Solve 2x � y � y for x.A. 2y � 2 B. y � 2 C. y D. 0 15.
16. Find the percent of change. original: 80 new: 64A. 25% B. 20% C. 16% D. 10% 16.
17. A calculator costs $32.00. If the sales tax is 6%, what is the total price?A. $31.40 B. $30.08 C. $32.60 D. $33.92 17.
18. How many liters of a 40% acid solution must be added to 12 liters of a 20% solution to obtain a 25% solution?A. 4 B. 1 C. 16 D. �
45� 18.
19. Mandy begins bicycling west at 30 miles per hour at 11 A.M. If Liz leaves from the same point 20 minutes later bicycling west at 36 miles per hour,when will she catch Mandy?A. 2:00 P.M. B. 1:00 P.M. C. 1:30 P.M. D. 2:30 P.M. 19.
20. GEOMETRY The formula for the volume of a cone is V � �13��r2h where V
represents the volume, r represents the radius of the base, and h represents the height. What is the height of a cone with a volume of 66 cubic centimeters and a base with a radius of 3 centimeters?
A. 21 cm B. 69.14 cm C. 7 cm D. 0.78 cm 20.
Bonus A mixture of 10% acid and 90% water is added to 5 liters B:of pure acid. The final mixture is 40% water. How many liters of water are in the final mixture?
NAME DATE PERIOD
Chapter 3 Test, Form 2A (continued)
NAME DATE PERIOD
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 195 Glencoe Algebra 1
Ass
essm
ent
Write the letter for the correct answer in the blank at the right of each question.
1. Solve 4 � n � (�3).A. 1 B. 7 C. �1 D. �7 1.
2. Solve x � 12 � 5.A. �17 B. �7 C. 17 D. 7 2.
3. Solve 6z � �84.A. �90 B. �78 C. �14 D. �504 3.
4. Solve �15 � ��w3�.
A. 5 B. 45 C. �18 D. �12 4.
5. Solve ��47�s � �28.
A. 49 B. �49 C. 16 D. �16 5.
6. Solve 2 � 7y � 44.
A. 6�47� B. 35 C. 49 D. 6 6.
7. Translate the following sentence into an equation.The product of five and a number y is two less than the quotient of four and y.
A. 5 � y � �4y� � 2 B. 5y � �
4y� � 2
C. 5y � 2 � �4y� D. 5 � y � 2 � �
4y� 7.
8. Translate the following equation into a verbal sentence.x(7 � 5y) � �2
x�
A. x times seven minus five times y equals x divided by two.B. The product of x and seven minus five times y equals the quotient of x
and two.C. x times the difference of seven and the product of five and y equals the
quotient of x and two.D. x times the sum of seven and five times y equals x divided by two. 8.
9. A number is divided by four. The result is added to five. This result is multiplied by three to give 27. What is the number?
A. 16 B. 1 C. 21�12� D. 3�
12� 9.
10. What ratio forms a proportion with �386�
?
A. �14� B. �2
67�
C. �370�
D. �27� 10.
33 Chapter 3 Test, Form 2B
© Glencoe/McGraw-Hill 196 Glencoe Algebra 1
11. Solve the proportion �18� � �2
7h�
.
A. 4 B. 28 C. 56 D. 16 11.
12. Solve 9a � 28 � 4a � 3.
A. �30 B. �20 C. 6�15� D. �5 12.
13. Solve 3x � 4(x � 8) � x � �35�(10x � 15).
A. 0 B. all numbers C. no solution D. 41 13.
14. Solve 4(3r � 2) � �3(r � 7).
A. ��1135�
B. �1�145�
C. 1�1145�
D. �1�130�
14.
15. Solve 3b � 6v � 3b, for v.A. 6b � 6 B. b C. b � 6 D. 0 15.
16. Find the percent of change. original: 45 new: 54
A. 33�13�% B. 25% C. 16�
23�% D. 20% 16.
17. Find the discounted price. radio: $45.00 discount: 30%A. $15.00 B. $31.50 C. $36.00 D. $42.00 17.
18. Nature Drinks wants to combine orange juice they sell for $0.09 per ounce with guava juice they sell for $0.14 per ounce to create an orange-guava drink. How many ounces of orange juice should they use to create a 16-ounce drink that would sell for $1.74?A. 10 B. 6 C. 16 D. 0 18.
19. Teri begins walking east at 2 miles per hour at 1 P.M. If Cindy leaves from the same point 30 minutes later walking east at 3 miles per hour, when will she catch Teri?A. 2:30 P.M. B. 1:30 P.M. C. 2:00 P.M. D. 3:00 P.M. 19.
20. GEOMETRY The formula for the volume of a cone is V � �13��r2h, where V
represents the volume, r represents the radius of the base, and h represents the height. What is the height of a cone with a volume of 110 cubic centimeters and a base with a radius of 5 centimeters?
A. 21 cm B. 0.47 cm C. 4.2 cm D. 41.49 cm 20.
Bonus In a bag of blue, green, and red marbles, 50% are blue B:and 30% are green. There are 6 red marbles in the bag.If you increase the number of blue marbles by 40%, how many blue marbles will be in the bag?
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33
NAME DATE PERIOD
Chapter 3 Test, Form 2B (continued)
NAME DATE PERIOD
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© Glencoe/McGraw-Hill 197 Glencoe Algebra 1
For Questions 1–8, solve each equation.
1. 12 � r � 3 1.
2. �15� � x � �
25� 2.
3. �12 � p � 7 3.
4. �7b � �35 4.
5. 31 � ��n6� 5.
6. ��58�w � �9 6.
7. �295�
� �1p25�
7.
8. �3a � 4 � �14 8.
9. Translate the following sentence into an equation. 9.A number x subtracted from 36 is three times the sum of four and x.
10. Translate the following equation into a verbal sentence. 10.3(x � y) � 2y � x
For Questions 11 and 12, write an equation for each problem.Then solve the equation.
11. What number decreased by 3.5 equals 12.7? 11.
12. Twelve is added to the product of a number and 5. 12.The result is �3. Find the number.
13. Solve the following problem by working backward. 13.Julie cashed a paycheck and repaid her brother $10 that she had borrowed from him. She then spent $30 on fuel for her car and half of the remaining money on a new tent for camping. She bought a pair of running shoes for $29.45 and had $17.75 left. How much did Julie receive when she cashed her paycheck?
14. Use cross products to determine whether the pair of 14.ratios �
46� and �
1241�
form a proportion. Write yes or no.
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NAME DATE PERIOD
SCORE Chapter 3 Test, Form 2C
© Glencoe/McGraw-Hill 198 Glencoe Algebra 1
15. Solve the proportion �6x
� � �29�. 15.
16. Solve the proportion �1125�
� �1b8�. 16.
For Questions 17–19, solve each equation.
17. �x � 4 � x � 6 17.
18. 5n � 7 � 7(n � 1) � 2n 18.
19. �4(p � 2) � 8 � 2(p � 1) � 7p � 15 19.
20. Solve �ab�x � c � 0 for x. 20.
21. State whether the percent of change is a percent of increase 21.or a percent of decrease. Then find the percent of change.original: 55 new: 44
22. A shirt costs $12.00. If the sales tax is 7%, find the 22.total cost.
23. How many liters of a 90% acid solution must be added to 23.6 liters of a 15% acid solution to obtain a 40% acid solution?
24. A freight train leaves a station traveling 60 miles per hour. 24.Thirty minutes later a passenger train leaves the station in the same direction on a parallel track at a speed of 72 miles per hour. How long will it take the passenger train to catch the freight train?
25. GEOMETRY A container company wants to make a 25.cylindrical can with a volume of 1188 cubic inches. The formula V � �r2h represents the volume of a cylinder. In this formula, V represents the volume, r represents the radius of the cylinder’s base, and h represents the height of the cylinder. Solve for h. What height should the company make the can if the radius of the base must be 6 inches?
Bonus A clown is preparing for a party by inflating one balloon B:for every invited guest. Just when she has half of the necessary balloons inflated, 3 of them pop. She inflates 5 more balloons, and two pop. Then 6 balloons are carried away by the wind. She finishes by inflating 16 more balloons, and then learns that only 12 guests will attend the party. How many extra balloons did the clown inflate?
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33
NAME DATE PERIOD NAME DATE PERIOD
Chapter 3 Test, Form 2C (continued)
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33
© Glencoe/McGraw-Hill 199 Glencoe Algebra 1
For Questions 1–8, solve each equation.
1. 7 � t � 11 1.
2. �19� � y � �
59� 2.
3. �5 � v � 12 3.
4. �8x � �56 4.
5. 14 � ��5s
� 5.
6. ��79�y � �6 6.
7. �1207�
� �1a35�
7.
8. 3 � 5b � �32 8.
9. Translate the following sentence into an equation. 9.A number n added to 18 is seven times the difference of n and three.
10. Translate the following equation into a verbal sentence. 10.
�3y� � 5 � x(y � 7)
For Questions 11 and 12, write an equation for each problem.Then solve the equation.
11. What number decreased by 8.1 equals 4.9? 11.
12. Fifteen is added to the product of a number and 6. 12.The result is 9. Find the number.
13. Solve the following problem by working backward. 13.During an evening out, Dean paid a cab driver $20. He then spent $25 on dinner and half of his remaining money on a painting. He bought an umbrella for $23.75 and had $42.15 left. How much money did Dean have at the beginning of the weekend?
14. Use cross products to determine whether the pair of ratios 14.
�291�
and �1226�
form a proportion. Write yes or no.
NAME DATE PERIOD
SCORE Chapter 3 Test, Form 2D
33
© Glencoe/McGraw-Hill 200 Glencoe Algebra 1
15. Solve the proportion �235�
� �1y5�
. 15.
16. Solve the proportion �192�
� �1a5�. 16.
For Questions 17–19, solve each equation.
17. 9 � t � t � 3 17.
18. 2(y � 6) � 3y � 12 � y 18.
19. 17 � 3(z � 2) � 11z � �7(z � 2) � 14 19.
20. Solve �rs� � t � 4v for r. 20.
21. State whether the percent of change is a percent of increase 21.or a percent of decrease. Then find the percent of change.original: 60, new: 75
22. Find the discounted price. 22.flashlight: $18.00 discount: 25%
23. Nature’s Best wants to combine nuts they sell for $3.60 a 23.pound with dried fruit they sell for $2.40 a pound to create a trail mix. How much of each snack should they use to make 10 pounds of trail mix that would sell for $3.30 a pound?
24. Paula leaves home driving 40 miles per hour. One hour 24.later, her brother Dan leaves home, driving in the same direction at a speed of 50 miles per hour. How long will it take Dan to catch up to Paula?
25. GEOMETRY A container company wants to make a 25.cylindrical cardboard container with a volume of 4752 cubic inches. The formula V � �r2h represents the volume of a cylinder. In this formula, V represents the volume, rrepresents the radius of the cylinder’s base, and hrepresents the height of the cylinder. Solve for h. What height should the company make the container if the radius of the base must be 9 inches?
Bonus A store has all board games on sale for 25% off the B:regular price. A checker set has a sale price of $12. It is then moved to a clearance table where every item is discounted 40% off its regular price. What is the clearance price of the checker set?
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Chapter 3 Test, Form 2D (continued)
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33
© Glencoe/McGraw-Hill 201 Glencoe Algebra 1
For Questions 1–6, solve each equation.
1. n � 39 � 12 1.
2. w � (�8) � �21 2.
3. �6n � 16 3.
4. �13 � ��n4� 4.
5. �34�h � ��
4552�
5.
6. ��a6� � 7 � �14 6.
7. If x � 5 � 12, what is the value of x � 9? 7.
8. Translate the following into an equation. 8.A number x is decreased by 45. The result is then divided by 12. Then 20 is added to this new result to give a final result of five times the difference of 32 and the number x.
For Questions 9 and 10, write an equation for each problem.Then solve the equation.
9. Three-fifths of what number equals one? 9.
10. The product of 2 more than a number and 10 is 36 more 10.than 8 times the number. What is the number?
11. Translate the following equation into a verbal sentence. 11.5(2x � 3y) � y2 � 2x3
12. Solve the following problem by working backward. 12.Shyam invested money in the stock market. In the first year, his stock increased 20%. He paid his stock broker $300 and then lost $450. He withdrew $500, and then his remaining investment doubled. Shyam’s investment is now worth $7100. How much was Shyam’s original investment?
13. Use cross products to determine whether the pair of ratios 13.
�4428�
and �6732�
form a proportion. Write yes or no.
14. Solve the proportion �tt��
42� � �
14�. 14.
15. A blueprint for a house states that 2 inches represents 15.8 feet. If the width of a window is 2.5 inches on the blueprint, what is the width of the actual window?
NAME DATE PERIOD
SCORE Chapter 3 Test, Form 3
33
© Glencoe/McGraw-Hill 202 Glencoe Algebra 1
For Questions 16–18, solve each equation.
16. 6 � 2y � 7y � 13 16.
17. 3x � 5(x � 6) � 2(10 � x) � 10 17.
18. 5(7 � a) � 3(a � 4) � 4 � 4(a �3) � 7 18.
19. Solve ax � n � r for x. 19.
20. Solve �4xr� t� � s for x. 20.
21. State whether the percent of change is a percent of 21.increase or a percent of decrease. Then find the percent of change.original: 75, new: 84
22. A jacket costs $75.00 retail. A warehouse outlet discounts 22.the price by 20%. If the sales tax is 6%, find the final price.
23. Calvin invested $7500 for one year, part at 12% annual 23.interest and the rest at 10% annual interest. His total interest for the year was $890. How much money did he invest at 12%?
24. Two airplanes leave the Atlanta airport at the same time, 24.traveling in opposite directions. One plane travels 30 miles per hour faster than the other. After 3 hours, the planes are 3150 miles apart. What is the rate of each plane?
25. PHYSICS A ball is thrown straight up at an initial velocity 25.of 53 feet per second. In the first 1.5 seconds, it travels
42 feet. The formula s � ��u �2
v�� t represents the vertical
distance s that an object travels in t seconds, where urepresents the initial velocity of the object and v represents the velocity of the object at the end of t seconds. Find the velocity of the ball at the end of 1.5 seconds.
Bonus Paloma Rey drove to work on Wednesday at 40 miles B:per hour and arrived one minute late. She left home at the same time on Thursday, drove 45 miles per hour,and arrived one minute early. How far does Ms. Rey drive to work?
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Chapter 3 Test, Form 3 (continued)
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Chapter 3 Open-Ended Assessment
© Glencoe/McGraw-Hill 203 Glencoe Algebra 1
Demonstrate your knowledge by giving a clear, concise solution to each problem. Be sure to include all relevant drawings and justify your answers. You may show your solution in more than one way or investigate beyond the requirements of the problem.
1. Phrase 1: x times y plus zPhrase 2: x times the sum of y and za. Discuss what is different between the two phrases.b. Find values for x, y and z that make the two phrases equal.
2. a. Solve �rym� s� � t � x for y, and explain each step in your
solution.b. Would there be any limitations for the value of each variable?
If so, explain the limitation.
3. You buy a stereo at a local store. The stereo has been discountedby 10%. The store then charges 10% tax.a. Compare the final price with the original price.b. Would the final price be different if the tax was added first
and then the discount was applied to this new amount?
4. Tony and Ivia started walking south from the same location atthe same time. Ivia walked 8 miles and walked 1 mile per hourfaster than Tony who walked 6 miles. They each walked for thesame amount of time.a. Describe how a proportion could be used to find the rate that
each person walked.b. The next day they both walked 6 miles, and Ivia again walked
1 mile per hour faster than Tony, who walked 3 miles per hour.Determine whether a proportion could be used to find howlong each person walked.
5. a. Write four equivalent equations to x � 8 using one of the fouroperations of addition, subtraction, multiplication and divisionfor each equivalent equation. Use each operation only once.
b. Write an equivalent equation to x � 8 that has the variable xon both sides.
c. Determine if �n6� � �
1158�
and 2(n � 1) � 3(n � 1) are equivalent
equations. Determine if either equation is equivalent to any ofthe equations created for parts a and b.
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© Glencoe/McGraw-Hill 204 Glencoe Algebra 1
Chapter 3 Vocabulary Test/Review
Write whether each sentence is true or false. If false, replace the underlined word or number to make a true sentence.
1. The Addition Property of Equality states that if the same 1.number is subtracted from each side of an equation, the resulting equation is true.
2. If the same number is added to each side of a true equation, 2.then the result is a true equation.
3. The Multiplication Property of Equality states that if each 3.side of a true equation is multiplied by the same number,the resulting equation is true.
4. Multi-step equations are equations with less than one 4.operation.
5. An equation that is false for every value of the variable is 5.called an identity.
6. A ratio is a comparison of two numbers by multiplication. 6.
7. The ratio of two measurements having different units of 7.measure is called a rate.
8. A percent of increase or decrease is called a 8.percent of change.
9. If the new number is less than the original number, the 9.percent of change is a percent of increase.
10. If the new number is greater than the original number, the 10.percent of change is a percent of decrease.
In your own words—Define each term.
11. proportion
12. formula
Addition Property of Equalityconsecutive integersdefining a variabledimensional analysisDivision Property of Equalityequivalent equationextremesformulafour-step problem-solving planidentity
meansmixture problemMultiplication Property of Equality
multi-step equationsnumber theorypercent of changepercent of decreasepercent of increaseproportion
rateratioscalesolve an equationSubtraction Property of Equality
uniform motion problemweighted averagework backward
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Chapter 3 Quiz (Lessons 3–1 through 3–3)33
© Glencoe/McGraw-Hill 205 Glencoe Algebra 1
Translate each sentence into an equation.
1. Two times a number n is three times the sum of n and nine. 1.
2. The difference of the square of y and twelve is the same as 2.the product of five and x.
Translate each equation into a verbal sentence.
3. 2b � 10 � 4 4. y � 3x2 � 5x
Solve each equation.
5. d � 8 � 6 6. �28 � p � 21
7. �3 � (�g) � �12 8. �7x � 63
9. ��5t� � �8 10. �
45�d � �32
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Chapter 3 Quiz (Lessons 3–4 and 3–5)
Solve each equation.
1. 3x � 8 � 29 2. �a6� � 5 � 9
3. 5r � 14 � �42 4. 7n � 6 � 4n � 9
5. 3b � 13 � 4b � 7b � 1 6. 5 � 3(w � 4) � w � 7
7. 2x � 5(x � 3) � 2(x � 10)
8. Standardized Test Practice Solve �6(2r � 8) � �10(r � 3).A. �11 B. �156 C. �39 D. 9
Solve each problem by working backward.
9. A number is multiplied by 4, and then 5 is subtracted from the product. The result is 3. What is the number?
10. Three is subtracted from a number, and then the difference is divided by 11. The result is 12. What is the number?
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3.
4.
5.
6.
7.
8.
9.
10.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
© Glencoe/McGraw-Hill 206 Glencoe Algebra 1
Use cross products to determine whether each pair of ratios forms a proportion. Write yes or no.
1. �57�, �
2208�
2. �1113�
, �2225�
3. �46..23�
, �00..35�
Solve each proportion.
4. �34� � �2
n0�
5. �64� � �1
x8�
6. �3b3� � �
1455�
For Questions 7 and 8, state whether the percent of change is a percent of increase or a percent of decrease.Then find the percent of change.
7. original: 25 8. original: 36new: 18 new: 45
9. The cost of a compact disc is $18. If the sales tax is 6%, 9.find the total price.
10. Find the discounted price. camera: $108 10.discount: 30%
Chapter 3 Quiz (Lessons 3–8 and 3–9)
For Questions 1 and 2, solve each equation or formula for the variable specified.
1. nx � m � p, for x 1.
2. �x �
ab
� � c, for b 2.
3. A chemist needs a 30% iron alloy. How many grams of a 3.70% iron alloy must be mixed with 16 grams of a 20% iron alloy to obtain the required 30% alloy?
4. On Mary’s walk she covered the 3-mile distance to the park 4.in one hour. However, the return trip took her one and a half hours. What was her average speed for the round trip?
5. The formula p � 2� � 2w represents the perimeter of a 5.rectangle. In this formula, � is the length of the rectangle and w is the width. Solve the formula for �. Find the length when the width is 4 meters and the perimeter is 36 meters.
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Chapter 3 Quiz (Lessons 3–6 and 3–7)33
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33
1.
2.
3.
4.
5.
6.
7.
8.
Chapter 3 Mid-Chapter Test (Lessons 3–1 through 3–5)
© Glencoe/McGraw-Hill 207 Glencoe Algebra 1
Write the letter for the correct answer in the blank at the right of each question.
1. Translate the following sentence into an equation.The product of five and the sum of a number x and three is twelve.A. 5 � 3x � 12 B. 5(x � 3) �12C. 5x � 3 �12 D. 5x � 3 �x 1.
2. Solve y � (�16) � �12.A. 192 B. �28 C. �
34� D. 4 2.
3. Solve ��a6� � 5 � 2.
A. 18 B. �6 C. �12� D. �9 3.
4. Solve �35�y � �9.
A. �5�25� B. �5 C. �15 D. ��
59� 4.
5. Solve �6d � �42.A. �48 B. 7 C. �36 D. 252 5.
6. Solve �18 � v � (�4).A. 22 B. �14 C. �22 D. 14 6.
For Questions 7–9, solve each equation.
7. 5(12 � 3p) � 15p � 60 7.
8. 3(y � 2) � 6(y � 1) � 3y 8.
9. 3a � 21 � 7 � 4a 9.
10. Solve the following problem by working backward. 10.Liza earned some money delivering newspapers. She bought a battery for $1.95, and gave her mother $30. She bought a ring for $7.20, and then spent half of the remaining money on a radio. If Liza has $38.50 left, how much money did she earn delivering newspapers?
For Questions 11 and 12, translate each equation into a verbal sentence.
11. 4n � m(5 � n) 11.
12. 3(y � 5) � 7y 12.
Part II
Part I
NAME DATE PERIOD
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© Glencoe/McGraw-Hill 208 Glencoe Algebra 1
Chapter 3 Cumulative Review (Chapters 1–3)
1. Evaluate 3y � x2z if x � 2, y � 14, and z � 5. (Lesson 1–2) 1.
2. Simplify 2(u � 3v) � 3(u � v). (Lesson 1–6) 2.
3. Miguel was riding his bike to school. He got halfway there 3.and realized he had forgotten his backpack. He turned around, went home, retrieved his backpack, and continued his ride to school. Sketch a reasonable graph to show his distance from school from the time he started to the time he arrived at school. Assume his rate is always the same.(Lesson 1–8)
Find each of the following. (Lessons 2–2 through 2–4, 2–7)
4. 13.7 � (�3.2) 5. 12(�32) 6.
6. 52 � (�4) 7. ��1.69� 7.
8. The values of the 14 highest recorded temperatures in the 8.United States are listed below.128 120 134 118 118 121 125122 121 120 119 120 120 118 Source: World Almanac
Make a line plot of the data. (Lesson 2–5)
9. A baseball player has a batting average of 0.250. What are 9.the odds that the next time the player bats he gets a hit?(Lesson 2–6)
10. Translate the following sentence into an algebraic equation. 10.Nine times a number y subtracted from 85 is seven times the sum of four and y. (Lesson 3–1)
11. Solve the following problem by working backward. Three is 11.added to a number. The result is divided by two, and then the new result is added to eighteen. The final result is 35.What is the number? (Lesson 3–4)
For Questions 12–14, solve each equation.(Lessons 3–2 through 3–5)
12. �27 � �6 � 3p 13. 7a � 2 �3a � 10
14. 2(x �3) � 6x � 3(9 � x) 14.
15. Solve q � �mn� � p for m. (Lesson 3–8) 15.
16. How many liters of water must be added to 7 liters of a 16.20% acid solution to obtain a 10% acid solution?(Lesson 3–9)
115 120 125 130 135
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4.
5.
12.
13.
Standardized Test Practice (Chapters 1–3)
© Glencoe/McGraw-Hill 209 Glencoe Algebra 1
1. Write an algebraic expression for the following verbal expression.The sum of n and 5. (Lesson 1–1)
A. 5n B. �n5� C. n � 5 D. n � 5 1.
2. State the hypothesis of the following statement.If I complete my algebra homework daily, then I will learn the concepts. (Lesson 1–7)
E. I will learn the concepts.F. I don’t do my algebra homework.G. I won’t learn the concepts.H. I complete my algebra homework daily. 2.
3. Simplify the expression 7(x � y) � 2(y � x) � 4x. (Lesson 1–5)
A. 13x � 9y B. 9x � 5y C. 9x � 9y D. 13x � 5y 3.
4. Evaluate a(b � c2) if a � �23�, b � �
34�, and c � �
12�. (Lesson 2–3)
E. �16� F. �
13� G. �
14� H. �
23� 4.
5. The heights in feet of the 10 largest National Champion trees are listed below. Source: World Almanac
275 321 159 191 281 83 108 232 219 102Which measure of central tendency best represents the data? (Lesson 2–5)
A. the mode B. the mean or the medianC. the mean or the mode D. the median or the mode 5.
6. A letter is chosen at random from the name Antarctica. What is the probability that the chosen letter is a vowel? (Lesson 2–6)
E. �25� F. �1
30�
G. �12� H. �
35� 6.
7. Solve ��34�y � �2
80�
. (Lesson 3–3)
A. �25� B. � �1
30�
C. �185�
D. ��185�
7.
8. Which equation has a solution of �2? (Lesson 3–4)
E. 4n � 3 � 11 F. 4 � 3n � 2G. 5(1 � n) � �5 H. 3(n � 1) � 2 8.
9. A car dealership has 180 cars on their lot. If they increase their inventory by 25%, how many cars will be on the lot? (Lesson 3–7)
A. 230 B. 225 C. 135 D. 205 9. DCBA
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Part 1: Multiple Choice
Instructions: Fill in the appropriate oval for the best answer.
NAME DATE PERIOD
33
Ass
essm
ent
© Glencoe/McGraw-Hill 210 Glencoe Algebra 1
Standardized Test Practice (continued)
10. Solve 2�13� � �
56� � t. (Lesson 1–3)
11. Find �13� � ( � �
14�). (Lesson 2–2)
12. Solve 7 � 3x � 4 � 9x. (Lesson 3–5)
13. Sasha drove from her house to the grocerystore in 20 minutes. Her return trip took 15 minutes. If the store is 7 miles from herhouse, what was Sasha’s average speed for the round trip, in miles per hour? (Lesson 3–9)
Column A Column B
14. 14.
(Lesson 1–4)
15. Let u � 4, v � �3, and t � 2. 15.
(Lesson 2–4)
16. Let �7x
� � �1228�
. 16.
(Lesson 3–6)
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Part 3: Quantitative Comparison
Instructions: Compare the quantities in columns A and B. Shade in if the quantity in column A is greater; if the quantity in column B is greater; if the quantities are equal; or if the relationship cannot be determined from the information given.
NAME DATE PERIOD
33
10. 11.
12. 13.
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Part 2: Grid In
Instructions: Enter your answer by writing each digit of the answer in a column boxand then shading in the appropriate oval that corresponds to that entry.
A
D
C
B
(4 � 1 � 4) � �15
�(10 � 5) (2 � 0)��12
�� � 5(7 � 3 � 2)
uv � t u � vt
�9x
� �1x
�
Unit 1 Test(Chapters 1–3)
© Glencoe/McGraw-Hill 211 Glencoe Algebra 1
1. Write an algebraic expression for 1.the difference of 5 and n cubed.
2. Evaluate 2x � 5y2 � 3z if x � 6, y � 4, and z � 7. 2.
3. Find the solution set for 3b � 4 � 8 if the replacement set 3.is {1, 2, 3, 4, 5}.
4. Name the property used in the equation 1 � 6n. Then find 4.the value of n.
For Questions 5–7, simplify each expression.
5. 2t2 � 5t2 � 3t 5.
6. 7(r � 2t) � 5t 6.
7. 5(4a � b) � 3a � b 7.
8. Identify the hypothesis and conclusion of the statement. 8.Then write the statement in if-then form.All triangles are polygons.
9. Draw a reasonable graph showing the relationship between 9.the temperature of a pizza as it is removed from an oven and placed on a counter at room temperature, and time.
10. A recent survey asked consumers to identify their favorite ice cream topping. The results are displayed in the circle graph. If 250 people were 10.surveyed, how many chose strawberries as their favorite topping?
11. Graph {4, 5, 6, 7, 8, …}. 11.
Find each sum, product, or quotient.
12. 31 � (�78) 12.
13. ���89����
34�� 13.
14. 37.6 � (�8) 14.
15. A card is selected at random from a standard deck of 15.52 cards. What is the probability of selecting a diamond?
16. Find the odds of rolling a number less than 6 on a die. 16.
�2�3 �1 0 1 2 4 5 6 7 83
TimeTe
mp
erat
ure
(F°
)
Ass
essm
ent
NAME DATE PERIOD
SCORE
Other18%
Caramel9%
Strawberries16%Chocolate
Syrup28%
Hot Fudge29%
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 212 Glencoe Algebra 1
Unit 1 Test (continued)
For Questions 17 and 18, use the list that shows the number of hours Mrs. Wentworth’s piano students spent practicing last week.
9 2 2 4 14 2 7 1 5 0 3 1 3 9 11 2
17. Make a line plot of the data. 17.
18. Which measure of central tendency best describes the data? 18.Explain.
19. Name the set or sets of numbers to which �48� belongs. 19.
20. Write �3.6�5�, �13�, �7251�
, ��158� in order from least to greatest. 20.
For Questions 21–27, solve each equation.
21. m � 5 � �23 21.
22. �4 � 8 � k 22.
23. �a2
� � 9 � 30 23.
24. ��27
�x � �16 24.
25. 5(c � 3) � 15 � 2(2c � 1) 25.
26. 10(a � 1) � 14a � 9 � (4a � 1) 26.
27. �170� � �
x �
31
� 27.
28. A magazine is on sale for 15% off the original price. If the 28.original price of the magazine is $4.60, what is the discounted price?
29. Solve �t �
rv
� � s, for v. 29.
30. How many pounds of peanuts costing $3.00 a pound should 30.be mixed with 4 pounds of cashews costing $4.50 a pound to obtain a mixture costing $3.50 a pound?
NAME DATE PERIOD
Standardized Test PracticeStudent Record Sheet (Use with pages 186–187 of the Student Edition.)
© Glencoe/McGraw-Hill A1 Glencoe Algebra 1
Select the best answer from the choices given and fill in the corresponding oval.
1 4 7
2 5 8
3 6
Solve the problem and write your answer in the blank.
For Questions 10, 12, and 14, also enter your answer by writing each number orsymbol in a box. Then fill in the corresponding oval for that number or symbol.
9 10 12 14
10 (grid in)
11
12 (grid in)
13
14 (grid in)
15
Select the best answer from the choices given and fill in the corresponding oval.
16
17
18
Record your answers for Questions 19–20 on the back of this paper.
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NAME DATE PERIOD
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An
swer
s
Part 3 Quantitative ComparisonPart 3 Quantitative Comparison
Part 2 Short Response/Grid InPart 2 Short Response/Grid In
Part 4 Open-EndedPart 4 Open-Ended
Part 1 Multiple ChoicePart 1 Multiple Choice
© Glencoe/McGraw-Hill A2 Glencoe Algebra 1
Stu
dy G
uid
e a
nd I
nte
rven
tion
Wri
tin
g E
qu
atio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
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____
____
__P
ER
IOD
____
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3-1
3-1
©G
lenc
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w-H
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7G
lenc
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lgeb
ra 1
Lesson 3-1
Wri
te E
qu
atio
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Wri
tin
g eq
uat
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s is
on
e st
rate
gy f
or s
olvi
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prob
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s.Yo
u c
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se a
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efer
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to i
n a
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blem
.Th
en y
ouca
n w
rite
a v
erba
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pres
sion
as
an a
lgeb
raic
exp
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.
Tra
nsl
ate
each
sen
ten
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nto
an
eq
uat
ion
or
afo
rmu
la.
a.T
en t
imes
a n
um
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x i
s eq
ual
to
2.8
tim
es t
he
dif
fere
nce
ym
inu
s z.
10 �
x�
2.8
�(y
�z)
Th
e eq
uat
ion
is
10x
�2.
8(y
�z)
.
b.
A n
um
ber
mm
inu
s 8
is t
he
sam
eas
a n
um
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ivid
ed b
y 2.
m�
8 �
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he
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atio
n i
s m
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he
area
of
a re
ctan
gle
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als
the
len
gth
tim
es t
he
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th.T
ran
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is s
ente
nce
in
to a
for
mu
la.
Let
A�
area
,��
len
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,an
d w
�w
idth
.F
orm
ula
:Are
a eq
ual
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imes
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th.
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wT
he
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th
e ar
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A�
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Use
th
e F
our-
Ste
p
Pro
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m-S
olvi
ng
Pla
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Th
e p
opu
lati
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f th
e U
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ed S
tate
s in
200
1w
as a
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4,00
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nit
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.Fin
d t
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kn
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hat
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ere
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284,
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ou w
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tep
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t th
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ion
.Let
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peop
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0 �
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284,
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ivid
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ide
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her
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e an
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.
Exam
ple1
Exam
ple1
Exam
ple2
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Exer
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Exer
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Tra
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each
sen
ten
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nto
an
eq
uat
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or
form
ula
.
1.T
hre
e ti
mes
a n
um
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tm
inu
s tw
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equ
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fort
y.3t
�12
�40
2.O
ne-
hal
f of
th
e di
ffer
ence
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aan
d b
is 5
4.(a
�b
) �
54
3.T
hre
e ti
mes
th
e su
m o
f d
and
4 is
32.
3(d
�4)
�32
4.T
he
area
Aof
a c
ircl
e is
th
e pr
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f �
and
the
radi
us
rsq
uar
ed.
A�
�r2
WEI
GH
T LO
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or E
xerc
ises
5–6
,use
th
e fo
llow
ing
info
rmat
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.
Lou
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ts t
o lo
se w
eigh
t to
au
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or a
par
t in
a p
lay.
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wei
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160
pou
nds
now
.He
wan
ts t
o w
eigh
150
pou
nds
.
5.If
pre
pres
ents
th
e n
um
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of p
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e w
ants
to
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,wri
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itu
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160
�p
�15
0
6.H
ow m
any
pou
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s h
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ose
to r
each
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lb
1 � 2
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Wri
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slat
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s in
to v
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nce
s.
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eq
uat
ion
in
to a
ver
bal
sen
ten
ce.
a.4n
�8
�12
.
4n�
8 �
12F
our
tim
es n
min
us
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t eq
ual
s tw
elve
.
b.
a2
�b2
�c2
a2�
b2�
c2
Th
e su
m o
f th
e sq
uar
es o
f a
and
b is
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al t
o th
e sq
uar
e of
c.
Tra
nsl
ate
each
eq
uat
ion
in
to a
ver
bal
sen
ten
ce.
1.4a
�5
�23
2.10
�k
�4k
4 ti
mes
am
inu
s 5
is e
qu
al t
o 2
3.T
he
sum
of
10 a
nd
kis
eq
ual
to
4
tim
es k
.
3.6x
y�
244.
x2�
y2�
8
6 ti
mes
th
e p
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uct
of
xan
d y
is
Th
e su
m o
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e sq
uar
es o
f x
and
eq
ual
to
24.
y is
eq
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to
8.
5.p
�3
�2p
6.b
�(h
�1)
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m o
f p
and
3 is
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ual
to
b
is
of
the
dif
fere
nce
of
han
d 1
.2
tim
es p
.
7.10
0 �
2x�
808.
3(g
�h
) �
12
100
min
us
2 ti
mes
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ual
3 ti
mes
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e su
m o
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12.
to 8
0.
9.p2
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10.C
�(F
�32
)
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f p
min
us
2 ti
mes
C
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al t
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of
the
dif
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nce
of
p is
eq
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to
9.
Fan
d 3
2.
11.V
�B
h12
.A
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b
Vis
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to
o
f th
e p
rod
uct
of
Ais
eq
ual
to
o
f th
e p
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uct
of
Ban
d h
.h
and
b.
1 � 21 � 3
1 � 21 � 3
5 � 9
5 � 91 � 31 � 3
Stu
dy G
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e a
nd I
nte
rven
tion
(c
onti
nued
)
Wri
tin
g E
qu
atio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-1
3-1
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 3-1)
© Glencoe/McGraw-Hill A3 Glencoe Algebra 1
An
swer
s
Skil
ls P
ract
ice
Wri
tin
g E
qu
atio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
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AT
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____
____
__P
ER
IOD
____
_
3-1
3-1
©G
lenc
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cGra
w-H
ill13
9G
lenc
oe A
lgeb
ra 1
Lesson 3-1
Tra
nsl
ate
each
sen
ten
ce i
nto
an
eq
uat
ion
.
1.T
wo
adde
d to
th
ree
tim
es a
nu
mbe
r m
is t
he
sam
e as
18.
3m�
2 �
18
2.T
wic
e a
incr
ease
d by
th
e cu
be o
f a
equ
als
b.2a
�a
3�
b
3.S
even
les
s th
an t
he
sum
of
pan
d q
is a
s m
uch
as
6.(p
�q
) �
7 �
6
4.T
he
sum
of
xan
d it
s sq
uar
e is
equ
al t
o y
tim
es z
.x
�x
2�
yz
5.F
our
tim
es t
he
sum
of
fan
d g
is i
den
tica
l to
six
tim
es g
.4
(f�
g)
�6g
Tra
nsl
ate
each
sen
ten
ce i
nto
a f
orm
ula
.
6.T
he
peri
met
er P
of a
squ
are
equ
als
fou
r ti
mes
th
e le
ngt
h o
f a
side
s.
P�
4s
7.T
he
area
Aof
a s
quar
e is
th
e le
ngt
h o
f a
side
ssq
uar
ed.
A�
s2
8.T
he
peri
met
er P
of a
tri
angl
e is
equ
al t
o th
e su
m o
f th
e le
ngt
hs
of s
ides
a,b
,an
d c.
P�
a�
b�
c9.
Th
e ar
ea A
of a
cir
cle
is p
i ti
mes
th
e ra
diu
s r
squ
ared
.A
��
r2
10.T
he
volu
me
Vof
a r
ecta
ngu
lar
pris
m e
qual
s th
e pr
odu
ct o
f th
e le
ngt
h �
,th
e w
idth
w,
and
the
hei
ght
h.
V�
�wh
Tra
nsl
ate
each
eq
uat
ion
in
to a
ver
bal
sen
ten
ce.
11.g
�10
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12.2
p�
4q�
20g
plu
s 10
is t
he
sam
e as
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e p
plu
s 4
tim
es q
is 2
0.3
tim
es g
.
13.4
(a�
b) �
9a14
.8 �
6x�
4 �
2x4
tim
es t
he
sum
of
aan
d b
8 m
inu
s 6
tim
es x
is 4
plu
s
is 9
tim
es a
.2
tim
es x
.
15.
(f�
y) �
f�
516
.s2
�n
2�
2b
Hal
f o
f th
e su
m o
f f
and
yis
s
squ
ared
min
us
nsq
uar
ed is
f
min
us
5.tw
ice
b.
Wri
te a
pro
ble
m b
ased
on
th
e gi
ven
in
form
atio
n.
17.c
�co
st p
er p
oun
d of
pla
in c
offe
e be
ans
18.p
�co
st o
f di
nn
erc
�3
�co
st p
er p
oun
d of
fla
vore
d co
ffee
bea
ns
0.15
p�
cost
of
a 15
% t
ip2c
�(c
�3)
�21
p�
0.15
p�
23S
amp
le a
nsw
er:T
he
cost
of
two
po
un
ds
Sam
ple
an
swer
:Th
e co
st o
fo
f p
lain
co
ffee
bea
ns
plu
s o
ne
po
un
d o
fd
inn
er p
lus
a 15
% t
ip w
as
flav
ore
d b
ean
s is
$21
.Ho
w m
uch
do
es
$23.
Ho
w m
uch
was
th
e 1
po
un
d o
f p
lain
bea
ns
cost
?d
inn
er?
1 � 2
©G
lenc
oe/M
cGra
w-H
ill14
0G
lenc
oe A
lgeb
ra 1
Tra
nsl
ate
each
sen
ten
ce i
nto
an
eq
uat
ion
.
1.F
ifty
-th
ree
plu
s fo
ur
tim
es c
is a
s m
uch
as
21.
53 �
4c�
21
2.T
he
sum
of
five
tim
es h
and
twic
e g
is e
qual
to
23.
5h�
2g�
23
3.O
ne
fou
rth
th
e su
m o
f r
and
ten
is
iden
tica
l to
rm
inu
s 4.
(r�
10)
�r
�4
4.T
hre
e pl
us
the
sum
of
the
squ
ares
of
wan
d x
is 3
2.3
�(w
2�
x2 )
�32
Tra
nsl
ate
each
sen
ten
ce i
nto
a f
orm
ula
.
5.D
egre
es K
elvi
n K
equ
als
273
plu
s de
gree
s C
elsi
us
C.
K�
273
�C
6.T
he
tota
l co
st C
of g
as i
s th
e pr
ice
ppe
r ga
llon
tim
es t
he
nu
mbe
r of
gal
lon
s g.
C�
pg
7.T
he
sum
S o
f th
e m
easu
res
of t
he
angl
es o
f a
poly
gon
is
equ
al t
o 18
0 ti
mes
th
e di
ffer
ence
of t
he
nu
mbe
r of
sid
es n
and
2.S
�18
0(n
�2)
Tra
nsl
ate
each
eq
uat
ion
in
to a
ver
bal
sen
ten
ce.
8.q
�(4
�p)
�q
qm
inu
s th
e su
m
9.t
�2
�t
of
4 an
d p
eq
ual
s ti
mes
q.
Two
mo
re t
han
o
f t
equ
als
t.
10.9
(y2
�x)
�18
9 ti
mes
th
e su
m
11.2
(m�
n)
�v
�7
Twic
e th
e q
uan
tity
o
f y
squ
ared
an
d x
is 1
8.m
min
us
nis
vp
lus
7.
Wri
te a
pro
ble
m b
ased
on
th
e gi
ven
in
form
atio
n.
12.a
�co
st o
f on
e ad
ult
’s t
icke
t to
zoo
13.c
�re
gula
r co
st o
f on
e ai
rlin
e ti
cket
a�
4 �
cost
of
one
chil
dren
’s t
icke
t to
zoo
0.20
c�
amou
nt o
f 20
% p
rom
otio
nal
disc
ount
2a�
4(a
�4)
�38
3(c
�0.
20c)
�33
0S
amp
le a
nsw
er:T
he
cost
of
two
S
amp
le a
nsw
er:T
he
cost
of
thre
e ad
ult
’s t
icke
ts a
nd
4 c
hild
ren
’s
airl
ine
tick
ets
that
are
dis
cou
nte
d
tick
ets
to t
he
zoo
is $
38.H
ow
20
% is
$33
0.W
hat
is t
he
reg
ula
r m
uch
is a
n a
du
lt’s
tic
ket?
cost
of
a ti
cket
?
14.G
EOG
RA
PHY
Abo
ut
15%
of
all
fede
rall
y-ow
ned
lan
d in
th
e 48
con
tigu
ous
stat
es o
f th
eU
nit
ed S
tate
s is
in
Nev
ada.
If F
repr
esen
ts t
he
area
of
fede
rall
y-ow
ned
lan
d in
th
ese
stat
es,a
nd
Nre
pres
ents
th
e po
rtio
n i
n N
evad
a,w
rite
an
equ
atio
n f
or t
his
sit
uat
ion
.0.
15F
�N
FITN
ESS
For
Exe
rcis
es 1
5–17
,use
th
e fo
llow
ing
info
rmat
ion
.D
ean
na
and
Pie
tra
each
go
for
wal
ks a
rou
nd
a la
ke a
few
tim
es p
er w
eek.
Las
t w
eek,
Dea
nn
a w
alke
d 7
mil
es m
ore
than
Pie
tra.
15.I
f p
repr
esen
ts t
he
nu
mbe
r of
mil
es P
ietr
a w
alke
d,w
rite
an
equ
atio
n t
hat
rep
rese
nts
th
eto
tal
nu
mbe
r of
mil
es T
the
two
girl
s w
alke
d.T
�p
�(p
�7)
16.I
f P
ietr
a w
alke
d 9
mil
es d
uri
ng
the
wee
k,h
ow m
any
mil
es d
id D
ean
na
wal
k?16
mi
17.I
f P
ietr
a w
alke
d 11
mil
es d
uri
ng
the
wee
k,h
ow m
any
mil
es d
id t
he
two
girl
s w
alk
toge
ther
?29
mi
3 � 51 � 3
3 � 51 � 3
1 � 4
Pra
ctic
e (
Ave
rag
e)
Wri
tin
g E
qu
atio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-1
3-1
Answers (Lesson 3-1)
© Glencoe/McGraw-Hill A4 Glencoe Algebra 1
Readin
g t
o L
earn
Math
em
ati
csW
riti
ng
Eq
uat
ion
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-1
3-1
©G
lenc
oe/M
cGra
w-H
ill14
1G
lenc
oe A
lgeb
ra 1
Lesson 3-1
Pre-
Act
ivit
yH
ow a
re e
qu
atio
ns
use
d t
o d
escr
ibe
hei
ghts
?
Rea
d th
e in
trod
uct
ion
to
Les
son
3-1
at
the
top
of p
age
120
in y
our
text
book
.
Doe
s th
e eq
uat
ion
305
�s
�15
4 al
so r
epre
sen
t th
e si
tuat
ion
?E
xpla
in.
Yes;
the
tota
l hei
gh
t m
inu
s th
e h
eig
ht
of
the
stat
ue
itse
lf g
ives
the
hei
gh
t o
f th
e p
edes
tal.
Rea
din
g t
he
Less
on
1.T
ran
slat
e ea
ch s
ente
nce
in
to a
n e
quat
ion
.
a.Tw
otim
esth
e su
m o
f x
and
thre
em
inus
four
equa
lsfo
urtim
esx.
2�
(x�
3)�
4�
4�
x
b.
The
diff
eren
ce o
f k
and
3is
two
times
kdi
vide
d by
five.
k�
3�
2�
k�
5
2.A
1 o
z se
rvin
g of
ch
ips
has
140
cal
orie
s.T
her
e ar
e ab
out
14 s
ervi
ngs
of
chip
s in
a b
ag.
How
man
y ca
lori
es a
re t
her
e in
a b
ag o
f ch
ips?
Wri
te w
hat
you
r so
luti
on w
ould
be
as y
ouu
se e
ach
ste
p in
th
e F
our-
Ste
p P
robl
em-S
olvi
ng
Pla
n.
Exp
lore
Wh
at d
o yo
u k
now
?
A 1
oz
serv
ing
of
chip
s h
as 1
40 c
alo
ries
an
d t
her
e ar
e 14
serv
ing
s o
f ch
ips
in a
bag
.W
hat
do
you
wan
t to
kn
ow?
Ho
w m
any
calo
ries
are
in a
bag
of
chip
s?
Pla
nW
rite
an
equ
atio
n.
140
�14
�x
Sol
veS
olve
th
e pr
oble
m.
140
�14
�19
60;T
her
e ar
e 19
60 c
alo
ries
in a
bag
of
chip
s.E
xam
ine
Doe
s yo
ur
answ
er m
ake
sen
se?
See
stu
den
ts’w
ork
.
Hel
pin
g Y
ou
Rem
emb
er
3.If
you
can
not
rem
embe
r al
l th
e st
eps
of t
he
Fou
r-S
tep
Pro
blem
-Sol
vin
g P
lan
,try
to
rem
embe
r th
e fi
rst
lett
ers
of t
he
firs
t w
ord
in e
ach
ste
p.W
rite
th
ose
lett
ers
her
e w
ith
thei
r as
soci
ated
wor
ds.
EP
SE
;E
xplo
re,P
lan
,So
lve,
Exa
min
e
©G
lenc
oe/M
cGra
w-H
ill14
2G
lenc
oe A
lgeb
ra 1
Rep
-Tile
sA
rep
-til
e is
a f
igu
re t
hat
can
be
subd
ivid
ed i
nto
sm
alle
r co
pies
of
itse
lf.T
he
larg
e fi
gure
is
sim
ilar
to
th
e sm
all
ones
an
d th
e sm
all
figu
res
are
all
con
gru
ent.
Sh
ow t
hat
eac
h f
igu
re i
s a
rep
-til
e b
y su
bd
ivid
ing
it i
nto
fou
r sm
alle
r an
d
sim
ilar
fig
ure
s.
1.2.
3.
4.5.
6.
Su
bd
ivid
e ea
ch r
ep-t
ile
into
nin
e sm
alle
r an
d s
imil
ar f
igu
res.
7.8.
9.10
.
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-1
3-1
Answers (Lesson 3-1)
© Glencoe/McGraw-Hill A5 Glencoe Algebra 1
An
swer
s
Stu
dy G
uid
e a
nd I
nte
rven
tion
So
lvin
g E
qu
atio
ns
by U
sin
g A
dd
itio
n a
nd
Su
btr
acti
on
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-2
3-2
©G
lenc
oe/M
cGra
w-H
ill14
3G
lenc
oe A
lgeb
ra 1
Lesson 3-2
Solv
e U
sin
g A
dd
itio
nIf
th
e sa
me
nu
mbe
r is
add
ed t
o ea
ch s
ide
of a
n e
quat
ion
,th
ere
sult
ing
equ
atio
n i
s eq
uiv
alen
t to
th
e or
igin
al o
ne.
In g
ener
al i
f th
e or
igin
al e
quat
ion
invo
lves
su
btra
ctio
n,t
his
pro
pert
y w
ill
hel
p yo
u s
olve
th
e eq
uat
ion
.
Ad
dit
ion
Pro
per
ty o
f E
qu
alit
yF
or a
ny n
umbe
rs a
, b,
and
c,
if a
�b,
the
n a
�c
�b
�c.
Sol
ve m
�32
�18
.
m�
32 �
18O
rigin
al e
quat
ion
m�
32 �
32 �
18 �
32A
dd 3
2 to
eac
h si
de.
m�
50S
impl
ify.
Th
e so
luti
on i
s 50
.
Sol
ve �
18 �
p�
12.
�18
�p
�12
Orig
inal
equ
atio
n
�18
�12
�p
�12
�12
Add
12
to e
ach
side
.
p�
�6
Sim
plify
.
Th
e so
luti
on i
s �
6.
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Sol
ve e
ach
eq
uat
ion
.Th
en c
hec
k y
our
solu
tion
.
1.h
�3
��
21
2.m
�8
��
12�
43.
p�
5 �
1520
4.20
�y
�8
285.
k�
0.5
�2.
32.
86.
w�
�1
7.h
�18
��
171
8.�
12 �
�24
�k
129.
j�
0.2
�1.
82
10.b
�40
��
400
11.m
�(�
12)
�10
�2
12.w
��
Wri
te a
n e
qu
atio
n f
or e
ach
pro
ble
m.T
hen
sol
ve t
he
equ
atio
n a
nd
ch
eck
th
eso
luti
on.
13.T
wel
ve s
ubt
ract
ed f
rom
a n
um
ber
equ
als
25.F
ind
the
nu
mbe
r.n
�12
�25
;37
14.W
hat
nu
mbe
r de
crea
sed
by 5
2 eq
ual
s �
12?
n�
52 �
�12
;40
15.F
ifty
su
btra
cted
fro
m a
nu
mbe
r eq
ual
s ei
ghty
.Fin
d th
e n
um
ber.
n�
50 �
80;
130
16.W
hat
nu
mbe
r m
inu
s on
e-h
alf
is e
qual
to
neg
ativ
e on
e-h
alf?
n�
�
�;
0
17.T
he
diff
eren
ce o
f a
nu
mbe
r an
d ei
ght
is e
qual
to
14.W
hat
is
the
nu
mbe
r?
n�
8 �
14;
22
18.A
nu
mbe
r de
crea
sed
by f
ourt
een
is
equ
al t
o ei
ghte
en.W
hat
is
the
nu
mbe
r?n
�14
�18
;32
1 � 21 � 2
7 � 41 � 4
3 � 2
1 � 85 � 8
1 � 2
©G
lenc
oe/M
cGra
w-H
ill14
4G
lenc
oe A
lgeb
ra 1
Solv
e U
sin
g S
ub
trac
tio
nIf
th
e sa
me
nu
mbe
r is
su
btra
cted
fro
m e
ach
sid
e of
an
equ
atio
n,t
he
resu
ltin
g eq
uat
ion
is
equ
ival
ent
to t
he
orig
inal
on
e.In
gen
eral
if
the
orig
inal
equ
atio
n i
nvo
lves
add
itio
n,t
his
pro
pert
y w
ill
hel
p yo
u s
olve
th
e eq
uat
ion
.
Su
btr
acti
on
Pro
per
ty o
f E
qu
alit
yF
or a
ny n
umbe
rs a
, b,
and
c,
if a
�b,
the
n a
�c
�b
�c.
Sol
ve 2
2 �
p�
�12
.
22 �
p�
�12
Orig
inal
equ
atio
n
22 �
p�
22 �
�12
�22
Sub
trac
t 22
fro
m e
ach
side
.
p�
�34
Sim
plify
.
Th
e so
luti
on i
s �
34.
Sol
ve e
ach
eq
uat
ion
.Th
en c
hec
k y
our
solu
tion
.
1.x
�12
�6
�6
2.z
�2
��
13�
153.
�17
�b
�4
�21
4.s
�(�
9) �
716
5.�
3.2
��
�(�
0.2)
�3
6.�
�x
�1
7.19
�h
��
4�
238.
�12
�k
�24
�36
9.j
�1.
2 �
2.8
1.6
10.b
�80
��
80�
160
11.m
�(�
8) �
210
12.w
��
�
Wri
te a
n e
qu
atio
n f
or e
ach
pro
ble
m.T
hen
sol
ve t
he
equ
atio
n a
nd
ch
eck
th
eso
luti
on.
13.T
wel
ve a
dded
to
a n
um
ber
equ
als
18.F
ind
the
nu
mbe
r.n
�12
�18
;6
14.W
hat
nu
mbe
r in
crea
sed
by 2
0 eq
ual
s �
10?
n�
20 �
�10
;�
30
15.T
he
sum
of
a n
um
ber
and
fift
y eq
ual
s ei
ghty
.Fin
d th
e n
um
ber.
n�
50 �
80;
30
16.W
hat
nu
mbe
r pl
us
one-
hal
f is
equ
al t
o fo
ur?
n�
�4;
3
17.T
he
sum
of
a n
um
ber
and
3 is
equ
al t
o �
15.W
hat
is
the
nu
mbe
r?n
�3
��
15;
�18
1 � 21 � 2
7 � 85 � 8
3 � 2
5 � 83 � 8
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
So
lvin
g E
qu
atio
ns
by U
sin
g A
dd
itio
n a
nd
Su
btr
acti
on
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-2
3-2
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 3-2)
© Glencoe/McGraw-Hill A6 Glencoe Algebra 1
Skil
ls P
ract
ice
So
lvin
g E
qu
atio
ns
by U
sin
g A
dd
itio
n a
nd
Su
btr
acti
on
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-2
3-2
©G
lenc
oe/M
cGra
w-H
ill14
5G
lenc
oe A
lgeb
ra 1
Lesson 3-2
Sol
ve e
ach
eq
uat
ion
.Th
en c
hec
k y
our
solu
tion
.
1.y
�7
�8
152.
w�
14 �
�8
�22
3.p
�4
�6
104.
�13
�5
�x
�18
5.98
�b
�34
646.
y�
32 �
�1
31
7.s
�(�
28)
�0
288.
y�
(�10
) �
616
9.�
1 �
s�
(�19
)18
10.j
�(�
17)
�36
19
11.1
4 �
d�
(�10
)24
12.u
�(�
5) �
�15
�10
13.1
1 �
�16
�y
2714
.c�
(�3)
�10
097
15.4
7 �
w�
(�8)
3916
.x�
(�74
) �
�22
�96
17.4
�(�
h)
�68
6418
.�56
�20
�(�
e)�
76
Wri
te a
n e
qu
atio
n f
or e
ach
pro
ble
m.T
hen
sol
ve t
he
equ
atio
n a
nd
ch
eck
you
rso
luti
on.
19.A
nu
mbe
r de
crea
sed
by 1
4 is
�46
.Fin
d th
e n
um
ber.
n�
14 �
�46
;�
32
20.T
hir
teen
su
btra
cted
fro
m a
nu
mbe
r is
�5.
Fin
d th
e n
um
ber.
n�
13 �
�5;
8
21.T
he
sum
of
a n
um
ber
and
67 i
s eq
ual
to
�34
.Fin
d th
e n
um
ber.
n�
67 �
�34
;�
101
22.W
hat
nu
mbe
r m
inu
s 28
equ
als
�2?
n�
28 �
�2;
26
23.A
nu
mbe
r pl
us
�73
is
equ
al t
o 27
.Wh
at i
s th
e n
um
ber?
n�
(�73
) �
27;
100
24.A
nu
mbe
r pl
us
�17
equ
als
�1.
Fin
d th
e n
um
ber.
n�
(�17
) �
�1;
16
25.W
hat
nu
mbe
r le
ss 5
is
equ
al t
o �
39?
n�
5 �
�39
;�
34
©G
lenc
oe/M
cGra
w-H
ill14
6G
lenc
oe A
lgeb
ra 1
Sol
ve e
ach
eq
uat
ion
.Th
en c
hec
k y
our
solu
tion
.
1.d
�8
�17
252.
v�
12 �
�5
�17
3.b
�2
��
11�
9
4.�
16 �
s�
71�
875.
29 �
a�
7610
56.
�14
�y
��
212
7.8
�(�
c) �
1�
78.
78 �
r�
�15
�93
9.f
�(�
3) �
�9
�6
10.4
.2 �
n�
7.3
�3.
111
.w�
1.9
��
2.5
�4.
412
.4.6
�(�
b) �
�0.
4�
5
13.y
�(�
1.5)
�0.
5�
114
.a�
0.13
��
0.58
�0.
4515
.k�
(�4.
21)
��
19�14
.79
16.r
��
17.
�q
�18
.�
h�
�
19.
�x
��
�20
.y�
��
21.�
�(�
n)
��
Wri
te a
n e
qu
atio
n f
or e
ach
pro
ble
m.T
hen
sol
ve t
he
equ
atio
n a
nd
ch
eck
you
rso
luti
on.
22.W
hat
nu
mbe
r m
inu
s 9
is e
qual
to
�18
?n
�9
��
18;
�9
23.A
nu
mbe
r pl
us
15 e
qual
s �
12.W
hat
is
the
nu
mbe
r?n
�15
��
12;
�27
24.T
he
sum
of
a n
um
ber
and
�3
is e
qual
to
�91
.Fin
d th
e n
um
ber.
n�
(�3)
��
91;
�88
25.N
egat
ive
seve
nte
en e
qual
s 63
plu
s a
nu
mbe
r.W
hat
is
the
nu
mbe
r?�
17 �
63 �
n;
�80
26.T
he
sum
of
neg
ativ
e 14
,a n
um
ber,
and
6 is
�5.
Wh
at i
s th
e n
um
ber?
�14
�n
�6
��
5;3
27.W
hat
nu
mbe
r pl
us
one
hal
f is
equ
al t
o th
ree
eigh
ths?
n�
�;
�
HIS
TORY
For
Exe
rcis
es 2
8 an
d 2
9,u
se t
he
foll
owin
g in
form
atio
n.
Gal
ileo
Gal
ilei
was
bor
n i
n 1
564.
Man
y ye
ars
late
r,in
164
2,S
ir I
saac
New
ton
was
bor
n.
28.W
rite
an
add
itio
n e
quat
ion
to
repr
esen
t th
e si
tuat
ion
.15
64 �
y�
1642
29.H
ow m
any
year
s af
ter
Gal
ileo
was
bor
n w
as I
saac
New
ton
bor
n?
78
HU
RR
ICA
NES
For
Exe
rcis
es 3
0 an
d 3
1,u
se t
he
foll
owin
g in
form
atio
n.
Th
e da
y af
ter
a h
urr
ican
e,th
e ba
rom
etri
c pr
essu
re i
n a
coa
stal
tow
n h
as r
isen
to
29.7
in
ches
of
mer
cury
,wh
ich
is
2.9
inch
es o
f m
ercu
ry h
igh
er t
han
th
e pr
essu
re w
hen
th
eey
e of
th
e h
urr
ican
e pa
ssed
ove
r.
30.W
rite
an
add
itio
n e
quat
ion
to
repr
esen
t th
e si
tuat
ion
.b
�2.
9 �
29.7
31.W
hat
was
th
e ba
rom
etri
c pr
essu
re w
hen
th
e ey
e pa
ssed
ove
r?26
.8 in
.of
mer
cury
1 � 83 � 8
1 � 2
7 � 247 � 12
7 � 81 � 20
3 � 44 � 5
5 � 67 � 12
1 � 4
1 � 152 � 5
1 � 31 � 9
2 � 35 � 9
7 � 109 � 10
1 � 5
Pra
ctic
e (
Ave
rag
e)
So
lvin
g E
qu
atio
ns
by U
sin
g A
dd
itio
n a
nd
Su
btr
acti
on
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-2
3-2
Answers (Lesson 3-2)
© Glencoe/McGraw-Hill A7 Glencoe Algebra 1
An
swer
s
Readin
g t
o L
earn
Math
em
ati
csS
olv
ing
Eq
uat
ion
s by
Usi
ng
Ad
dit
ion
an
d S
ub
trac
tio
n
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-2
3-2
©G
lenc
oe/M
cGra
w-H
ill14
7G
lenc
oe A
lgeb
ra 1
Lesson 3-2
Pre-
Act
ivit
yH
ow c
an e
qu
atio
ns
be
use
d t
o co
mp
are
dat
a?
Rea
d th
e in
trod
uct
ion
to
Les
son
3-2
at
the
top
of p
age
128
in y
our
text
book
.
In t
he
equ
atio
n m
�66
�5,
the
nu
mbe
r 5
repr
esen
ts
the
dif
fere
nce
bet
wee
n t
he
per
cen
t o
f g
row
th f
or
med
ical
as
sist
ants
an
d t
he
per
cen
t o
f g
row
th f
or
trav
el a
gen
ts,
and
the
nu
mbe
r 66
rep
rese
nts
the
rate
of
gro
wth
fo
r tr
avel
ag
ents
.
Rea
din
g t
he
Less
on
1.T
o so
lve
x�
17 �
46 u
sin
g th
e S
ubt
ract
ion
Pro
pert
y of
Equ
alit
y,yo
u w
ould
su
btra
ct
from
eac
h s
ide.
2.T
o so
lve
y�
9 �
�30
usi
ng
the
Add
itio
n P
rope
rty
of E
qual
ity,
you
wou
ld a
dd
to e
ach
sid
e.
3.W
rite
an
equ
atio
n t
hat
you
cou
ld s
olve
by
subt
ract
ing
32 f
rom
eac
h s
ide.
Sam
ple
an
swer
:m
�32
�50
4.A
stu
den
t u
sed
the
Su
btra
ctio
n P
rope
rty
of E
qual
ity
to s
olve
an
equ
atio
n.E
xpla
in w
hy
itw
ould
als
o be
pos
sibl
e to
use
th
e A
ddit
ion
Pro
pert
y of
Equ
alit
y to
sol
ve t
he
equ
atio
n.
Su
btr
acti
ng
on
e n
um
ber
fro
m a
no
ther
giv
es t
he
sam
e re
sult
as
add
ing
the
op
po
site
of
the
nu
mb
er t
hat
was
su
btr
acte
d.
Hel
pin
g Y
ou
Rem
emb
er
5.E
xpla
in h
ow y
ou d
ecid
e w
het
her
to
use
th
e A
ddit
ion
Pro
pert
y or
th
e S
ubt
ract
ion
Pro
pert
y of
Equ
alit
y to
sol
ve a
n e
quat
ion
.S
amp
le a
nsw
er:
If t
he
giv
en e
qu
atio
n h
as a
nu
mb
er a
dd
ed t
o t
he
vari
able
,th
en u
se t
he
Su
btr
acti
on
Pro
per
ty o
f E
qu
alit
y.If
th
e eq
uat
ion
has
a n
um
ber
su
btr
acte
d f
rom
th
e va
riab
le,t
hen
use
th
e A
dd
itio
nP
rop
erty
of
Eq
ual
ity.
917
©G
lenc
oe/M
cGra
w-H
ill14
8G
lenc
oe A
lgeb
ra 1
Co
un
tin
g-O
ff P
uzz
les
Sol
ve e
ach
pu
zzle
.
1.T
wen
ty-f
ive
peop
le a
re s
tan
din
g in
a c
ircl
e.S
tart
ing
wit
h p
erso
n 1
,th
ey c
oun
t of
f fr
om
1 to
7 a
nd
then
sta
rt o
ver
wit
h 1
.Eac
h
pers
on w
ho
says
“7”
drop
s ou
t of
th
e ci
rcle
.W
ho
is t
he
last
per
son
lef
t?n
um
ber
15
2.F
orty
peo
ple
stan
d in
a c
ircl
e.T
hey
cou
nt
off
so t
hat
eve
ry t
hir
d pe
rson
dro
ps o
ut.
Wh
ich
tw
o pe
ople
are
th
e la
st o
nes
lef
t?13
th a
nd
28t
h p
eop
le
3.O
nly
hal
f of
th
e 30
stu
den
ts i
n
Sh
aron
’s c
lass
can
go
on a
fie
ld
trip
.Sh
aron
arr
ange
s th
e bo
ys
and
girl
s as
sh
own
.Th
ey c
oun
t of
f fr
om 1
to
9 an
d ev
ery
nin
thpe
rson
dro
ps o
ut
un
til
only
15
peo
ple
are
left
.Wh
o ge
ts t
o go
on
th
e fi
eld
trip
.th
e g
irls
A g
rou
p o
f p
eop
le s
tan
d i
n a
cir
cle
and
cou
nt
off
1,2,
1,2,
1 an
d
so o
n.E
very
sec
ond
per
son
dro
ps
out.
Per
son
nu
mb
er 1
is
the
last
per
son
lef
t.
4.D
raw
a d
iagr
am t
o sh
ow w
hy
the
nu
mbe
r of
peo
ple
in t
he
circ
le m
ust
be
even
.Th
en,e
xpla
in y
our
answ
er.
If t
he
nu
mb
er
is o
dd
,per
son
1 w
ou
ld d
rop
ou
t af
ter
the
firs
t ro
un
d.
5.W
hen
th
e co
un
t re
turn
s to
per
son
nu
mbe
r 1
for
the
firs
t ti
me,
how
man
y pe
ople
hav
e dr
oppe
d ou
t?h
alf
of
the
ori
gin
al n
um
ber
6.F
ind
the
nu
mbe
r of
peo
ple
in t
he
circ
le i
f th
e n
um
ber
is
betw
een
10
and
20.D
o th
e sa
me
if t
he
nu
mbe
r is
bet
wee
n
30 a
nd
40.W
hat
can
you
con
clu
de a
bou
t th
e or
igin
al
nu
mbe
r of
peo
ple?
16;
32;T
he
nu
mb
er m
ust
be
a p
ow
er o
f 2.
G
GG
G
GG
GG
G
GG
GG
G
GB
B
BB
B
BB
BB
BB
BB
B
B1
23
45
67
89
1011
12
13
14
15
1617
1819
2021
2223
2425
2627
28
2930
12
34
56
7
8 9 10
11
1213
1415
1617
18
19
20
2122
23
2425
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-2
3-2
Answers (Lesson 3-2)
© Glencoe/McGraw-Hill A8 Glencoe Algebra 1
Stu
dy G
uid
e a
nd I
nte
rven
tion
So
lvin
g E
qu
atio
ns
by U
sin
g M
ult
iplic
atio
n a
nd
Div
isio
n
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-3
3-3
©G
lenc
oe/M
cGra
w-H
ill14
9G
lenc
oe A
lgeb
ra 1
Lesson 3-3
Solv
e U
sin
g M
ult
iplic
atio
nIf
eac
h s
ide
of a
n e
quat
ion
is
mu
ltip
lied
by
the
sam
en
um
ber,
the
resu
ltin
g eq
uat
ion
is
equ
ival
ent
to t
he
give
n o
ne.
You
can
use
th
e pr
oper
ty t
oso
lve
equ
atio
ns
invo
lvin
g m
ult
ipli
cati
on a
nd
divi
sion
.
Mu
ltip
licat
ion
Pro
per
ty o
f E
qu
alit
yF
or a
ny n
umbe
rs a
, b,
and
c,
if a
�b,
the
n ac
�bc
.
Sol
ve 3
p�
1.
3p
�1
Orig
inal
equ
atio
n
p�
Rew
rite
each
mix
ed n
umbe
r as
an
impr
oper
fra
ctio
n.
�p �
��
�M
ultip
ly e
ach
side
by
.
p�
Sim
plify
.
Th
e so
luti
on i
s .
3 � 7
3 � 7
2 � 7
3 � 22 � 7
7 � 22 � 7
3 � 27 � 2
1 � 21 � 2
1 � 21 � 2
Sol
ve �
n�
16.
�n
�16
Orig
inal
equ
atio
n
�4 ��
n��
�4(
16)
Mul
tiply
eac
h si
de b
y �
4.
n�
�64
Sim
plify
.
Th
e so
luti
on i
s �
64.
1 � 41 � 4
1 � 4Ex
ampl
e1Ex
ampl
e1Ex
ampl
e2Ex
ampl
e2
Exer
cises
Exer
cises
Sol
ve e
ach
eq
uat
ion
.Th
en c
hec
k y
our
solu
tion
.
1.�
�2
�6
2.m
�6
483.
p�
3
4.5
�60
5.�
k�
�2.
510
6.�
��
5
7.�
1h
�4
�8.
�12
��
k8
9.�
1
10.�
3b
�5
�1
11.
m�
1014
12.
��
�1
Wri
te a
n e
qu
atio
n f
or e
ach
pro
ble
m.T
hen
sol
ve t
he
equ
atio
n.
13.O
ne-
fift
h o
f a
nu
mbe
r eq
ual
s 25
.Fin
d th
e n
um
ber.
n�
25;
125
14.W
hat
nu
mbe
r di
vide
d by
2 e
qual
s �
18?
��
18;
�36
15.A
nu
mbe
r di
vide
d by
eig
ht
equ
als
3.F
ind
the
nu
mbe
r.�
3;24
16.O
ne
and
a h
alf
tim
es a
nu
mbe
r eq
ual
s 6.
Fin
d th
e n
um
ber.
1n
�6;
41 � 2
n � 8
n � 2
1 � 5
1 � 41 � 4
p � 52 � 7
7 � 101 � 2
1 � 3
1 � 52 � 5
j � 33 � 2
8 � 31 � 2
5 � 8m � 8
1 � 4y � 12
3 � 51 � 5
1 � 8h � 3
©G
lenc
oe/M
cGra
w-H
ill15
0G
lenc
oe A
lgeb
ra 1
Solv
e U
sin
g D
ivis
ion
To
solv
e eq
uat
ion
s w
ith
mu
ltip
lica
tion
an
d di
visi
on,y
ou c
an a
lso
use
th
e D
ivis
ion
Pro
pert
y of
Equ
alit
y.If
eac
h s
ide
of a
n e
quat
ion
is
divi
ded
by t
he
sam
en
um
ber,
the
resu
ltin
g eq
uat
ion
is
tru
e.
Div
isio
n P
rop
erty
of
Eq
ual
ity
For
any
num
bers
a,
b, a
nd c
, w
ith c
�0,
if a
�b,
the
n �
.b � c
a � c
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
So
lvin
g E
qu
atio
ns
by U
sin
g M
ult
iplic
atio
n a
nd
Div
isio
n
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-3
3-3
Sol
ve 8
n�
64.
8n�
64O
rigin
al e
quat
ion
�D
ivid
e ea
ch s
ide
by 8
.
n�
8S
impl
ify.
Th
e so
luti
on i
s 8.
64 � 88n � 8
Sol
ve �
5n�
60.
�5n
�60
Orig
inal
equ
atio
n
�D
ivid
e ea
ch s
ide
by �
5.
n�
�12
Sim
plify
.
Th
e so
luti
on i
s �
12.
60 � �5
�5n
� �5
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Sol
ve e
ach
eq
uat
ion
.Th
en c
hec
k y
our
solu
tion
.
1.3h
��
42�
142.
8m�
162
3.�
3t�
51�
17
4.�
3r�
�24
85.
8k�
�64
�8
6.�
2m�
16�
8
7.12
h�
48.
�2.
4p�
7.2
�3
9.0.
5j�
510
10.�
25 �
5m�
511
.6m
�15
212
.�1.
5p�
�75
50
Wri
te a
n e
qu
atio
n f
or e
ach
pro
ble
m.T
hen
sol
ve t
he
equ
atio
n.
13.F
our
tim
es a
nu
mbe
r eq
ual
s 64
.Fin
d th
e n
um
ber.
4n�
64;
16
14.W
hat
nu
mbe
r m
ult
ipli
ed b
y �
4 eq
ual
s �
16?
�4n
��
16;
4
15.A
nu
mbe
r ti
mes
eig
ht
equ
als
�36
.Fin
d th
e n
um
ber.
8n�
�36
;�
41 � 2
1 � 2
1 � 3
Answers (Lesson 3-3)
© Glencoe/McGraw-Hill A9 Glencoe Algebra 1
An
swer
s
Skil
ls P
ract
ice
So
lvin
g E
qu
atio
ns
by U
sin
g M
ult
iplic
atio
n a
nd
Div
isio
n
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-3
3-3
©G
lenc
oe/M
cGra
w-H
ill15
1G
lenc
oe A
lgeb
ra 1
Lesson 3-3
Sol
ve e
ach
eq
uat
ion
.Th
en c
hec
k y
our
solu
tion
.
1.12
z�
108
92.
�7t
�49
�7
3.18
e�
�21
6�
124.
�22
�11
v�
2
5.�
6d�
�42
76.
96 �
�24
a�
4
7.�
1664
8.�
914
4
9.�
84 �
�25
210
.��
�13
91
11.
��
13�
5212
.31
��
n�
186
13.�
6 �
z�
914
.q
��
4�
14
15.
p�
�10
�18
16.
�4
17.�
0.4b
�5.
2�
1318
.1.6
m�
�4
�2.
5
Wri
te a
n e
qu
atio
n f
or e
ach
pro
ble
m.T
hen
sol
ve t
he
equ
atio
n.
19.T
he
oppo
site
of
a n
um
ber
is �
9.W
hat
is
the
nu
mbe
r?�
n�
�9;
9
20.F
ourt
een
tim
es a
nu
mbe
r is
�42
.Fin
d th
e n
um
ber.
14n
��
42;
�3
21.E
igh
t ti
mes
a n
um
ber
equ
als
128.
Wh
at i
s th
e n
um
ber?
8n�
128;
16
22.N
egat
ive
twel
ve t
imes
a n
um
ber
equ
als
�13
2.F
ind
the
nu
mbe
r.�
12n
��
132;
11
23.N
egat
ive
eigh
teen
tim
es a
nu
mbe
r is
�54
.Wh
at i
s th
e n
um
ber?
�18
n�
�54
;3
24.O
ne
sixt
h o
f a
nu
mbe
r is
�17
.Fin
d th
e n
um
ber.
n�
�17
;�
102
25.N
egat
ive
thre
e fi
fth
s of
a n
um
ber
is �
15.W
hat
is
the
nu
mbe
r?�
n�
�15
;25
3 � 5
1 � 6
2 � 5a � 10
5 � 9
2 � 72 � 3
1 � 6t � 4
d � 7d � 3
a � 16c � 4
©G
lenc
oe/M
cGra
w-H
ill15
2G
lenc
oe A
lgeb
ra 1
Sol
ve e
ach
eq
uat
ion
.Th
en c
hec
k y
our
solu
tion
.
1.8j
�96
122.
�13
z�
�39
33.
�18
0 �
15m
�12
4.24
3 �
27c
95.
��
8�
726.
��
�8
96
7.�
128.
�6
9.�
4
10.�
1 �
�t
11.�
w�
�9
2412
.�s
�4
�20
13.�
3x�
�14
.a
�15
.h
�
16.5
n�
17.2
.5k
�20
818
.�3.
4e�
�3.
741.
1
19.�
1.7b
�2.
21�
1.3
20.0
.26p
�0.
104
0.4
21.4
.2q
��
3.36
�0.
8
Wri
te a
n e
qu
atio
n f
or e
ach
pro
ble
m.T
hen
sol
ve t
he
equ
atio
n.
22.N
egat
ive
nin
e ti
mes
a n
um
ber
equ
als
�11
7.F
ind
the
nu
mbe
r.�
9n�
�11
7;13
23.N
egat
ive
one
eigh
th o
f a
nu
mbe
r is
�.W
hat
is
the
nu
mbe
r?�
n�
�;
6
24.F
ive
sixt
hs
of a
nu
mbe
r is
�.F
ind
the
nu
mbe
r.n
��
;�
25.2
.7 t
imes
a n
um
ber
equ
als
8.37
.Wh
at i
s th
e n
um
ber?
2.7n
�8.
37;
3.1
26.O
ne
and
one
fou
rth
tim
es a
nu
mbe
r is
on
e an
d on
e th
ird.
Wh
at i
s th
e n
um
ber?
1n
�1
;1
27.P
UB
LISH
ING
Tw
o u
nit
s of
mea
sure
use
d in
pu
blis
hin
g ar
e th
e pi
caan
d th
e po
int.
A p
ica
is o
ne
sixt
h o
f an
in
ch.T
her
e ar
e 12
poi
nts
in
a p
ica,
so P
oin
ts �
12 ·
Pic
as.H
ow m
any
pica
s ar
e eq
uiv
alen
t to
108
poi
nts
?9
pic
as
RO
LLER
CO
AST
ERS
For
Exe
rcis
es 2
8 an
d 2
9,u
se t
he
foll
owin
g in
form
atio
n.
Su
perm
an t
he
Esc
ape
in C
alif
orn
ia i
s th
e fa
stes
t ro
ller
coa
ster
in
th
e w
orld
.Rid
ers
fall
41
5 fe
et i
n 7
sec
onds
.Spe
eds
reac
h a
max
imu
m o
f 10
0 m
iles
per
hou
r.
28.I
f x
repr
esen
ts t
he
aver
age
rate
of
fall
of
the
roll
er c
oast
er,w
rite
an
exp
ress
ion
to
repr
esen
t th
e si
tuat
ion
(H
int:
Use
th
e di
stan
ce f
orm
ula
d�
rt.)
7x�
415
29.W
hat
is
the
aver
age
rate
th
at r
ider
s fa
ll i
n f
eet
per
seco
nd?
abo
ut
59.3
ft/
s
1 � 151 � 3
1 � 4
2 � 35 � 9
5 � 65 � 9
3 � 41 � 8
3 � 4
11 � 2011 � 4
11 � 1011 � 6
5 � 35 � 6
4 � 38 � 5
1 � 23 � 2
3 � 153 � 8
7 � 44 � 7
1 � 6q � 24
2 � 9g � 27
4 � 5a � 15
j� 12
y � 9
Pra
ctic
e (
Ave
rag
e)
So
lvin
g E
qu
atio
ns
by U
sin
g M
ult
iplic
atio
n a
nd
Div
isio
n
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-3
3-3
Answers (Lesson 3-3)
© Glencoe/McGraw-Hill A10 Glencoe Algebra 1
Readin
g t
o L
earn
Math
em
ati
csS
olv
ing
Eq
uat
ion
s by
Usi
ng
Mu
ltip
licat
ion
an
d D
ivis
ion
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-3
3-3
©G
lenc
oe/M
cGra
w-H
ill15
3G
lenc
oe A
lgeb
ra 1
Lesson 3-3
Pre-
Act
ivit
yH
ow c
an e
qu
atio
ns
be
use
d t
o fi
nd
how
lon
g it
tak
es l
igh
t to
rea
chE
arth
?
Rea
d th
e in
trod
uct
ion
to
Les
son
3-3
at
the
top
of p
age
135
in y
our
text
book
.
•In
th
e eq
uat
ion
d�
rt,s
how
n i
n t
he
intr
odu
ctio
n,w
hat
nu
mbe
r is
use
dfo
r r?
for
d?
5,87
0,00
0,00
0,00
0;31
1,11
0,00
0,00
0,00
0•
Wh
at e
quat
ion
cou
ld y
ou u
se t
o fi
nd
the
tim
e it
tak
es l
igh
t to
rea
ch E
arth
from
th
e fa
rth
est
star
in
th
e B
ig D
ippe
r?
5,87
0,00
0,00
0,00
0t�
821,
800,
000,
000,
000
Rea
din
g t
he
Less
on
Com
ple
te t
he
sen
ten
ce a
fter
eac
h e
qu
atio
n t
o te
ll h
ow y
ou w
ould
sol
ve t
he
equ
atio
n.
1.�
16ea
ch s
ide
by
.
2.5x
�12
5ea
ch s
ide
by
,or
mu
ltip
ly e
ach
sid
e by
.
3.�
8k�
96D
ivid
e ea
ch s
ide
by
,or
mu
ltip
ly e
ach
sid
e by
.
4.E
xpla
in h
ow r
ewri
tin
g 4
x�
2as
x
�h
elps
you
sol
ve t
he
equ
atio
n.
It m
akes
it e
asie
r fo
r yo
u t
o s
ee w
hat
nu
mb
er y
ou
nee
d t
o m
ult
iply
by
on
each
sid
e.
Hel
pin
g Y
ou
Rem
emb
er
5.O
ne
way
to
rem
embe
r so
met
hin
g is
to
expl
ain
it
to s
omeo
ne
else
.Wri
te h
ow y
ou w
ould
expl
ain
to
a cl
assm
ate
how
to
solv
e th
e eq
uat
ion
x
�12
.
Sam
ple
an
swer
:M
ult
iply
eac
h s
ide
of
the
equ
atio
n b
y th
e re
cip
roca
l of
so y
ou
can
iso
late
xo
n t
he
left
sid
e.2 � 3
2 � 3
17 � 813 � 3
1 � 81 � 3
��1 8�
�8
�1 5�5
Div
ide
7M
ult
iply
x � 7
©G
lenc
oe/M
cGra
w-H
ill15
4G
lenc
oe A
lgeb
ra 1
Dis
sect
ion
Pu
zzle
s:M
ake
the
Sq
uar
eIn
a d
isse
ctio
n p
uzz
le,y
ou a
re t
o cu
t ap
art
one
figu
re u
sin
g on
lyst
raig
ht
cuts
an
d th
en r
earr
ange
th
e pi
eces
to
mak
e a
new
fig
ure
.U
sual
ly t
he
puzz
le-s
olve
r m
ust
fig
ure
ou
t w
her
e to
mak
e th
e gi
ven
nu
mbe
r of
cu
ts.H
owev
er,f
or t
hes
e pu
zzle
s,th
e cu
t li
nes
are
sh
own
.Yo
u m
ust
dis
cove
r h
ow t
o re
arra
nge
th
e pi
eces
.
Cu
t ap
art
each
fig
ure
.Th
en r
earr
ange
th
e p
iece
s to
for
m a
sq
uar
e.
1. 2. 3. 4.H
int:
Cu
t on
e of
th
e tr
ian
gles
in
to t
wo
piec
es t
o m
ake
this
squ
are.
AA
AA
A
2x2x
2x
x
A
AA
A
AA
AA
B
A
AA
A
B
2x2x
x
x
A
C D
A
C
B
B
D
AB
BB
B
A
BB
BB
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-3
3-3
Answers (Lesson 3-3)
© Glencoe/McGraw-Hill A11 Glencoe Algebra 1
An
swer
s
Stu
dy G
uid
e a
nd I
nte
rven
tion
So
lvin
g M
ult
i-S
tep
Eq
uat
ion
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-4
3-4
©G
lenc
oe/M
cGra
w-H
ill15
5G
lenc
oe A
lgeb
ra 1
Lesson 3-4
Wo
rk B
ackw
ard
Wor
kin
g b
ack
war
dis
on
e of
man
y pr
oble
m-s
olvi
ng
stra
tegi
es t
hat
you
can
use
to
solv
e pr
oble
ms.
To
wor
k ba
ckw
ard,
star
t w
ith
th
e re
sult
giv
en a
t th
e en
d of
apr
oble
m a
nd
un
do e
ach
ste
p to
arr
ive
at t
he
begi
nn
ing
nu
mbe
r.
A n
um
ber
is
div
ided
by
2,an
d t
hen
8 i
s su
btr
acte
d f
rom
the
qu
otie
nt.
Th
e re
sult
is
16.W
hat
is t
he
nu
mb
er?
Sol
ve t
he p
robl
em b
y w
orki
ng b
ackw
ard.
Th
e fi
nal
nu
mbe
r is
16.
Un
dosu
btra
ctin
g 8
by a
ddin
g 8
to g
et 2
4.T
ou
ndo
div
idin
g 24
by
2,m
ult
iply
24
by 2
to g
et 4
8.T
he
orig
inal
nu
mbe
r is
48.
A b
acte
ria
cult
ure
dou
ble
sea
ch h
alf
hou
r.A
fter
3 h
ours
,th
ere
are
6400
bac
teri
a.H
ow m
any
bac
teri
a w
ere
ther
e to
beg
in w
ith
?
Sol
ve t
he
prob
lem
by
wor
kin
g ba
ckw
ard.
Th
e ba
cter
ia h
ave
grow
n f
or 3
hou
rs.S
ince
th
ere
are
2 on
e-ha
lf h
our
peri
ods
in o
ne h
our,
in 3
hou
rsth
ere
are
6 on
e-h
alf
hou
r pe
riod
s.S
ince
th
eba
cter
ia c
ult
ure
has
gro
wn
for
6 t
ime
peri
ods,
ith
as d
oubl
ed 6
tim
es.U
ndo
th
e do
ubl
ing
byh
alvi
ng
the
nu
mbe
r of
bac
teri
a 6
tim
es.
6,40
0 �
��
��
��
6,40
0 �
�10
0
Th
ere
wer
e 10
0 ba
cter
ia t
o be
gin
wit
h.
1 � 641 � 2
1 � 21 � 2
1 � 21 � 2
1 � 2
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Sol
ve e
ach
pro
ble
m b
y w
ork
ing
bac
kw
ard
.
1.A
nu
mbe
r is
div
ided
by
3,an
d th
en 4
is
adde
d to
th
e qu
otie
nt.
Th
e re
sult
is
8.F
ind
the
nu
mbe
r.12
2.A
nu
mbe
r is
mu
ltip
lied
by
5,an
d th
en 3
is
subt
ract
ed f
rom
th
e pr
odu
ct.T
he
resu
lt i
s 12
.F
ind
the
nu
mbe
r.3
3.E
igh
t is
su
btra
cted
fro
m a
nu
mbe
r,an
d th
en t
he
diff
eren
ce i
s m
ult
ipli
ed b
y 2.
Th
e re
sult
is 2
4.F
ind
the
nu
mbe
r.20
4.T
hre
e ti
mes
a n
um
ber
plu
s 3
is 2
4.F
ind
the
nu
mbe
r.7
5.C
AR
REN
TAL
An
gela
ren
ted
a ca
r fo
r $2
9.99
a d
ay p
lus
a on
e-ti
me
insu
ran
ce c
ost
of$5
.00.
Her
bil
l w
as $
124.
96.F
or h
ow m
any
days
did
sh
e re
nt
the
car?
4 d
ays
6.M
ON
EYM
ike
wit
hdr
ew a
n a
mou
nt
of m
oney
fro
m h
is b
ank
acco
un
t.H
e sp
ent
one
fou
rth
for
gas
olin
e an
d h
ad $
90 l
eft.
How
mu
ch m
oney
did
he
wit
hdr
aw?
$120
7.TE
LEV
ISIO
NS
In 1
999,
68%
of
hous
ehol
ds w
ith
TV
’s s
ubsc
ribe
d to
cab
le T
V.If
8,0
00 m
ore
subs
crib
ers
are
adde
d to
th
e n
um
ber
of h
ouse
hol
ds w
ith
cab
le,t
he
tota
l n
um
ber
ofh
ouse
hol
ds w
ith
cab
le T
V w
ould
be
67,6
00,0
00.H
ow m
any
hou
seh
olds
wer
e th
ere
wit
hT
V i
n 1
999?
Sou
rce:
Wor
ld A
lman
ac99
,400
,000
ho
use
ho
lds
©G
lenc
oe/M
cGra
w-H
ill15
6G
lenc
oe A
lgeb
ra 1
Solv
e M
ult
i-St
ep E
qu
atio
ns
To
solv
e eq
uat
ion
s w
ith
mor
e th
an o
ne
oper
atio
n,o
ften
call
ed m
ult
i-st
ep e
qu
atio
ns,
un
do o
pera
tion
s by
wor
kin
g ba
ckw
ard.
Rev
erse
th
e u
sual
orde
r of
ope
rati
ons
as y
ou w
ork.
Sol
ve 5
x�
3 �
23.
5x�
3�
23O
rigin
al e
quat
ion.
5x�
3 �
3�
23 �
3S
ubtr
act
3 fr
om e
ach
side
.
5x�
20S
impl
ify.
�D
ivid
e ea
ch s
ide
by 5
.
x�
4S
impl
ify.
Sol
ve e
ach
eq
uat
ion
.Th
en c
hec
k y
our
solu
tion
.
1.5x
�2
�27
52.
6x�
9 �
273
3.5x
�16
�51
7
4.14
n�
8 �
343
5.0.
6x�
1.5
�1.
85.
56.
p�
4 �
1016
7.16
�23
68.
8 �
�13
209.
�3
��
1380
10.
�10
�7
11.0
.2x
�8
��
230
12.3
.2y
�1.
8 �
31.
5
13.�
4 �
414
.8 �
�12
��
8015
.0 �
10y
�40
4
Wri
te a
n e
qu
atio
n a
nd
sol
ve e
ach
pro
ble
m.
16.F
ind
thre
e co
nse
cuti
ve i
nte
gers
wh
ose
sum
is
96.
n�
(n�
1) �
(n�
2) �
96;
31,3
2,33
17.F
ind
two
con
secu
tive
odd
in
tege
rs w
hos
e su
m i
s 17
6.n
�(n
�2)
�17
6;87
,89
18.
Fin
d th
ree
con
secu
tive
in
tege
rs w
hos
e su
m i
s �
93.
n�
(n�
1) �
(n�
2) �
�93
;�
32,�
31,�
30
k� �
43 � 7
7x�
(�1)
��
�8
4b�
8�
�2
g� �
53n � 12
d�
12�
14
7 � 8
20 � 55x � 5
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
So
lvin
g M
ult
i-S
tep
Eq
uat
ion
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-4
3-4
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 3-4)
© Glencoe/McGraw-Hill A12 Glencoe Algebra 1
Skil
ls P
ract
ice
So
lvin
g M
ult
i-S
tep
Eq
uat
ion
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-4
3-4
©G
lenc
oe/M
cGra
w-H
ill15
7G
lenc
oe A
lgeb
ra 1
Lesson 3-4
Sol
ve e
ach
pro
ble
m b
y w
ork
ing
bac
kw
ard
.
1.A
nu
mbe
r is
div
ided
by
2,an
d th
en t
he
quot
ien
t is
add
ed t
o 8.
Th
e re
sult
is
33.F
ind
the
nu
mbe
r.50
2.T
wo
is s
ubt
ract
ed f
rom
a n
um
ber,
and
then
th
e di
ffer
ence
is
divi
ded
by 3
.Th
e re
sult
is
30.F
ind
the
nu
mbe
r.92
3.A
nu
mbe
r is
mu
ltip
lied
by
2,an
d th
en t
he
prod
uct
is
adde
d to
9.T
he
resu
lt i
s 49
.Wh
atis
th
e n
um
ber?
20
4.A
LLO
WA
NC
EA
fter
Ric
ardo
rec
eive
d h
is a
llow
ance
for
th
e w
eek,
he
wen
t to
th
e m
all
wit
h s
ome
frie
nds
.He
spen
t h
alf
of h
is a
llow
ance
on
a n
ew p
aper
back
boo
k.T
hen
he
bou
ght
him
self
a s
nac
k fo
r $1
.25.
Wh
en h
e ar
rive
d h
ome,
he
had
$5.
00 l
eft.
How
mu
chw
as h
is a
llow
ance
?$1
2.50
Sol
ve e
ach
eq
uat
ion
.Th
en c
hec
k y
our
solu
tion
.
5.5x
�3
�23
46.
4 �
3a�
146
7.2y
�5
�19
7
8.6
�5c
��
29�
79.
8 �
5w�
�37
910
.18
�4v
�42
�6
11.
�8
��
218
12.5
��
1�
1613
.��
4 �
13�
51
14.�
�12
��
711
415
.�
2 �
955
16.
�3
��
1�
28
17.
q�
7 �
820
18.
g�
6 �
�12
�27
19.
z�
8 �
�3
2
20.
m�
2 �
65
21.
�3
1722
.�
25
Wri
te a
n e
qu
atio
n a
nd
sol
ve e
ach
pro
ble
m.
23.T
wic
e a
nu
mbe
r pl
us
fou
r eq
ual
s 6.
Wh
at i
s th
e n
um
ber?
2n�
4 �
6;1
24.S
ixte
en i
s se
ven
plu
s th
ree
tim
es a
nu
mbe
r.F
ind
the
nu
mbe
r.16
�7
�3n
;3
25.F
ind
two
con
secu
tive
in
tege
rs w
hos
e su
m i
s 35
.n
�(n
�1)
�35
;17
,18
26.F
ind
thre
e co
nse
cuti
ve i
nte
gers
wh
ose
sum
is
36.
n�
(n�
1) �
(n�
2) �
36;
11,1
2,13
b�
1�
3c
�5
�4
4 � 5
5 � 22 � 3
3 � 4
w � 7a � 5
d � 6
h � 3x � 4
n � 3
©G
lenc
oe/M
cGra
w-H
ill15
8G
lenc
oe A
lgeb
ra 1
Sol
ve e
ach
pro
ble
m b
y w
ork
ing
bac
kw
ard
.
1.T
hre
e is
add
ed t
o a
nu
mbe
r,an
d th
en t
he
sum
is
mu
ltip
lied
by
4.T
he
resu
lt i
s 16
.Fin
dth
e n
um
ber.
1
2.A
nu
mbe
r is
div
ided
by
4,an
d th
e qu
otie
nt
is a
dded
to
3.T
he
resu
lt i
s 24
.Wh
at i
s th
en
um
ber?
84
3.T
wo
is s
ubt
ract
ed f
rom
a n
um
ber,
and
then
th
e di
ffer
ence
is
mu
ltip
lied
by
5.T
he
resu
ltis
30.
Fin
d th
e n
um
ber.
8
4.B
IRD
WA
TCH
ING
Wh
ile
Mic
hel
le s
at o
bser
vin
g bi
rds
at a
bir
d fe
eder
,on
e fo
urt
h o
f th
ebi
rds
flew
aw
ay w
hen
th
ey w
ere
star
tled
by
a n
oise
.Tw
o bi
rds
left
th
e fe
eder
to
go t
oan
oth
er s
tati
oned
a f
ew f
eet
away
.Th
ree
mor
e bi
rds
flew
in
to t
he
bran
ches
of
a n
earb
ytr
ee.F
our
bird
s re
mai
ned
at
the
feed
er.H
ow m
any
bird
s w
ere
at t
he
feed
er i
nit
iall
y?12
Sol
ve e
ach
eq
uat
ion
.Th
en c
hec
k y
our
solu
tion
.
5.�
12n
�19
�77
�8
6.17
�3f
�14
�1
7.15
t�
4 �
493
8.�
6 �
2�
209.
�3
�15
�48
10.
�6
��
212
11.
y�
�2
12.�
32 �
f�
�17
�25
13.8
�k
��
432
14.
�1
�1
15.
��
942
16.
�16
29
17.
�0.
5 �
2.5
2118
.2.5
g�
0.45
�0.
950.
219
.0.4
m�
0.7
�0.
222.
3
Wri
te a
n e
qu
atio
n a
nd
sol
ve e
ach
pro
ble
m.
20.S
even
les
s th
an f
our
tim
es a
nu
mbe
r eq
ual
s 13
.Wh
at i
s th
e n
um
ber?
4n�
7 �
13;
5
21.F
ind
two
con
secu
tive
odd
in
tege
rs w
hos
e su
m i
s 11
6.n
�(n
�2)
�11
6;57
,59
22.F
ind
two
con
secu
tive
eve
n i
nte
gers
wh
ose
sum
is
126.
n�
(n�
2) �
126;
62,6
4
23.F
ind
thre
e co
nse
cuti
ve o
dd i
nte
gers
wh
ose
sum
is
117.
n�
(n�
2) �
(n�
4) �
117;
37,3
9,41
24.C
OIN
CO
LLEC
TIN
GJu
ng
has
a t
otal
of
92 c
oin
s in
his
coi
n c
olle
ctio
n.T
his
is
8 m
ore
than
th
ree
tim
es t
he
nu
mbe
r of
qu
arte
rs i
n t
he
coll
ecti
on.H
ow m
any
quar
ters
doe
s Ju
ng
hav
e in
his
col
lect
ion
?28
x � 7
3k�
7�
515
�a
�3
r�
13�
12
3 � 83 � 5
7 � 81 � 8
1 � 2
b � 3d
� �4
u � 5
Pra
ctic
e (
Ave
rag
e)
So
lvin
g M
ult
i-S
tep
Eq
uat
ion
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-4
3-4
Answers (Lesson 3-4)
© Glencoe/McGraw-Hill A13 Glencoe Algebra 1
An
swer
s
Readin
g t
o L
earn
Math
em
ati
csS
olv
ing
Mu
lti-
Ste
p E
qu
atio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-4
3-4
©G
lenc
oe/M
cGra
w-H
ill15
9G
lenc
oe A
lgeb
ra 1
Lesson 3-4
Pre-
Act
ivit
yH
ow c
an e
qu
atio
ns
be
use
d t
o es
tim
ate
the
age
of a
n a
nim
al?
Rea
d th
e in
trod
uct
ion
to
Les
son
3-4
at
the
top
of p
age
142
in y
our
text
book
.
•W
rite
th
e eq
uat
ion
8 �
12a
�12
4 in
wor
ds.
Eig
ht
plu
s tw
elve
tim
es a
equ
als
on
e h
un
dre
d t
wen
ty-f
ou
r.•
How
man
y op
erat
ion
s ar
e in
volv
ed i
n t
he
equ
atio
n?
two
Rea
din
g t
he
Less
on
1.W
hat
doe
s th
e ph
rase
un
do
the
oper
atio
ns
mea
n t
o yo
u?
Giv
e an
exa
mpl
e.
Usi
ng
th
e o
pp
osi
te o
per
atio
ns
in t
he
op
po
site
ord
er u
nd
oes
th
eo
per
atio
ns;
sub
trac
tio
n u
nd
oes
ad
dit
ion
.
2.a.
If w
e u
ndo
ope
rati
ons
in r
ever
se o
f th
e or
der
of o
pera
tion
s,w
hat
ope
rati
ons
do w
e do
firs
t?ad
dit
ion
or
sub
trac
tio
n
b.
Wh
at o
pera
tion
s do
we
do l
ast?
mu
ltip
licat
ion
or
div
isio
n
3.S
upp
ose
you
wan
t to
sol
ve
�6.
a.W
hat
is
the
grou
pin
g sy
mbo
l in
th
e eq
uat
ion
�
6?th
e fr
acti
on
bar
b.
Wh
at i
s th
e fi
rst
step
in
sol
vin
g th
e eq
uat
ion
?M
ult
iply
eac
h s
ide
by 5
.
c.W
hat
is
the
nex
t st
ep i
n s
olvi
ng
the
equ
atio
n?
Su
btr
act
3 fr
om
eac
h s
ide.
4.W
rite
an
equ
atio
n f
or t
he
prob
lem
bel
ow.
Sev
entim
esk
min
usfiv
eeq
uals
nega
tive
fort
y-se
ven
7•
k�
5�
�47
Hel
pin
g Y
ou
Rem
emb
er
5.E
xpla
in w
hy
wor
kin
g ba
ckw
ard
is a
use
ful
stra
tegy
for
sol
vin
g eq
uat
ion
s.
Sam
ple
an
swer
:Yo
u c
an u
nd
o t
he
op
erat
ion
s to
get
bac
k to
th
e va
lue
of
the
vari
able
th
at w
ill m
ake
the
equ
atio
n t
rue.
Th
at v
alu
e is
th
e so
luti
on
.
x�
3�
5
x�
3�
5
©G
lenc
oe/M
cGra
w-H
ill16
0G
lenc
oe A
lgeb
ra 1
Co
nse
cuti
ve In
teg
er P
rob
lem
sM
any
type
s of
pro
blem
s an
d pu
zzle
s in
volv
e th
e id
ea o
f co
nse
cuti
vein
tege
rs.K
now
ing
how
to
repr
esen
t th
ese
inte
gers
alg
ebra
ical
ly c
anh
elp
to s
olve
th
e pr
oble
m.
Fin
d f
our
con
secu
tive
od
d i
nte
gers
wh
ose
sum
is
�80
.
An
odd
in
tege
r ca
n b
e w
ritt
en a
s 2n
�1,
wh
ere
nis
an
y in
tege
r.If
2n
+ 1
is
the
firs
t od
d in
tege
r,th
en a
dd 2
to
get
the
nex
t la
rges
t od
din
tege
r,an
d so
on
.N
ow w
rite
an
equ
atio
n t
o so
lve
this
pro
blem
.(2
n�
1) �
(2n
�3)
�(2
n�
5) �
(2n
�7)
��
80
Wri
te a
n e
qu
atio
n f
or e
ach
pro
ble
m.T
hen
sol
ve.
1.C
ompl
ete
the
solu
tion
to
the
prob
lem
in
th
e ex
ampl
e.
�23
,�21
,�19
,�17
2.F
ind
thre
e co
nse
cuti
ve e
ven
in
tege
rs w
hos
e su
m i
s 13
2.
2n�
(2n
�2)
�(2
n�
4) �
132;
n�
21;
42,4
4,46
3.F
ind
two
con
secu
tive
in
tege
rs w
hos
e su
m i
s 19
.
n�
(n�
1) �
19;
9,10
4.F
ind
two
con
secu
tive
in
tege
rs w
hos
e su
m i
s 10
0.
n�
(n�
1) �
100;
no
so
luti
on
5.T
he
less
er o
f tw
o co
nse
cuti
ve e
ven
in
tege
rs i
s 10
mor
e th
an
one-
hal
f th
e gr
eate
r.F
ind
the
inte
gers
.
2n�
10 �
(2n
�2)
;22
an
d 2
4
6.T
he
grea
ter
of t
wo
con
secu
tive
eve
n i
nte
gers
is
6 le
ss t
han
th
ree
tim
es t
he
less
er.F
ind
the
inte
gers
.
2n�
2 �
3(2n
) �
6;4,
6
7.F
ind
fou
r co
nse
cuti
ve i
nte
gers
su
ch t
hat
tw
ice
the
sum
of
the
two
grea
ter
inte
gers
exc
eeds
th
ree
tim
es t
he
firs
t by
91.
2[(n
�2)
�(n
�3)
] �
3n�
91;
81,8
2,83
,84
8.F
ind
a se
t of
fou
r co
nse
cuti
ve p
osit
ive
inte
gers
su
ch t
hat
th
e gr
eate
st i
nte
ger
in t
he
set
is t
wic
e th
e le
ast
inte
ger
in t
he
set.
n�
3 �
2n;
{3,4
,5,6
}
1 � 2
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-4
3-4
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 3-4)
© Glencoe/McGraw-Hill A14 Glencoe Algebra 1
Stu
dy G
uid
e a
nd I
nte
rven
tion
So
lvin
g E
qu
atio
ns
wit
h t
he
Var
iab
le o
n E
ach
Sid
e
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-5
3-5
©G
lenc
oe/M
cGra
w-H
ill16
1G
lenc
oe A
lgeb
ra 1
Lesson 3-5
Var
iab
les
on
Eac
h S
ide
To
solv
e an
equ
atio
n w
ith
th
e sa
me
vari
able
on
eac
h s
ide,
firs
t u
se t
he
Add
itio
n o
r th
e S
ubt
ract
ion
Pro
pert
y of
Equ
alit
y to
wri
te a
n e
quiv
alen
teq
uat
ion
th
at h
as t
he
vari
able
on
just
on
e si
de o
f th
e eq
uat
ion
.Th
en s
olve
th
e eq
uat
ion
.
Sol
ve 5
y�
8 �
3y�
12.
5y�
8�
3y�
125y
�8
�3y
�3y
�12
�3y
2y�
8�
122y
�8
�8
�12
�8
2y�
20
�
y�
10
Th
e so
luti
on i
s 10
.
20 � 22y � 2
Sol
ve �
11 �
3y�
8y�
1.
�11
�3y
�8y
�1
�11
�3y
�3y
�8y
�1
�3y
�11
�11
y�
1�
11 �
1 �
11y
�1
�1
�12
�11
y
�
�1
�y
Th
e so
luti
on i
s �
1.
1 � 11
1 � 11
11y
� 11�
12�11
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Sol
ve e
ach
eq
uat
ion
.Th
en c
hec
k y
our
solu
tion
.
1.6
�b
�5b
�30
2.5y
�2y
�3y
�2
3.5x
�2
�2x
�10
�4
no
so
luti
on
�4
4.4n
�8
�3n
�2
5.1.
2x�
4.3
�2.
1 �
x 6.
4.4s
�6.
2 �
8.8s
�1.
8
10�
1
7.b
�4
�b
�88
8.k
�5
�k
�1
9.8
�5p
�4p
�1
224
81
10.4
b�
8 �
10 �
2b11
.0.2
x�
8 �
�2
�x
12.3
y�
1.8
�3y
�1.
8
35
all n
um
ber
s
13.�
4 �
3x�
7x�
614
.8 �
4k�
�10
�k
15.2
0 �
a �
10a
�2
�6
2
16.
n�
8 �
n�
217
.y
�8
�9
�y
18.�
4r�
5 �
5 �
4r
�36
17al
l nu
mb
ers
19.�
4 �
3x�
6x�
620
.18
�4k
��
10 �
4k21
.12
�2y
�10
y�
12
no
so
luti
on
32 � 9
3 � 52 � 5
1 � 22 � 31 � 5
1 � 43 � 4
1 � 81 � 2
20 � 11
©G
lenc
oe/M
cGra
w-H
ill16
2G
lenc
oe A
lgeb
ra 1
Gro
up
ing
Sym
bo
lsW
hen
sol
vin
g eq
uat
ion
s th
at c
onta
in g
rou
pin
g sy
mbo
ls,f
irst
use
the
Dis
trib
uti
ve P
rope
rty
to e
lim
inat
e gr
oupi
ng
sym
bols
.Th
en s
olve
.
Sol
ve 4
(2a
�1)
��
10(a
�5)
.
4(2a
�1)
��
10(a
�5)
Orig
inal
equ
atio
n
8a�
4 �
�10
a�
50D
istr
ibut
ive
Pro
pert
y
8a�
4 �
10a
��
10a
�50
�10
aA
dd 1
0ato
eac
h si
de.
18a
�4
�50
Sim
plify
.
18a
�4
�4
�50
�4
Add
4 t
o ea
ch s
ide.
18a
�54
Sim
plify
.
�D
ivid
e ea
ch s
ide
by 1
8.
a�
3S
impl
ify.
Th
e so
luti
on i
s 3.
Sol
ve e
ach
eq
uat
ion
.Th
en c
hec
k y
our
solu
tion
.
1.�
3(x
�5)
�3(
x�
1)2.
2(7
�3t
) �
�t
3.3(
a�
1) �
5 �
3a�
2
�2
�2
all n
um
ber
s
4.75
�9g
�5(
�4
�2g
)5.
5(f
�2)
�2(
3 �
f)6.
4(p
�3)
�36
5�
6
7.18
�3(
2c�
2)8.
3(d
�8)
�3d
9.
5(p
�3)
�9
�3(
p�
2) �
6
2n
o s
olu
tio
n�
12
10.4
(b�
2) �
2(5
�b)
11.1
.2(x
�2)
�2
�x
12.
�
32
�2
13.
�14
.2(4
�2k
) �
10 �
k15
.2(w
�1)
�4
�4(
w�
1)
�4
�6
�1
16.6
(n�
1) �
2(2n
�4)
17.2
[2 �
3(y
�1)
] �
2218
.�4(
r�
2) �
4(2
�4r
)
74
1
19.�
3(x
�8)
�24
20.4
(4 �
4k)
��
10 �
16k
21.6
(2 �
2y)
�5(
2y�
2)
0n
o s
olu
tio
n1
1 � 3
2a�
5�
3a
�8
�12
�y
�8
3 �
y�
4
4 � 7
54 � 1818
a� 18S
tudy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
So
lvin
g E
qu
atio
ns
wit
h t
he
Var
iab
le o
n E
ach
Sid
e
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-5
3-5
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 3-5)
© Glencoe/McGraw-Hill A15 Glencoe Algebra 1
An
swer
s
Skil
ls P
ract
ice
So
lvin
g E
qu
atio
ns
wit
h t
he
Var
iab
le o
n E
ach
Sid
e
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-5
3-5
©G
lenc
oe/M
cGra
w-H
ill16
3G
lenc
oe A
lgeb
ra 1
Lesson 3-5
Ju
stif
y ea
ch s
tep
.
1.4k
�3
�2k
�5
4k�
3 �
2k�
2k�
5 �
2ka.
Su
btr
act
2kfr
om
eac
h s
ide.
2k�
3 �
5b
.S
imp
lify.
2k�
3 �
3 �
5 �
3c.
Ad
d 3
to
eac
h s
ide.
2k�
8d
.S
imp
lify.
�e.
Div
ide
each
sid
e by
2.
k�
4f.
Sim
plif
y.
2.2(
8u�
2) �
3(2u
�7)
16u
�4
�6u
�21
a.D
istr
ibu
tive
Pro
per
ty
16u
�4
�6u
�6u
�21
�6u
b.
Su
btr
act
6ufr
om
eac
h s
ide.
10u
�4
��
21c.
Sim
plif
y.
10u
�4
�4
��
21 �
4d
.S
ub
trac
t 4
fro
m e
ach
sid
e.
10u
��
25e.
Sim
plif
y.
�f.
Div
ide
each
sid
e by
10.
u�
�2.
5g.
Sim
plif
y.
Sol
ve e
ach
eq
uat
ion
.Th
en c
hec
k y
our
solu
tion
.
3.2m
�12
�3m
�31
434.
2h�
8 �
h�
1725
5.7a
�3
�3
�2a
6.4n
�12
�12
�4n
3
7.4x
�9
�7x
�12
�7
8.�
6y�
3 �
3 �
6yn
o s
olu
tio
n
9.5
�3r
�5r
�19
1210
.�9
�8k
�7
�4k
4
11.8
q�
12 �
4(3
�2q
)al
l nu
mb
ers
12.3
(5j
�2)
�2(
3j�
6)�
2
13.6
(�3v
�1)
�5(
�2v
�2)
214
.�7(
2b�
4) �
5(�
2b�
6)�
0.5
or
�
15.3
(8 �
3t)
�5(
2 �
t)1
16.2
(3u
�7)
��
4(3
�2u
)13
17.8
(2f
�2)
�7(
3f�
2)�
618
.5(�
6 �
3d)
�3(
8 �
7d)
�1.
5 o
r �
1
19.6
(w�
1) �
3(3w
�5)
�7
20.7
(�3y
�2)
�8(
3y�
2)
21.
v�
6 �
6 �
v9
22.
�x
�x
��
27 � 2
7 � 85 � 8
1 � 22 � 3
2 � 3
2 � 3
1 � 21 � 2
2 � 3
�25
�10
10u
� 10
8 � 22k � 2
©G
lenc
oe/M
cGra
w-H
ill16
4G
lenc
oe A
lgeb
ra 1
Sol
ve e
ach
eq
uat
ion
.Th
en c
hec
k y
our
solu
tion
.
1.5x
�3
�13
�3x
22.
�4c
�11
�4c
�21
�4
3.1
�s
�6
�6s
14.
14 �
5n�
�4n
�17
5.k
�3
�2
�k
46.
(6 �
z) �
z2
7.3(
�2
�3x
) �
�9x
�4
no
so
luti
on
8.4(
4 �
w)
�3(
2w�
2)1
9.9(
4b�
1) �
2(9b
�3)
10.3
(6 �
5y)
�2(
�5
�4y
)�
4
11.�
5x�
10 �
2 �
(x�
4)�
212
.6 �
2(3j
�2)
�4(
1 �
j)1
13.
t�
t�
3 �
tn
o s
olu
tio
n14
.1.4
f�
1.1
�8.
3 �
f3
15.
x�
�x
�6
16.2
�z
�z
�9
�8
17.
(3g
�2)
�18
.(c
�1)
�(3
c�
5)7
19.
(5 �
2h)
�1
20.
(2m
�16
) �
(2m
�4)
�7 al
l nu
mb
ers
21.3
(d�
8) �
5 �
9(d
�2)
�1
�8
22.2
(a�
8) �
7 �
5(a
�2)
�3a
�19
23.T
wo
thir
ds o
f a
nu
mbe
r re
duce
d by
11
is e
qual
to
4 m
ore
than
th
e n
um
ber.
Fin
d th
en
um
ber.
�45
24.F
ive
tim
es t
he
sum
of
a n
um
ber
and
3 is
th
e sa
me
as 3
mu
ltip
lied
by
1 le
ss t
han
tw
ice
the
nu
mbe
r.W
hat
is
the
nu
mbe
r?18
25.N
UM
BER
TH
EORY
Tri
plin
g th
e gr
eate
r of
tw
o co
nsec
utiv
e ev
en i
nteg
ers
give
s th
e sa
me
resu
lt a
s su
btra
ctin
g 10
fro
m t
he
less
er e
ven
in
tege
r.W
hat
are
th
e in
tege
rs?
�8,
�6
26.G
EOM
ETRY
Th
e fo
rmu
la f
or t
he
peri
met
er o
f a
rect
angl
e is
P�
2��
2w,w
her
e �
isth
e le
ngt
h a
nd
wis
th
e w
idth
.A r
ecta
ngl
e h
as a
per
imet
er o
f 24
in
ches
.Fin
d it
sdi
men
sion
s if
its
len
gth
is
3 in
ches
gre
ater
th
an i
ts w
idth
.4.
5 in
.by
7.5
in.
1 � 31 � 9
1 � 4h � 2
1 � 4
1 � 61 � 3
3 � 4g � 6
1 � 2
1 � 83 � 4
5 � 61 � 2
1 � 62 � 3
3 � 25 � 2
5 � 6
1 � 23 � 4
1 � 2
1 � 3
Pra
ctic
e (
Ave
rag
e)
So
lvin
g E
qu
atio
ns
wit
h t
he
Var
iab
le o
n E
ach
Sid
e
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-5
3-5
Answers (Lesson 3-5)
© Glencoe/McGraw-Hill A16 Glencoe Algebra 1
Readin
g t
o L
earn
Math
em
ati
csS
olv
ing
Eq
uat
ion
s w
ith
th
e V
aria
ble
on
Eac
h S
ide
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-5
3-5
©G
lenc
oe/M
cGra
w-H
ill16
5G
lenc
oe A
lgeb
ra 1
Lesson 3-5
Pre-
Act
ivit
yH
ow c
an a
n e
qu
atio
n b
e u
sed
to
det
erm
ine
wh
en t
wo
pop
ula
tion
sar
e eq
ual
?
Rea
d th
e in
trod
uct
ion
to
Les
son
3-5
at
the
top
of p
age
149
in y
our
text
book
.
In t
he
equ
atio
n 1
2 �
7.6x
�6
�8x
,wh
at d
o 7.
6xan
d 8x
repr
esen
t?
7.6x
rep
rese
nts
th
e in
crea
se (
in m
illio
ns)
in t
he
nu
mb
er o
fm
ale
Inte
rnet
use
rs,a
nd
8x
rep
rese
nts
th
e in
crea
se (
inm
illio
ns)
in t
he
nu
mb
er o
f fe
mal
e In
tern
et u
sers
.
Rea
din
g t
he
Less
on
1.S
upp
ose
you
wan
t to
hel
p a
frie
nd
solv
e 6k
�7
�3k
�8.
Wh
at w
ould
you
adv
ise
her
to
do f
irst
? W
hy?
Su
btr
act
3kfr
om
eac
h s
ide;
afte
r sh
e d
oes
th
at a
nd
sim
plif
ies,
all o
f th
eva
riab
les
will
be
on
th
e le
ft s
ide.
2.W
hen
sol
vin
g 2(
3x�
4)�
3(x
�5)
,wh
y is
it
hel
pfu
l fi
rst
to u
se t
he
Dis
trib
uti
ve P
rope
rty
to r
emov
e th
e gr
oupi
ng
sym
bols
?
On
ce y
ou
hav
e re
mov
ed t
he
gro
up
ing
sym
bo
ls,y
ou
can
tel
l wh
at y
ou
nee
dto
add
or
sub
trac
t to
eac
h s
ide
to g
et a
ll o
f th
e va
riab
les
on
on
e si
de.
3.O
n a
qu
iz,J
ason
sol
ved
thre
e eq
uat
ion
s.H
is t
each
er s
aid
all
the
wor
k w
as c
orre
ct,b
ut
she
aske
d h
im t
o w
rite
sh
ort
sen
ten
ces
to t
ell
wh
at t
he
solu
tion
s w
ere.
In w
hat
fol
low
s,yo
u s
ee t
he
last
equ
atio
n i
n h
is w
ork
for
each
equ
atio
n.W
rite
sen
ten
ces
to d
escr
ibe
the
solu
tion
s.
a.x
��
4T
he
solu
tio
n is
�4.
b.
6m�
6mA
ll n
um
ber
s ar
e so
luti
on
s.c.
12 �
37T
her
e ar
e n
o s
olu
tio
ns.
4.In
Qu
esti
on 3
,on
e of
th
e eq
uat
ion
s Ja
son
sol
ved
was
an
ide
nti
ty.W
hic
h e
quat
ion
was
it?
Exp
lain
how
you
kn
ow.
Th
e o
ne
for
wh
ich
th
e la
st s
tep
was
6m
�6m
;th
e ex
pre
ssio
ns
on
th
e le
ftan
d r
igh
t si
des
are
th
e sa
me.
Hel
pin
g Y
ou
Rem
emb
er
5.A
n e
quat
ion
wit
h v
aria
bles
is
an i
den
tity
wh
en t
he
equ
atio
n i
s al
way
s tr
ue.
In o
ther
wor
ds,t
he
expr
essi
ons
on t
he
left
an
d ri
ght
side
s al
way
s h
ave
the
sam
e va
lue.
Loo
k u
pth
e w
ord
iden
tity
in t
he
dict
ion
ary.
Wri
te a
ll t
he
defi
nit
ion
s th
at a
re s
imil
ar t
o th
em
ath
emat
ical
def
init
ion
.S
ee s
tud
ents
’wo
rk.
©G
lenc
oe/M
cGra
w-H
ill16
6G
lenc
oe A
lgeb
ra 1
Iden
titi
esA
n e
quat
ion
th
at i
s tr
ue
for
ever
y va
lue
of t
he
vari
able
is
call
ed a
nid
enti
ty.W
hen
you
try
to
solv
e an
ide
nti
ty,y
ou e
nd
up
wit
h a
stat
emen
t th
at i
s al
way
s tr
ue.
Her
e is
an
exa
mpl
e.
Sol
ve 8
�(5
�6x
) �
3(1
�2x
).
8 �
(5 �
6x)
�3(
1 �
2x)
8 �
5 �
(�6x
)�
3(1
�2x
)
8 �
5 �
6x�
3 �
6x
3 �
6x�
3 �
6x
Sta
te w
het
her
eac
h e
qu
atio
n i
s an
id
enti
ty.I
f it
is
not
,fin
d i
ts s
olu
tion
.
1.2(
2 �
3x)
�3(
3 �
x) �
42.
5(m
�1)
�6
�3(
4 �
m)
�(2
m�
1)
x�
�1
iden
tity
3.(5
t�
9) �
(3t
�13
) �
2(11
�t)
4.14
�(6
�3c
) �
4c �
c
iden
tity
no
so
luti
on
5.3y
�2(
y�
19)
�9y
�3(
9 �
y)6.
3(3h
�1)
�4(
h�
3)
y�
�1
h�
3
7.U
se t
he
tru
e eq
uat
ion
3x
�2
�3x
�2
to c
reat
e an
ide
nti
ty o
f yo
ur
own
.
Sam
ple
an
swer
: 6x
�4
�2(
3x�
2)
8.U
se t
he
fals
e eq
uat
ion
1 �
2 to
cre
ate
an e
quat
ion
wit
h n
o so
luti
on.
Sam
ple
an
swer
: 2x
�1
�2x
�2
9.C
reat
e an
equ
atio
n w
hos
e so
luti
on i
s x
�3.
Sam
ple
an
swer
: 3x
�2(
x�
1) �
20
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-5
3-5
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 3-5)
© Glencoe/McGraw-Hill A17 Glencoe Algebra 1
An
swer
s
Stu
dy G
uid
e a
nd I
nte
rven
tion
Rat
ios
and
Pro
po
rtio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-6
3-6
©G
lenc
oe/M
cGra
w-H
ill16
7G
lenc
oe A
lgeb
ra 1
Lesson 3-6
Rat
ios
and
Pro
po
rtio
ns
A r
atio
is a
com
pari
son
of
two
nu
mbe
rs b
y di
visi
on.T
he
rati
o
of x
to y
can
be
expr
esse
d as
xto
y,x
:yor
.R
atio
s ar
e u
sual
ly e
xpre
ssed
in
sim
ples
t fo
rm.
An
equ
atio
n s
tati
ng
that
tw
o ra
tios
are
equ
al i
s ca
lled
a p
rop
orti
on.T
o de
term
ine
wh
eth
ertw
o ra
tios
for
m a
pro
port
ion
,exp
ress
bot
h r
atio
s in
sim
ples
t fo
rm o
r ch
eck
cros
s pr
odu
cts.
x � y
Det
erm
ine
wh
eth
er t
he
rati
os
and
fo
rm a
pro
por
tion
.
�w
hen
exp
ress
ed i
n s
impl
est
form
.
�w
hen
exp
ress
ed i
n s
impl
est
form
.
Th
e ra
tios
an
d fo
rm a
pro
port
ion
beca
use
th
ey a
re e
qual
wh
en e
xpre
ssed
in
sim
ples
t fo
rm.
12 � 1824 � 36
2 � 312 � 18
2 � 324 � 36
12 � 1824 � 36
Use
cro
ss p
rod
uct
s to
det
erm
ine
wh
eth
er
and
fo
rm a
pro
por
tion
.
�W
rite
the
prop
ortio
n.
10(4
5) �
18(2
5)C
ross
pro
duct
s
450
�45
0S
impl
ify.
Th
e cr
oss
prod
uct
s ar
e eq
ual
,so
�.
Sin
ce t
he
rati
os a
re e
qual
,th
ey f
orm
apr
opor
tion
.
25 � 4510 � 18
25 � 4510 � 18
25 � 4510 � 18
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Use
cro
ss p
rod
uct
s to
det
erm
ine
wh
eth
er e
ach
pai
r of
rat
ios
form
s a
pro
por
tion
.
1.,
2.,
3.,
yes
no
no
4.,
5.,
6.,
no
no
yes
7.,
8.,
9.,
yes
yes
yes
10.2
:3,2
0:3
011
.5 t
o 9,
25 t
o 45
12.
,
yes
yes
yes
13.5
:5,3
0:2
014
.18
to 2
4,50
to
7515
.100
:75,
44:3
3
no
no
yes
16.
,17
.,
18.
,
yes
yes
yes
0.45
� 0.9
0.1
� 0.2
6 � 81.
5�2
1 � 200.
05�
1
9 � 872 � 64
20 � 3014 � 21
9 � 1215 � 20
5� 10
00.
1�2
12 � 274 � 9
3 � 1612 � 32
15 � 2025 � 36
25 � 4910 � 20
10 � 155 � 8
16 � 321 � 2
©G
lenc
oe/M
cGra
w-H
ill16
8G
lenc
oe A
lgeb
ra 1
Solv
e Pr
op
ort
ion
sIf
a p
ropo
rtio
n in
volv
es a
var
iabl
e,yo
u ca
n us
e cr
oss
prod
ucts
to
solv
e
the
prop
orti
on.I
n t
he
prop
orti
on
�,x
and
13 a
re c
alle
d ex
trem
esan
d 5
and
10 a
re
calle
d m
ean
s.In
a p
ropo
rtio
n,th
e pr
oduc
t of
the
ext
rem
es is
equ
al t
o th
e pr
oduc
t of
the
mea
ns.
Mea
ns-
Ext
rem
es P
rop
erty
of
Pro
po
rtio
ns
For
any
num
bers
a,
b, c
,an
d d,
if
�,
then
ad
�bc
.
Sol
ve
�.
�O
rigin
al p
ropo
rtio
n
13(x
) �
5(10
)C
ross
pro
duct
s
13x
�50
Sim
plify
.
�D
ivid
e ea
ch s
ide
by 1
3.
x�
3S
impl
ify.
Th
e so
luti
on i
s 3
.
Sol
ve e
ach
pro
por
tion
.
1.�
�12
2.�
3.�
10
4.�
25.
�12
6.�
1
7.�
268.
�9.
�15
10.
�14
11.
�n
o s
olu
tio
n12
.�
�2
13.
�68
14.
�n
o s
olu
tio
n15
.�
6
Use
a p
rop
orti
on t
o so
lve
each
pro
ble
m.
16. M
OD
ELS
To
mak
e a
mod
el o
f th
e G
uad
elou
pe R
iver
bed
,Her
mie
use
d 1
inch
of
clay
for
5 m
iles
of
the
rive
r’s
actu
al l
engt
h.H
is m
odel
riv
er w
as 5
0 in
ches
lon
g.H
ow l
ong
is t
he
Gu
adel
oupe
Riv
er?
250
mi
17.E
DU
CA
TIO
NJo
sh f
inis
hed
24
mat
h p
robl
ems
in o
ne
hou
r.A
t th
at r
ate,
how
man
yh
ours
wil
l it
tak
e h
im t
o co
mpl
ete
72 p
robl
ems?
3 h
12 � 92
� w
�6
24 � k12 � k
15 � 3a
�8
�12
�y
�8
3 �
y�
412 � x
1.5
�x
4 � 124
� b�
2
p � 245 � 8
1 � 218 � 3
3 � d18 � 54
9� y
�1
3 � 63x � 21
8 � x4 � 6
3 � 4x
�1
�4
0.5
�x
0.1
�2
3 � 55 � 3
1 � t2 � 8
�3
�x
11 � 13
11 � 13
50 � 1313
x� 13
10 � 13x � 5
10 � 13x � 5
c � da � b
10 � 13x � 5
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Rat
ios
and
Pro
po
rtio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-6
3-6
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 3-6)
© Glencoe/McGraw-Hill A18 Glencoe Algebra 1
Skil
ls P
ract
ice
Rat
ios
and
Pro
po
rtio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-6
3-6
©G
lenc
oe/M
cGra
w-H
ill16
9G
lenc
oe A
lgeb
ra 1
Lesson 3-6
Use
cro
ss p
rod
uct
s to
det
erm
ine
wh
eth
er e
ach
pai
r of
rat
ios
form
s a
pro
por
tion
.W
rite
yes
or n
o.
1.,
yes
2.,
no
3.,
yes
4.,
yes
5.,
no
6.,
yes
7.,
yes
8.,
no
Sol
ve e
ach
pro
por
tion
.If
nec
essa
ry,r
oun
d t
o th
e n
eare
st h
un
dre
dth
.
9.�
710
.�
15
11.
�6
12.
�18
13.
�10
14.
�3
15.
�21
16.
�18
17.
�8
18.
�63
19.
�42
20.
�44
21.
�13
22.
�48
23.
�16
24.
�60
25.B
OA
TIN
GH
ue’
s bo
at u
sed
5 ga
llon
s of
gas
olin
e in
4 h
ours
.At
this
rat
e,h
ow m
any
gall
ons
of g
asol
ine
wil
l th
e bo
at u
se i
n 1
0 h
ours
?12
.5 g
al
11 � 3022 � x
s � 844 � 21
20 � g5 � 12
27 � 399 � c
n � 6011 � 15
30 � m10 � 14
1 � 97 � b
6 � f42 � 56
y � 696 � 23
36 � s12 � 7
35 � 215 � e
3 � 56 � z
1 � 63 � a
15 � 109 � g
3 � 95 � b
2 � 141 � a
50 � 8512 � 17
21 � 983 � 14
26 � 3813 � 19
42 � 907 � 16
72 � 818 � 9
24 � 286 � 7
7 � 115 � 9
20 � 254 � 5
©G
lenc
oe/M
cGra
w-H
ill17
0G
lenc
oe A
lgeb
ra 1
Use
cro
ss p
rod
uct
s to
det
erm
ine
wh
eth
er e
ach
pai
r of
rat
ios
form
s a
pro
por
tion
.W
rite
yes
or n
o.
1.,
no
2.,
no
3.,
yes
4.,
yes
5.,
yes
6.,
yes
7.,
yes
8.,
no
9.,
no
Sol
ve e
ach
pro
por
tion
.If
nec
essa
ry,r
oun
d t
o th
e n
eare
st h
un
dre
dth
.
10.
�9
11.
�68
12.
�5
13.
�7
14.
�18
15.
�16
16.
�12
17.
�77
18.
�1
19.
�12
220
.�
2421
.�
7
22.
�10
23.
�3
24.
�3
25.
�1
26.
�2.
8827
.�
1.02
28.
�7
29.
�2
30.
�5
31.
�32
.�
333
.�
4
34.P
AIN
TIN
GY
sidr
a pa
ints
a r
oom
th
at h
as 4
00 s
quar
e fe
et o
f w
all
spac
e in
2h
ours
.At
this
rat
e,h
ow l
ong
wil
l it
tak
e h
er t
o pa
int
a ro
om t
hat
has
720
squ
are
feet
of
wal
lsp
ace?
4h
35.V
AC
ATI
ON
PLA
NS
Wal
ker
is p
lan
nin
g a
sum
mer
vac
atio
n.H
e w
ants
to
visi
t P
etri
fied
Nat
ion
al F
ores
t an
d M
eteo
r C
rate
r,A
rizo
na,
the
50,0
00-y
ear-
old
impa
ct s
ite
of a
lar
gem
eteo
r.O
n a
map
wit
h a
sca
le w
her
e 2
inch
es e
qual
s 75
mil
es,t
he
two
area
s ar
e ab
out
1in
ches
apa
rt.W
hat
is
the
dist
ance
bet
wee
n P
etri
fied
Nat
ion
al F
ores
t an
d M
eteo
r
Cra
ter?
abo
ut
56.2
5 m
i
1 � 2
1 � 2
1 � 24 � 7x
�2
�6
3 � 75 � 7
r�
2�
72 � 3
x�
1�
45 � 12
2 � 4m
�1
�8
2� y
�6
3 � 1214 � 6
7� a
�4
3� 0.
516 � n
12 � b3
� 0.72
7� 1.
61v
� 0.23
3 � 45 � 8
m � 63 � 5
5 � 63 � q
2 � 78 � c
7 � 9
2 � a14 � 49
6 � 4g � 16
12 � h6 � 61
z � 173 � 51
35 � x5 � 11
10 � 602 � y
48 � 9y � 3
27 � 162
3 � u4 � w
28 � 49
k � 740 � 56
34 � 23v � 46
30 � 545 � a
3.9
� 0.9
7.6
� 1.8
2.9
� 2.4
1.7
� 1.2
7.14
� 10.9
23.
4� 5.
2
1 � 61.
5�9
72 � 818 � 9
108
� 9912 � 11
36 � 4818 � 24
15 � 663 � 11
52 � 487 � 6
Pra
ctic
e (
Ave
rag
e)
Rat
ios
and
Pro
po
rtio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-6
3-6
Answers (Lesson 3-6)
© Glencoe/McGraw-Hill A19 Glencoe Algebra 1
An
swer
s
Readin
g t
o L
earn
Math
em
ati
csR
atio
s an
d P
rop
ort
ion
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-6
3-6
©G
lenc
oe/M
cGra
w-H
ill17
1G
lenc
oe A
lgeb
ra 1
Lesson 3-6
Pre-
Act
ivit
yH
ow a
re r
atio
s u
sed
in
rec
ipes
?
Rea
d th
e in
trod
uct
ion
to
Les
son
3-6
at
the
top
of p
age
155
in y
our
text
book
.
•H
ow m
any
serv
ings
of
hon
ey f
roze
n y
ogu
rt a
re m
ade
by t
his
rec
ipe?
4 se
rvin
gs
•H
ow m
any
reci
pes
wou
ld b
e n
eede
d to
mak
e en
ough
hon
ey f
roze
n y
ogu
rtfo
r al
l th
e st
ude
nts
in
you
r cl
ass?
See
stu
den
ts’w
ork
.
Rea
din
g t
he
Less
on
1.C
ompl
ete
the
foll
owin
g se
nte
nce
.
A r
atio
is
a co
mpa
riso
n o
f tw
o n
um
bers
by
.
2.D
escr
ibe
two
way
s to
dec
ide
wh
eth
er t
he
sen
ten
ce
�is
a p
ropo
rtio
n.
Exp
ress
th
e ra
tio
s in
sim
ple
st f
orm
to
see
if t
hey
are
eq
ual
.Ch
eck
to s
eew
het
her
th
e cr
oss
pro
du
cts
are
equ
al.
3.F
or e
ach
pro
port
ion
,tel
l w
hat
th
e ex
trem
es a
re a
nd
wh
at t
he
mea
ns
are.
a.�
Ext
rem
es:
Mea
ns:
b.
�E
xtre
mes
:M
ean
s:
4.A
jet
flyi
ng
at a
ste
ady
spee
d tr
avel
ed 8
25 m
iles
in
2 h
ours
.If
you
sol
ved
the
prop
orti
on
�,w
hat
wou
ld t
he
answ
er t
ell
you
abo
ut
the
jet?
ho
w f
ar t
he
jet
trav
eled
in 1
.5 h
Hel
pin
g Y
ou
Rem
emb
er
5.W
rite
how
you
wou
ld e
xpla
in s
olvi
ng
a pr
opor
tion
to
a fr
ien
d w
ho
mis
sed
Les
son
3-6
.
Use
cro
ss p
rod
uct
s.W
rite
an
eq
uat
ion
wit
h t
he
pro
du
ct o
f th
e ex
trem
eso
n t
he
left
sid
e an
d t
he
pro
du
ct o
f th
e m
ean
s o
n t
he
rig
ht
sid
e.T
hen
solv
e th
is s
eco
nd
eq
uat
ion
.
x� 1.
582
5�
2
8 an
d 1
26
and
16
12 � 166 � 8
35 a
nd
614
an
d 1
56 � 15
14 � 35
8 � 202 � 5div
isio
n
©G
lenc
oe/M
cGra
w-H
ill17
2G
lenc
oe A
lgeb
ra 1
An
gle
s o
f a
Tria
ng
leIn
geo
met
ry,m
any
stat
emen
ts a
bou
t ph
ysic
al s
pace
are
pro
ven
to
betr
ue.
Su
ch s
tate
men
ts a
re c
alle
d th
eore
ms.
Her
e ar
e tw
o ex
ampl
es o
fge
omet
ric
theo
rem
s.
a.T
he
sum
of
the
mea
sure
s of
th
e an
gles
of
a tr
ian
gle
is 1
80°.
b.
If t
wo
side
s of
a t
rian
gle
hav
e eq
ual
mea
sure
,th
en t
he
two
angl
esop
posi
te t
hos
e si
des
also
hav
e eq
ual
mea
sure
.
For
eac
h o
f th
e tr
ian
gles
,wri
te a
n e
qu
atio
n a
nd
th
en s
olve
for
x.(
A t
ick
mar
k o
ntw
o or
mor
e si
des
of
a tr
ian
gle
ind
icat
es t
hat
th
e si
des
hav
e eq
ual
mea
sure
.)
1.x
�60
2.
x�
45
3.x
�45
4.
x�
20
5.x
�22
.5
6.x
�10
7.x
�33
8.
x�
100
9.x
�60
10
.x
�50
11.T
wo
angl
es o
f a
tria
ngl
e h
ave
the
sam
e12
.Th
e m
easu
re o
f on
e an
gle
of a
tri
angl
e is
m
easu
re.T
he
sum
of
the
mea
sure
s of
tw
ice
the
mea
sure
of
a se
con
d an
gle.
Th
e th
ese
angl
es i
s on
e-h
alf
the
mea
sure
of
mea
sure
of
the
thir
d an
gle
is 1
2 le
ss t
han
th
e th
ird
angl
e.F
ind
the
mea
sure
s of
th
e su
m o
f th
e ot
her
tw
o.F
ind
the
the
angl
es o
f th
e tr
ian
gle.
mea
sure
s of
th
e an
gles
of
the
tria
ngl
e.30
,30
,12
064
,32
,84
x2x
30°
x
40°
x
x �
15°
3 x
x �
30°
90°
4 x
5x
5x
2xx
x �
30°
x5x
� 1
0°
90°
x
90°
45°
x70
°
50°
x
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-6
3-6
Answers (Lesson 3-6)
© Glencoe/McGraw-Hill A20 Glencoe Algebra 1
Stu
dy G
uid
e a
nd I
nte
rven
tion
Per
cen
t o
f C
han
ge
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-7
3-7
©G
lenc
oe/M
cGra
w-H
ill17
3G
lenc
oe A
lgeb
ra 1
Lesson 3-7
Perc
ent
of
Ch
ang
eW
hen
an
in
crea
se o
r de
crea
se i
n a
n a
mou
nt
is e
xpre
ssed
as
ape
rcen
t,th
e pe
rcen
t is
cal
led
the
per
cen
t of
ch
ange
.If
the
new
nu
mbe
r is
gre
ater
th
an t
he
orig
inal
nu
mbe
r,th
e pe
rcen
t of
ch
ange
is
a p
erce
nt
of i
ncr
ease
.If
the
new
nu
mbe
r is
les
sth
an t
he
orig
inal
nu
mbe
r,th
e pe
rcen
t of
ch
ange
is
the
per
cen
t of
dec
reas
e.
Fin
d t
he
per
cen
t of
in
crea
se.
orig
inal
:48
new
:60
Fir
st,s
ubt
ract
to
fin
d th
e am
oun
t of
incr
ease
.Th
e am
oun
t of
in
crea
se i
s 60
�48
�12
.T
hen
fin
d th
e pe
rcen
t of
in
crea
se b
y u
sin
gth
e or
igin
al n
um
ber,
48,a
s th
e ba
se.
�P
erce
nt p
ropo
rtio
n
12(1
00)
�48
(r)
Cro
ss p
rodu
cts
1200
�48
rS
impl
ify.
�D
ivid
e ea
ch s
ide
by 4
8.
25 �
rS
impl
ify.
Th
e pe
rcen
t of
in
crea
se i
s 25
%.
48r
� 4812
00�
48
r� 10
012 � 48
Fin
d t
he
per
cen
t of
dec
reas
e.or
igin
al:3
0n
ew:2
2
Fir
st,s
ubt
ract
to
fin
d th
e am
oun
t of
decr
ease
.Th
e am
oun
t of
dec
reas
e is
30
�22
�8.
Th
en f
ind
the
perc
ent
of d
ecre
ase
by u
sin
gth
e or
igin
al n
um
ber,
30,a
s th
e ba
se.
�P
erce
nt p
ropo
rtio
n
8(10
0) �
30(r
)C
ross
pro
duct
s
800
�30
rS
impl
ify.
�D
ivid
e ea
ch s
ide
by 3
0.
26�
rS
impl
ify.
Th
e pe
rcen
t of
dec
reas
e is
26
%,o
r ab
out
27%
.
2 � 3
2 � 3
30r
� 3080
0� 30
r� 10
08 � 30
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Sta
te w
het
her
eac
h p
erce
nt
of c
han
ge i
s a
per
cen
t of
in
crea
se o
r a
per
cen
t of
dec
reas
e.T
hen
fin
d e
ach
per
cen
t of
ch
ange
.Rou
nd
to
the
nea
rest
wh
ole
per
cen
t.
1.or
igin
al:5
02.
orig
inal
:90
3.or
igin
al:4
5n
ew:8
0n
ew:1
00n
ew:2
0in
crea
se;
60%
incr
ease
:11
%d
ecre
ase;
56%
4.or
igin
al:7
7.5
5.or
igin
al:1
406.
orig
inal
:135
new
:62
new
:150
new
:90
dec
reas
e;20
%in
crea
se:
7%d
ecre
ase;
33%
7.or
igin
al:1
208.
orig
inal
:90
9.or
igin
al:2
7.5
new
:180
new
:270
new
:25
incr
ease
;50
%in
crea
se:
200%
dec
reas
e;9%
10.o
rigi
nal
:84
11.o
rigi
nal
:12.
512
.ori
gin
al:2
50n
ew:9
8n
ew:1
0n
ew:5
00in
crea
se;
17%
dec
reas
e:20
%in
crea
se;
100%
©G
lenc
oe/M
cGra
w-H
ill17
4G
lenc
oe A
lgeb
ra 1
Solv
e Pr
ob
lem
sD
isco
un
ted
pric
es a
nd
pric
es i
ncl
udi
ng
tax
are
appl
icat
ion
s of
per
cen
tof
ch
ange
.Dis
cou
nt
is t
he
amou
nt
by w
hic
h t
he
regu
lar
pric
e of
an
ite
m i
s re
duce
d.T
hu
s,th
e di
scou
nte
d pr
ice
is a
n e
xam
ple
of p
erce
nt
of d
ecre
ase.
Sal
es t
ax i
s am
oun
t th
at i
s ad
ded
to t
he
cost
of
an i
tem
,so
the
pric
e in
clu
din
g ta
x is
an
exa
mpl
e of
per
cen
t of
in
crea
se.
A c
oat
is o
n s
ale
for
25%
off
th
e or
igin
al p
rice
.If
the
orig
inal
pri
ceof
th
e co
at i
s $7
5,w
hat
is
the
dis
cou
nte
d p
rice
?
Th
e di
scou
nt
is 2
5% o
f th
e or
igin
al p
rice
.
25%
of
$75
�0.
25 �
7525
% �
0.25
�18
.75
Use
a c
alcu
lato
r.
Su
btra
ct $
18.7
5 fr
om t
he
orig
inal
pri
ce.
$75
�$1
8.75
�$5
6.25
Th
e di
scou
nte
d pr
ice
of t
he
coat
is
$56.
25.
Fin
d t
he
fin
al p
rice
of
each
ite
m.W
hen
a d
isco
un
t an
d a
sal
es t
ax a
re l
iste
d,
com
pu
te t
he
dis
cou
nt
pri
ce b
efor
e co
mp
uti
ng
the
tax.
1.C
ompa
ct d
isc:
$16
2.T
wo
con
cert
tic
kets
:$28
3.A
irli
ne
tick
et:$
248.
00D
isco
un
t:15
%S
tude
nt
disc
oun
t:28
%S
upe
rair
dis
cou
nt:
33%
$13.
60$2
0.16
$166
.16
4.S
hir
t:$2
4.00
5.C
D p
laye
r:$1
42.0
06.
Cel
ebri
ty c
alen
dar:
$10.
95S
ales
tax
:4%
Sal
es t
ax:5
.5%
Sal
es t
ax:7
.5%
$24.
96$1
49.8
1$1
1.77
7.C
lass
rin
g:$8
9.00
8.S
oftw
are:
$44.
009.
Vid
eo r
ecor
der:
$110
.95
Gro
up
disc
oun
t:17
%D
isco
un
t:21
%D
isco
un
t:20
%S
ales
tax
:5%
Sal
es t
ax:6
%S
ales
tax
:5%
$77.
56$3
6.85
$93.
20
10.V
IDEO
ST
he
orig
inal
sel
lin
g pr
ice
of a
new
spo
rts
vide
o w
as $
65.0
0.D
ue
to t
he
dem
and
the
pric
e w
as i
ncr
ease
d to
$87
.75.
Wh
at w
as t
he
perc
ent
of i
ncr
ease
ove
r th
e or
igin
alpr
ice?
35%
11.S
CH
OO
LA
hig
h s
choo
l pa
per
incr
ease
d it
s sa
les
by 7
5% w
hen
it
ran
an
iss
ue
feat
uri
ng
a co
nte
st t
o w
in a
cla
ss p
arty
.Bef
ore
the
con
test
iss
ue,
10%
of
the
sch
ool’s
800
stu
den
tsbo
ugh
t th
e pa
per.
How
man
y st
ude
nts
bou
ght
the
con
test
iss
ue?
140
stu
den
ts
12.B
ASE
BA
LLB
aseb
all
tick
ets
cost
$15
for
gen
eral
adm
issi
on o
r $2
0 fo
r bo
x se
ats.
Th
esa
les
tax
on e
ach
tic
ket
is 8
%,a
nd
the
mu
nic
ipal
tax
on
eac
h t
icke
t is
an
add
itio
nal
10%
of t
he
base
pri
ce.W
hat
is
the
fin
al c
ost
of e
ach
typ
e of
tic
ket?
$17.
70;
$23.
60
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Per
cen
t o
f C
han
ge
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-7
3-7
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 3-7)
© Glencoe/McGraw-Hill A21 Glencoe Algebra 1
An
swer
s
Skil
ls P
ract
ice
Per
cen
t o
f C
han
ge
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-7
3-7
©G
lenc
oe/M
cGra
w-H
ill17
5G
lenc
oe A
lgeb
ra 1
Lesson 3-7
Sta
te w
het
her
eac
h p
erce
nt
of c
han
ge i
s a
per
cen
t of
in
crea
se o
r a
per
cen
t of
dec
reas
e.T
hen
fin
d e
ach
per
cen
t of
ch
ange
.Rou
nd
to
the
nea
rest
wh
ole
per
cen
t.
1.or
igin
al:2
52.
orig
inal
:50
new
:10
new
:75
dec
reas
e;60
%in
crea
se;
50%
3.or
igin
al:5
54.
orig
inal
:25
new
:50
new
:28
dec
reas
e;9%
incr
ease
;12
%
5.or
igin
al:5
06.
orig
inal
:90
new
:30
new
:95
dec
reas
e;40
%in
crea
se;
6%
7.or
igin
al:4
88.
orig
inal
:60
new
:60
new
:45
incr
ease
;25
%d
ecre
ase;
25%
Fin
d t
he
tota
l p
rice
of
each
ite
m.
9.dr
ess:
$69.
0010
.bin
der:
$14.
50ta
x:5%
tax:
7%$7
2.45
$15.
52
11.h
ardc
over
boo
k:$2
8.95
12.g
roce
ries
:$47
.52
tax:
6%ta
x:3%
$30.
69$4
8.95
13.f
ille
r pa
per:
$6.0
014
.sh
oes:
$65.
00ta
x:6.
5%ta
x:4%
$6.3
9$6
7.60
15.b
aske
tbal
l:$1
7.00
16.c
once
rt t
icke
ts:$
48.0
0ta
x:6%
ta
x:7.
5%$1
8.02
$51.
60
Fin
d t
he
dis
cou
nte
d p
rice
of
each
ite
m.
17.b
ackp
ack:
$56.
2518
.mon
itor
:$15
0.00
disc
oun
t:20
%di
scou
nt:
50%
$45.
00$7
5.00
19.C
D:$
15.9
920
.sh
irt:
$25.
50di
scou
nt:
20%
disc
oun
t:40
%$1
2.79
$15.
30
21.s
leep
ing
bag:
$125
22.c
offe
e m
aker
:$10
2.00
disc
oun
t:25
%di
scou
nt:
45%
$93.
75$5
6.10
©G
lenc
oe/M
cGra
w-H
ill17
6G
lenc
oe A
lgeb
ra 1
Sta
te w
het
her
eac
h p
erce
nt
of c
han
ge i
s a
per
cen
t of
in
crea
se o
r a
per
cen
t of
dec
reas
e.T
hen
fin
d e
ach
per
cen
t of
ch
ange
.Rou
nd
to
the
nea
rest
wh
ole
per
cen
t.
1.or
igin
al:1
82.
orig
inal
:140
3.or
igin
al:2
00n
ew:1
0n
ew:1
60n
ew:3
20d
ecre
ase;
44%
incr
ease
;14
%in
crea
se;
60%
4.or
igin
al:1
05.
orig
inal
:76
6.or
igin
al:1
28n
ew:2
5n
ew:6
0n
ew:1
20in
crea
se;
150%
dec
reas
e;21
%d
ecre
ase;
6%
7.or
igin
al:1
58.
orig
inal
:98.
69.
orig
inal
:58.
8n
ew:3
5.5
new
:64
new
:65.
7in
crea
se;
137%
dec
reas
e;35
%in
crea
se;
12%
Fin
d t
he
tota
l p
rice
of
each
ite
m.
10.c
oncr
ete
bloc
ks:$
95.0
011
.cri
b:$2
40.0
012
.jac
ket:
$125
.00
tax:
6%ta
x:6.
5%ta
x:5.
5%$1
00.7
0$2
55.6
0$1
31.8
8
13.c
lass
rin
g:$3
25.0
014
.bla
nke
t:$2
4.99
15.k
ite:
$18.
90ta
x:6%
tax:
7%ta
x:5%
$344
.50
$26.
74$1
9.85
Fin
d t
he
dis
cou
nte
d p
rice
of
each
ite
m.
16.d
ry c
lean
ing:
$25.
0017
.com
pute
r ga
me:
$49.
9918
.lu
ggag
e:$1
85.0
0di
scou
nt:
15%
disc
oun
t:25
%di
scou
nt:
30%
$21.
25$3
7.49
$129
.50
19.s
tati
oner
y:$1
2.95
20.p
resc
ript
ion
gla
sses
:$14
921
.pai
r of
sh
orts
:$24
.99
disc
oun
t:10
%di
scou
nt:
20%
disc
oun
t:45
%$1
1.66
$119
.20
$13.
74
Fin
d t
he
fin
al p
rice
of
each
ite
m.
22.t
elev
isio
n:$
375.
0023
.DV
D p
laye
r:$2
69.0
024
.pri
nte
r:$2
55.0
0di
scou
nt:
25%
disc
oun
t:20
%di
scou
nt:
30%
tax:
6%ta
x:7%
tax:
5.5%
$298
.13
$230
.26
$188
.32
25.I
NV
ESTM
ENTS
Th
e pr
ice
per
shar
e of
an
in
tern
et-r
elat
ed s
tock
dec
reas
ed f
rom
$90
per
shar
e to
$36
per
sh
are
earl
y in
200
1.B
y w
hat
per
cen
t di
d th
e pr
ice
of t
he
stoc
kde
crea
se?
60%
26.H
EATI
NG
CO
STS
Cu
stom
ers
of a
uti
lity
com
pan
y re
ceiv
ed n
otic
es i
n t
hei
r m
onth
ly b
ills
that
hea
tin
g co
sts
for
the
aver
age
cust
omer
had
in
crea
sed
125%
ove
r la
st y
ear
beca
use
of a
n u
nu
sual
ly s
ever
e w
inte
r.In
Jan
uar
y of
las
t ye
ar,t
he
Gar
cia’
s pa
id $
120
for
hea
tin
g.W
hat
sh
ould
th
ey e
xpec
t to
pay
th
is J
anu
ary
if t
hei
r bi
ll i
ncr
ease
d by
125
%?
$270
Pra
ctic
e (
Ave
rag
e)
Per
cen
t o
f C
han
ge
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-7
3-7
Answers (Lesson 3-7)
© Glencoe/McGraw-Hill A22 Glencoe Algebra 1
Readin
g t
o L
earn
Math
em
ati
csP
erce
nt
of
Ch
ang
e
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-7
3-7
©G
lenc
oe/M
cGra
w-H
ill17
7G
lenc
oe A
lgeb
ra 1
Lesson 3-7
Pre-
Act
ivit
yH
ow c
an p
erce
nts
des
crib
e gr
owth
ove
r ti
me?
Rea
d th
e in
trod
uct
ion
to
Les
son
3-7
at
the
top
of p
age
160
in y
our
text
book
.
•H
ow m
any
area
cod
es w
ere
in u
se i
n 1
947?
84 a
rea
cod
es•
How
man
y m
ore
area
cod
es w
ere
in u
se i
n 1
999?
201
area
co
des
Rea
din
g t
he
Less
on
1.If
you
use
(or
igin
al a
mou
nt)
— (
new
am
oun
t) t
o fi
nd
the
chan
ge f
or a
per
cen
t of
ch
ange
pr
oble
m,t
hen
th
e pr
oble
m i
nvo
lves
a p
erce
nt
of
(in
crea
se/d
ecre
ase)
.
2.If
you
use
(n
ew a
mou
nt)
— (
orig
inal
am
oun
t) t
o fi
nd
the
chan
ge f
or a
per
cen
t of
ch
ange
pr
oble
m,t
hen
th
e pr
oble
m i
nvo
lves
a p
erce
nt
of
(in
crea
se/d
ecre
ase)
.
Com
ple
te t
he
char
t.
Ori
gin
alN
ew
Per
cen
t In
crea
se o
r A
mo
un
tA
mo
un
tP
erce
nt
Pro
po
rtio
nP
erce
nt
Dec
reas
e?
3.10
13�
incr
ease
4.10
7�
dec
reas
e
5.50
42�
dec
reas
e
6.50
58�
incr
ease
7.W
hen
you
fin
d a
disc
oun
t pr
ice,
do y
ou a
dd t
o or
su
btra
ct f
rom
th
e or
igin
al p
rice
?su
btr
act
Hel
pin
g Y
ou
Rem
emb
er
8.If
you
rem
embe
r on
ly t
wo
thin
gs a
bou
t th
e ra
tio
use
d fo
r fi
ndi
ng
perc
ent
of c
han
ge,w
hat
shou
ld t
hey
be?
Su
btr
act
the
pri
ces,
th
en d
ivid
e b
y th
e o
rig
inal
nu
mb
er.
r�
8 �→ →
chan
ge
�
r�
8 �→ →
chan
ge
�
r�
3 �→ →
chan
ge
�
r�
3 �→ →
chan
ge
�
incr
ease
dec
reas
e
©G
lenc
oe/M
cGra
w-H
ill17
8G
lenc
oe A
lgeb
ra 1
Usi
ng
Per
cen
tU
se w
hat
you
hav
e le
arn
ed a
bou
t p
erce
nt
to s
olve
eac
h p
rob
lem
.
A T
V m
ovie
had
a “
rati
ng”
of 1
5 an
d a
25 “
shar
e.”
Th
e ra
tin
g is
th
e pe
rcen
tage
of t
he
nat
ion
’s t
otal
TV
hou
seh
olds
th
at w
ere
tun
ed i
n t
o th
is s
how
.Th
e sh
are
is t
he
perc
enta
ge o
f h
omes
wit
h T
Vs
turn
ed o
n t
hat
wer
e tu
ned
to
the
mov
ie.
How
man
y T
V h
ouse
hol
ds h
ad t
hei
r T
Vs
turn
ed o
ff a
t th
is t
ime?
To
fin
d ou
t,le
t T
�th
e n
um
ber
of T
V h
ouse
hol
dsan
d x
�th
e n
um
ber
of T
V h
ouse
hol
ds w
ith
th
e T
V o
ff.
Th
en T
�x
�th
e n
um
ber
of T
V h
ouse
hol
ds w
ith
th
e T
V o
n.
Sin
ce 0
.15T
and
0.25
(T�
x) b
oth
rep
rese
nt
the
nu
mbe
r of
hou
seh
olds
tu
ned
to t
he
mov
ie, 0.
15T
�0.
25(T
�x)
0.15
T�
0.25
T�
0.25
x.S
olve
for
x.
0.25
x�
0.10
T
x�
�0.
40T
Fort
y pe
rcen
t of
the
TV
hou
seho
lds
had
thei
r T
Vs
off
whe
n th
e m
ovie
was
air
ed.
An
swer
eac
h q
ues
tion
.
1.D
urin
g th
at s
ame
wee
k,a
spor
ts b
road
cast
had
a r
atin
g of
22.
1 an
d a
43 s
hare
.S
how
tha
t th
e pe
rcen
t of
TV
hou
seho
lds
wit
h th
eir
TV
s of
f w
as a
bout
48.
6%.
0.22
1T�
0.43
T�
0.43
xx
� �0.
486T
2.F
ind
the
perc
ent
of T
V h
ouse
hol
ds w
ith
th
eir
TV
s tu
rned
off
du
rin
g a
show
w
ith
a r
atin
g of
18.
9 an
d a
29 s
har
e.34
.8%
3.S
how
th
at i
f T i
s th
e n
um
ber
of T
V h
ouse
hol
ds,r
is
the
rati
ng,
and
s is
th
e
shar
e,th
en t
he
nu
mbe
r of
TV
hou
seh
olds
wit
h t
he
TV
off
is
.S
olv
e rT
�s
(T�
x)
for
x.
4.If
th
e fr
acti
on o
f TV
hou
seh
olds
wit
h n
o T
V o
n i
s th
en s
how
th
at t
he
frac
tion
of T
V h
ouse
hol
ds w
ith
TV
s on
is
.
5.F
ind
the
perc
ent
of T
V h
ouse
hol
ds w
ith
TV
s on
du
rin
g th
e m
ost
wat
ched
se
rial
pro
gram
in
his
tory
:th
e la
st e
piso
de o
f M
*A*S
*H,w
hic
h h
ad a
60.
3 ra
tin
g an
d a
77 s
har
e.�
78.3
%
6.A
loca
l sta
tion
now
has
a 2
sha
re.E
ach
shar
e is
wor
th $
50,0
00 in
adv
erti
sing
re
venu
e pe
r m
onth
.The
sta
tion
is t
hink
ing
of g
oing
com
mer
cial
fre
e fo
r th
e th
ree
mon
ths
of s
umm
er t
o ga
in m
ore
list
ener
s.W
hat
wou
ld it
s ne
w s
hare
ha
ve t
o be
for
the
last
4 m
onth
s of
the
yea
r to
mak
e m
ore
mon
ey f
or t
he y
ear
than
it w
ould
hav
e m
ade
had
it n
ot g
one
com
mer
cial
fre
e?g
reat
er t
han
3.5
60.3
�
r � s
s –
r�
s
(s�
r)T
�s
0.22
1T�
0.43
T�
�
0.10
T� 0.
25
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-7
3-7
1 �
�r �
s�
r�
Answers (Lesson 3-7)
© Glencoe/McGraw-Hill A23 Glencoe Algebra 1
An
swer
s
Stu
dy G
uid
e a
nd I
nte
rven
tion
So
lvin
g E
qu
atio
ns
and
Fo
rmu
las
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-8
3-8
©G
lenc
oe/M
cGra
w-H
ill17
9G
lenc
oe A
lgeb
ra 1
Lesson 3-8
Solv
e fo
r V
aria
ble
sS
omet
imes
you
may
wan
t to
sol
ve a
n eq
uati
on s
uch
as V
��w
hfo
ron
e of
its
var
iabl
es.F
or e
xam
ple,
if y
ou k
now
th
e va
lues
of
V,w
,an
d h
,th
en t
he
equ
atio
n
��
is m
ore
use
ful
for
fin
din
g th
e va
lue
of �
.If
an e
quat
ion
th
at c
onta
ins
mor
e th
an o
ne
vari
able
is
to b
e so
lved
for
a s
peci
fic
vari
able
,use
th
e pr
oper
ties
of
equ
alit
y to
iso
late
th
esp
ecif
ied
vari
able
on
on
e si
de o
f th
e eq
uat
ion
.
V � wh
Sol
ve 2
x�
4y�
8 fo
r y.
2x�
4y�
82x
�4y
�2x
�8
�2x
�4y
�8
�2x
�
y�
or
Th
e va
lue
of y
is
.2x
�8
�4
2x�
8�
48
�2x
��
4
8 �
2x�
�4
�4y
� �4
Sol
ve 3
m�
n�
km
�8
for
m.
3m�
n�
km�
83m
�n
�km
�km
�8
�km
3m�
n�
km�
�8
3m�
n�
km�
n�
�8
�n
3m�
km�
�8
�n
m(3
�k)
��
8 �
n
�
m�
,or
Th
e va
lue
of m
is
.Sin
ce d
ivis
ion
by
0 is
un
defi
ned
,3 �
k�
0,or
k�
3.
n�
8� 3
�k
n�
8� 3
�k
�8
�n
�3
�k
�8
�n
�3
�k
m(3
�k)
��
3 �
k
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Sol
ve e
ach
eq
uat
ion
or
form
ula
for
th
e va
riab
le s
pec
ifie
d.
1.ax
�b
�c
for
x2.
15x
�1
�y
for
x3.
(x�
f) �
2 �
jfo
r x
x�
,a
0x
�x
�j�
2 �
f
4.xy
�z
�9
for
y5.
x(4
�k)
�p
for
k6.
7x�
3y�
mfo
r y
y�
,x
0k
�4
�,x
0
y�
7.4(
c�
3) �
tfo
r c
8.2x
�b
�c
for
x9.
x(1
�y)
�z
for
x
c�
�3
x�
x�
,y
�1
10.1
6z�
4x�
yfo
r x
11.d
�rt
for
r12
.A�
for
h
x�
r�
,t
0h
�,a
�
b
13.C
�(F
�32
) fo
r F
14.P
�2�
�2w
for
w15
.A�
�wfo
r �
F�
C�
32w
��
�,w
0
A � wP
�2�
�2
9 � 5
5 � 9
2A� a
�b
d � ty
�16
z�
4
h(a
�b)
�� 2z
� 1 �
yc
�b
�2
t � 4
m�
7x�
3p � x
9 �
z�
x
y�
1�
15c
�b
�a
©G
lenc
oe/M
cGra
w-H
ill18
0G
lenc
oe A
lgeb
ra 1
Use
Fo
rmu
las
Man
y re
al-w
orld
pro
blem
s re
quir
e th
e u
se o
f fo
rmu
las.
Som
etim
es s
olvi
ng
a fo
rmu
la f
or a
spe
cifi
ed v
aria
ble
wil
l h
elp
solv
e th
e pr
oble
m.
Th
e fo
rmu
la C
��
dre
pre
sen
ts t
he
circ
um
fere
nce
of
a ci
rcle
,or
the
dis
tan
ce a
rou
nd
th
e ci
rcle
,wh
ere
dis
th
e d
iam
eter
.If
an a
irp
lan
e co
uld
fly
aro
un
dE
arth
at
the
equ
ator
wit
hou
t st
opp
ing,
it w
ould
hav
e tr
avel
ed a
bou
t 24
,900
mil
es.
Fin
d t
he
dia
met
er o
f E
arth
.
C�
�d
Giv
en f
orm
ula
d�
Sol
ve f
or d
.
d�
Use
��
3.14
.
d�
7930
Sim
plify
.
Th
e di
amet
er o
f E
arth
is
abou
t 79
30 m
iles
.
1.G
EOM
ETRY
Th
e vo
lum
e of
a c
ylin
der
Vis
giv
en b
y th
e fo
rmu
la V
��
r2h
,wh
ere
ris
the
radi
us
and
his
th
e h
eigh
t.
a.S
olve
th
e fo
rmu
la f
or h
.h
�
b.
Fin
d th
e h
eigh
t of
a c
ylin
der
wit
h v
olu
me
2500
�fe
et a
nd
radi
us
10 f
eet.
25 f
t
2.W
ATE
R P
RES
SUR
ET
he
wat
er p
ress
ure
on
a s
ubm
erge
d ob
ject
is
give
n b
y P
�64
d,
whe
re P
is t
he p
ress
ure
in p
ound
s pe
r sq
uare
foo
t,an
d d
is t
he d
epth
of
the
obje
ct i
n fe
et.
a.S
olve
th
e fo
rmu
la f
or d
.d
�
b.
Fin
d th
e de
pth
of a
sub
mer
ged
obje
ct if
the
pre
ssur
e is
672
pou
nds
per
squa
re f
oot.
10.5
ft
3.G
RA
PHS
Th
e eq
uat
ion
of
a li
ne
con
tain
ing
the
poin
ts (
a,0)
an
d (0
,b)
is g
iven
by
the
form
ula
�
�1.
a.S
olve
th
e eq
uat
ion
for
y.
y�
b�1
��
b.
Su
ppos
e th
e li
ne
con
tain
s th
e po
ints
(4,
0),a
nd
(0,�
2).I
f x
�3,
fin
d y.
�
4.G
EOM
ETRY
Th
e su
rfac
e ar
ea o
f a
rect
angu
lar
soli
d is
giv
en b
y th
e fo
rmu
la
S�
2�w
�2�
h�
2wh
,wh
ere
��
len
gth
,w�
wid
th,a
nd
h�
hei
ght.
a.S
olve
th
e fo
rmu
la f
or h
.h
�
b.
Th
e su
rfac
e ar
ea o
f a
rect
angu
lar
soli
d w
ith
len
gth
6 c
enti
met
ers
and
wid
th
3 ce
nti
met
ers
is 7
2 sq
uar
e ce
nti
met
ers.
Fin
d th
e h
eigh
t.2
cm
S�
2�w
��
2��
2w
1 � 2
x � a
y � bx � a
P � 64V � �r2
24,9
00�
3.14
C � �
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
So
lvin
g E
qu
atio
ns
and
Fo
rmu
las
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-8
3-8
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 3-8)
© Glencoe/McGraw-Hill A24 Glencoe Algebra 1
Skil
ls P
ract
ice
So
lvin
g E
qu
atio
ns
and
Fo
rmu
las
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-8
3-8
©G
lenc
oe/M
cGra
w-H
ill18
1G
lenc
oe A
lgeb
ra 1
Lesson 3-8
Sol
ve e
ach
eq
uat
ion
or
form
ula
for
th
e va
riab
le s
pec
ifie
d.
1.7t
�x,
for
tt
�2.
e�
wp,
for
pp
�
3.q
�r
�r,
for
rr
�4.
4m�
n�
m,f
or m
m�
5.7a
�b
�15
a,fo
r a
a�
�6.
�5c
�d
�2c
,for
cc
�
7.x
�2y
�1,
for
yy
�8.
m �
3n�
1,fo
r n
n�
9.7f
�g
�5,
for
ff
�10
.ax
�c
�b,
for
xx
�
11.r
t�
2n�
y,fo
r t
t�
12.b
c�
3g�
2k,f
or c
c�
13.k
n�
4f�
9v,f
or n
n�
14.8
c�
6j�
5p,f
or c
c�
15.
�d
,for
xx
�c
�2d
16.
�d
,for
cc
�x
�2d
17.
�q,
for
pp
�5q
�9
18.
�a,
for
bb
�7a
�4z
Wri
te a
n e
qu
atio
n a
nd
sol
ve f
or t
he
vari
able
sp
ecif
ied
.
19.F
ive
mor
e th
an a
nu
mbe
r g
is s
ix l
ess
than
tw
ice
a n
um
ber
h.S
olve
for
g.
g �
5 �
2h�
6;g
�2h
�11
20.O
ne
fou
rth
of
a n
um
ber
qis
th
ree
mor
e th
an t
hre
e ti
mes
a n
um
ber
w.S
olve
for
q.
q�
3w�
3;q
�12
w�
12
21.E
igh
t le
ss t
han
a n
um
ber
sis
th
ree
mor
e th
an f
our
tim
es a
nu
mbe
r t.
Sol
ve f
or s
.
s�
8 �
4t�
3;s
�4t
�11
1 � 4
b�
4z�
7p
�9
�5
x�
c�
2x
�c
�2
5p�
6j�
89v
�4f
�k
2k�
3g�
b2n
�y
�r
b�
c�
a5
�g
�7
1 �
m�
3x
�1
�2
d � 7b � 8
n � 3q � 2
e � wx � 7
©G
lenc
oe/M
cGra
w-H
ill18
2G
lenc
oe A
lgeb
ra 1
Sol
ve e
ach
eq
uat
ion
or
form
ula
for
th
e va
riab
le s
pec
ifie
d.
1.d
�rt
,for
rr
�2.
6w�
y�
2z,f
or w
w�
3.m
x�
4y�
3c,f
or x
x�
4.9s
�5g
��
4u,f
or s
s�
5.ab
�3c
�2d
,for
bb
�6.
2p�
kx�
q,fo
r x
x�
7.m
�a
�a
�c,
for
mm
�c
8.h
�g
�d
,for
hh
�(d
�g
)
9.y
�v
�s,
for
yy
�(s
�v)
10.
a�
q�
k,fo
r a
a�
(k�
q)
11.
�h
,for
xx
�12
.�
c,fo
r b
b�
13.2
w�
y�
7w�
2,fo
r w
w�
14.3
��
y�
5 �
5�,f
or �
��
Wri
te a
n e
qu
atio
n a
nd
sol
ve f
or t
he
vari
able
sp
ecif
ied
.
15.T
hre
e ti
mes
a n
um
ber
spl
us
4 ti
mes
a n
um
ber
yis
1 m
ore
than
6 t
imes
th
e n
um
ber
s.S
olve
for
s.
3s�
4y�
6s�
1;s
�
16.F
ive
tim
es a
nu
mbe
r k
min
us
9 is
tw
o th
irds
of
a n
um
ber
j.S
olve
for
j.
5k�
9 �
j;j�
(5k
�9)
ELEC
TRIC
ITY
For
Exe
rcis
es 1
7 an
d 1
8,u
se t
he
foll
owin
g in
form
atio
n.
Th
e fo
rmu
la f
or O
hm
’s L
aw i
s E
�IR
,wh
ere
Ere
pres
ents
vol
tage
mea
sure
d in
vol
ts,
Ire
pres
ents
cu
rren
t m
easu
red
in a
mpe
res,
and
Rre
pres
ents
res
ista
nce
mea
sure
d in
oh
ms.
17.S
olve
th
e fo
rmu
la f
or R
.R
�
18.S
upp
ose
a cu
rren
t of
0.2
5 am
pere
flo
ws
thro
ugh
a r
esis
tor
con
nec
ted
to a
12-
volt
bat
tery
.W
hat
is
the
resi
stan
ce i
n t
he
circ
uit
?48
oh
ms
MO
TIO
NF
or E
xerc
ises
19
and
20,
use
th
e fo
llow
ing
info
rmat
ion
.
In u
nif
orm
cir
cula
r m
otio
n,t
he
spee
d v
of a
poi
nt
on t
he
edge
of
a sp
inn
ing
disk
is
v�
r,
wh
ere
ris
th
e ra
diu
s of
th
e di
sk a
nd
Tis
th
e ti
me
it t
akes
th
e po
int
to t
rave
l on
ce a
rou
nd
the
circ
le.
19.S
olve
th
e fo
rmu
la f
or r
.r
�
20.S
upp
ose
a m
erry
-go-
rou
nd
is s
pin
nin
g on
ce e
very
3 s
econ
ds.I
f a
poin
t on
th
e ou
tsid
eed
ge h
as a
spe
ed o
f 12
.56
feet
per
sec
ond,
wh
at i
s th
e ra
diu
s of
th
e m
erry
-go-
rou
nd?
(U
se 3
.14
for
�.)
6 ft
Tv
� 2�
2� � T
E � I
3 � 22 � 3
4y�
1�
3
y�
5�
22
�y
�5
2c�
4�
33b
�4
�2
5h�
9�
rrx
�9
�5
4 � 33 � 4
3 � 22 � 3
5 � 22 � 5
3 � 22 � 3
2p�
q�
k2d
�3c
�a
�4u
�5g
�� 9
3c�
4y�
m
2z�
y�
6d � t
Pra
ctic
e (
Ave
rag
e)
So
lvin
g E
qu
atio
ns
and
Fo
rmu
las
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-8
3-8
Answers (Lesson 3-8)
© Glencoe/McGraw-Hill A25 Glencoe Algebra 1
An
swer
s
Readin
g t
o L
earn
Math
em
ati
csS
olv
ing
Eq
uat
ion
s an
d F
orm
ula
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-8
3-8
©G
lenc
oe/M
cGra
w-H
ill18
3G
lenc
oe A
lgeb
ra 1
Lesson 3-8
Pre-
Act
ivit
yH
ow a
re e
qu
atio
ns
use
d t
o d
esig
n r
olle
r co
aste
rs?
Rea
d th
e in
trod
uct
ion
to
Les
son
3-8
at
the
top
of p
age
166
in y
our
text
book
.
Th
e eq
uat
ion
g(1
95 �
h)
�v2
con
tain
s se
vera
l va
riab
les.
Wh
at
nu
mbe
r va
lues
do
you
kn
ow f
or t
hes
e va
riab
les
in t
his
sit
uat
ion
?
32 f
or
gan
d 4
9 fo
rv
Rea
din
g t
he
Less
on
1.S
upp
ose
you
hav
e an
equ
atio
n w
ith
sev
eral
var
iabl
es.Y
ou w
ant
to s
olve
for
a p
arti
cula
rva
riab
le.H
ow d
oes
the
proc
edu
re c
ompa
re w
ith
th
at f
or s
olvi
ng
an e
quat
ion
wit
h ju
ston
e va
riab
le?
How
doe
s th
e so
luti
on c
ompa
re w
ith
th
e so
luti
on f
or a
n e
quat
ion
wit
h o
ne
vari
able
?
Sam
ple
an
swer
: T
he
pro
ced
ure
is b
asic
ally
th
e sa
me.
Yo
u u
se p
rop
erti
eso
f o
per
atio
ns
and
eq
ual
ity
to is
ola
te t
he
vari
able
in w
hic
h y
ou
are
inte
rest
ed. T
he
solu
tio
n w
ill p
rob
ably
co
nta
in v
aria
ble
s in
stea
d o
f ju
st a
nu
mb
er.
2.D
escr
ibe
wh
at d
imen
sion
al a
nal
ysis
in
volv
es.
Sam
ple
an
swer
: Yo
u u
se t
he
un
its
alo
ng
wit
h n
um
ber
val
ues
as
you
do
calc
ula
tio
ns.
Yo
u t
reat
th
e u
nit
s p
rett
y m
uch
th
e sa
me
way
yo
u w
ou
ldva
riab
les.
Fo
r ex
amp
le, y
ou
can
div
ide
them
an
d u
se e
xpo
nen
ts w
ithth
em.
3.W
hat
do
you
hav
e to
be
care
ful
abou
t w
hen
you
use
var
iabl
es i
n d
enom
inat
ors
offr
acti
ons?
You
hav
e to
be
sure
th
at y
ou
do
no
t u
se v
alu
es t
hat
wo
uld
mak
e th
ed
eno
min
ato
r 0.
Hel
pin
g Y
ou
Rem
emb
er
4.W
hen
you
giv
e th
e di
men
sion
s of
a r
ecta
ngl
e,yo
u h
ave
to t
ell
how
man
y u
nit
s lo
ng
it i
san
d h
ow m
any
un
its
wid
e it
is.
How
can
th
is h
elp
you
rem
embe
r w
hat
dim
ensi
onal
anal
ysis
in
volv
es.
Sam
ple
an
swer
: K
eep
th
e w
ord
s d
imen
sio
nan
d u
nit
in m
ind
. In
dim
ensi
on
al a
nal
ysis
, yo
u in
clu
de
un
its
for
dim
ensi
on
s in
cal
cula
tio
ns.
1 � 2
©G
lenc
oe/M
cGra
w-H
ill18
4G
lenc
oe A
lgeb
ra 1
Dr.
Ber
nar
do
Ho
uss
ay
Eve
n t
hou
gh r
esea
rch
ers
hav
e be
en s
tudy
ing
the
dise
ase
dia
bete
sm
elli
tus
for
hu
ndr
eds
of y
ears
,sci
enti
sts
hav
e on
ly r
ecen
tly
disc
over
edth
e ca
use
of
the
dise
ase
and
deve
lope
d m
eth
ods
for
redu
cin
g it
sse
veri
ty.D
r.B
ern
ardo
Hou
ssay
,an
Arg
enti
ne
phys
iolo
gist
,was
on
e of
the
pion
eers
of
this
mor
e m
oder
n r
esea
rch
.He
stu
died
th
e re
lati
onsh
ipbe
twee
n d
iabe
tes
and
the
pitu
itar
y gl
and,
and
in 1
947
beca
me
the
firs
tL
atin
Am
eric
an t
o w
in t
he
Nob
el P
rize
in
Med
icin
e an
d P
hys
iolo
gy.
Tho
ugh
ther
e is
no
cure
for
dia
bete
s,sp
ecif
ic d
iets
and
exe
rcis
e ca
n he
lppe
ople
con
trol
the
dis
ease
.The
Am
eric
an D
iabe
tes
Ass
ocia
tion
(A
DA
)ha
s he
lped
est
abli
sh f
lexi
ble
diet
ary
guid
elin
es f
or c
onsu
mer
s to
fol
low
.T
hese
gui
deli
nes
incl
ude
som
e of
the
fol
low
ing
gene
ral
nutr
itio
n ru
les.
•Fa
t in
take
sh
ould
be
equ
al t
o or
les
s th
an 3
0% o
f da
ily
calo
ries
.
•S
atu
rate
d fa
t in
take
sh
ould
be
equ
al t
o or
les
s th
an 1
0% o
f da
ily
calo
ries
.
•P
rote
in s
hou
ld b
e li
mit
ed t
o 10
% t
o 20
% o
f da
ily
calo
ries
.Per
son
ssh
owin
g th
e in
itia
l si
gns
of d
iabe
tes-
indu
ced
kidn
ey d
isea
se s
hou
ldli
mit
pro
tein
to
10%
of
dail
y ca
lori
es.
•C
hol
este
rol
inta
ke s
hou
ld b
e 30
0 m
illi
gram
s or
les
s da
ily.
Ref
er t
o th
e in
form
atio
n a
bov
e fo
r E
xerc
ises
1–4
.
1.R
ober
t co
nsu
med
210
0 ca
lori
es o
n T
ues
day.
His
fat
in
take
tot
aled
70 g
ram
s,an
d of
th
at 7
0 gr
ams,
14 w
ere
satu
rate
d.
a.W
hat
per
cen
tage
of
his
cal
orie
con
sum
ptio
n w
as f
at,a
nd
wh
atpe
rcen
tage
of
that
fat
was
sat
ura
ted?
(T
o fi
nd
the
perc
enta
ge o
fca
lori
es f
rom
fat
,mu
ltip
ly t
he
nu
mbe
r of
fat
gra
ms
by 9
bef
ore
divi
din
g by
th
e n
um
ber
of c
alor
ies.
) 30
%;
20%
b.
Did
Rob
ert
stay
wit
hin
th
e re
com
men
ded
allo
wan
ce o
f fa
ts?
yes
2.A
nn
a's
chol
este
rol
inta
ke w
as 3
30 m
illi
gram
s on
Su
nda
y.B
y w
hat
perc
enta
ge d
oes
she
nee
d to
red
uce
her
ch
oles
tero
l co
nsu
mpt
ion
to
rem
ain
wit
hin
th
e gu
idel
ines
? 10
%
3.W
hat
nu
mbe
r of
fat
gra
ms
is 3
0% o
f 24
0 ca
lori
es?
8
4.S
har
on f
ollo
ws
a di
et t
hat
pro
vide
s ab
out
50 g
ram
s of
pro
tein
eac
hda
y.S
har
on's
doc
tor
has
just
tol
d h
er t
o re
duce
her
dai
ly p
rote
inin
take
by
30%
.Abo
ut
how
mu
ch p
rote
in w
ill
be i
n h
er r
edu
ced
prot
ein
die
t?35
gra
ms
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-8
3-8
Answers (Lesson 3-8)
© Glencoe/McGraw-Hill A26 Glencoe Algebra 1
Stu
dy G
uid
e a
nd I
nte
rven
tion
Wei
gh
ted
Ave
rag
es
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-9
3-9
©G
lenc
oe/M
cGra
w-H
ill18
5G
lenc
oe A
lgeb
ra 1
Lesson 3-9
Mix
ture
Pro
ble
ms
Wei
gh
ted
Ave
rag
eT
he w
eigh
ted
aver
age
Mof
a s
et o
f da
ta is
the
sum
of
the
prod
uct
of e
ach
num
ber
in
the
set
and
its w
eigh
t di
vide
d by
the
sum
of
all t
he w
eigh
ts.
Mix
ture
Pro
ble
ms
are
prob
lem
s w
her
e tw
o or
mor
e pa
rts
are
com
bin
ed i
nto
a w
hol
e.T
hey
invo
lve
wei
ghte
d av
erag
es.I
n a
mix
ture
pro
blem
,th
e w
eigh
t is
usu
ally
a p
rice
or
a pe
rcen
tof
som
eth
ing.
Del
ecta
ble
Coo
kie
Com
pan
y se
lls
choc
olat
e ch
ip c
ook
ies
for
$6.9
5p
er p
oun
d a
nd
wh
ite
choc
olat
e co
okie
s fo
r $5
.95
per
pou
nd
.How
man
y p
oun
ds
ofch
ocol
ate
chip
coo
kie
s sh
ould
be
mix
ed w
ith
4 p
oun
ds
of w
hit
e ch
ocol
ate
cook
ies
to o
bta
in a
mix
ture
th
at s
ells
for
$6.
75 p
er p
oun
d.
Let
w�
the
nu
mbe
r of
pou
nds
of
choc
olat
e ch
ip c
ooki
es
Nu
mb
er o
f P
ou
nd
sP
rice
per
Po
un
dTo
tal P
rice
Ch
oco
late
Ch
ipw
6.95
6.95
w
Wh
ite
Ch
oco
late
45.
954(
5.95
)
Mix
ture
w�
46.
756.
75(w
�4)
Equ
atio
n:6
.95w
�4(
5.95
) �
6.75
(w�
4)S
olve
th
e eq
uat
ion
.6.
95w
�4(
5.95
)�
6.75
(w�
4)O
rigin
al e
quat
ion
6.95
w�
23.8
0�
6.75
w�
27S
impl
ify.
6.95
w�
23.8
0 �
6.75
w�
6.75
w�
27 �
6.75
wS
ubtr
act
6.75
wfr
om e
ach
side
.
0.2w
�23
.80
�27
Sim
plify
.
0.2w
�23
.80
�23
.80
�27
�23
.80
Sub
trac
t 23
.80
from
eac
h si
de.
0.2w
�3.
2S
impl
ify.
w�
16S
impl
ify.
16 p
ound
s of
cho
cola
te c
hip
cook
ies
shou
ld b
e m
ixed
wit
h 4
poun
ds o
f w
hite
cho
cola
te c
ooki
es.
1.SO
LUTI
ON
SH
ow m
any
gram
s of
su
gar
mu
st b
e ad
ded
to 6
0 gr
ams
of a
sol
uti
on t
hat
is
32%
su
gar
to o
btai
n a
sol
uti
on t
hat
is
50%
su
gar?
21.6
g
2.N
UTS
Th
e Q
uik
Mar
t h
as t
wo
kin
ds o
f n
uts
.Pec
ans
sell
for
$1.
55 p
er p
oun
d an
dw
aln
uts
sel
l fo
r $1
.95
per
pou
nd.
How
man
y po
un
ds o
f w
aln
uts
mu
st b
e ad
ded
to 1
5po
un
ds o
f pe
can
s to
mak
e a
mix
ture
th
at s
ells
for
$1.
75 p
er p
oun
d?15
lb
3.IN
VES
TMEN
TSA
lice
Gle
ason
in
vest
ed a
por
tion
of
$32,
000
at 9
% i
nte
rest
an
d th
eba
lan
ce a
t 11
% i
nte
rest
.How
mu
ch d
id s
he
inve
st a
t ea
ch r
ate
if h
er t
otal
in
com
e fr
ombo
th i
nve
stm
ents
was
$3,
200.
$16,
000
at 9
% a
nd
$16
,000
at
11%
4.M
ILK
Wh
ole
mil
k is
4%
bu
tter
fat.
How
mu
ch s
kim
mil
k w
ith
0%
bu
tter
fat
shou
ld b
ead
ded
to 3
2 ou
nce
s of
wh
ole
mil
k to
obt
ain
a m
ixtu
re t
hat
is
2.5%
bu
tter
fat?
19.2
oz
Exam
ple
Exam
ple
Exer
cises
Exer
cises
©G
lenc
oe/M
cGra
w-H
ill18
6G
lenc
oe A
lgeb
ra 1
Un
ifo
rm M
oti
on
Pro
ble
ms
Mot
ion
pro
blem
s ar
e an
oth
er a
ppli
cati
on o
f w
eigh
ted
aver
ages
.Un
ifor
m m
otio
n p
rob
lem
sar
e pr
oble
ms
wh
ere
an o
bjec
t m
oves
at
a ce
rtai
nsp
eed,
or r
ate.
Use
th
e fo
rmu
la d
�rt
to s
olve
th
ese
prob
lem
s,w
her
e d
is t
he
dist
ance
,ris
the
rate
,an
d t
is t
he
tim
e.
Bil
l G
uti
erre
z d
rove
at
a sp
eed
of
65 m
iles
per
hou
r on
an
exp
ress
way
for
2 h
ours
.He
then
dro
ve f
or 1
.5 h
ours
at
a sp
eed
of
45 m
iles
per
hou
r on
a s
tate
hig
hw
ay.W
hat
was
his
ave
rage
sp
eed
?
M�
Def
initi
on o
f w
eigh
ted
aver
age
�56
.4S
impl
ify.
Bil
l dr
ove
at a
n a
vera
ge s
peed
of
abou
t 56
.4 m
iles
per
hou
r.
1.TR
AV
ELM
r.A
nde
rs a
nd
Ms.
Ric
h e
ach
dro
ve h
ome
from
a b
usi
nes
s m
eeti
ng.
Mr.
An
ders
trav
eled
eas
t at
100
kil
omet
ers
per
hou
r an
d M
s.R
ich
tra
vele
d w
est
at 8
0 ki
lom
eter
s pe
rh
ours
.In
how
man
y h
ours
wer
e th
ey 1
00 k
ilom
eter
s ap
art.
h
2.A
IRPL
AN
ESA
n a
irpl
ane
flie
s 75
0 m
iles
du
e w
est
in 1
hou
rs a
nd
750
mil
es d
ue
sou
th
in 2
hou
rs.W
hat
is
the
aver
age
spee
d of
th
e ai
rpla
ne?
abo
ut
429
mp
h
3.TR
AC
KS
prin
ter
A r
un
s 10
0 m
eter
s in
15
seco
nds
,wh
ile
spri
nte
r B
sta
rts
1.5
seco
nds
late
r an
d ru
ns
100
met
ers
in 1
4 se
con
ds.I
f ea
ch o
f th
em r
un
s at
a c
onst
ant
rate
,wh
o is
furt
her
in
10
seco
nds
aft
er t
he
star
t of
th
e ra
ce?
Exp
lain
.
Sp
rin
ter
A;
sin
ce s
pri
nte
r A
ru
ns
100
m in
15
s,th
is s
pri
nte
r ru
ns
at a
rate
of
m/s
.In
10
seco
nd
s,sp
rin
ter
A w
ill h
ave
run
(1
0) �
66.7
m.
Sp
rin
ter
B’s
rat
e is
.I
n 1
0 se
con
ds,
wit
h t
he
del
ayed
sta
rt,s
pri
nte
r B
has
ru
n
(10
�1.
5) �
60.7
m.
4.TR
AIN
SA
n e
xpre
ss t
rain
tra
vels
90
kilo
met
ers
per
hou
r fr
om S
mal
lvil
le t
o M
egat
own
.A
loc
al t
rain
tak
es 2
.5 h
ours
lon
ger
to t
rave
l th
e sa
me
dist
ance
at
50 k
ilom
eter
s pe
rh
our.
How
far
apa
rt a
re S
mal
lvil
le a
nd
Meg
atow
n?
281.
25 k
m
5.C
YC
LIN
GT
wo
cycl
ists
beg
in t
rave
lin
g in
th
e sa
me
dire
ctio
n o
n t
he
sam
e bi
ke p
ath
.On
etr
avel
s at
15
mil
es p
er h
our,
and
the
oth
er t
rave
ls a
t 12
mil
es p
er h
our.
Wh
en w
ill
the
cycl
ists
be
10 m
iles
apa
rt?
3h
6.TR
AIN
ST
wo
trai
ns
leav
e C
hic
ago,
one
trav
elin
g ea
st a
t 30
mil
es p
er h
our
and
one
trav
elin
g w
est
at 4
0 m
iles
per
hou
r.W
hen
wil
l th
e tr
ain
s be
210
mil
es a
part
?3
h
1 � 3
100
� 14
100
� 14
100
� 1510
0� 15
1 � 2
5 � 9
65
2 �
45
1.5
��
2 �
1.5
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Wei
gh
ted
Ave
rag
es
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-9
3-9
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 3-9)
© Glencoe/McGraw-Hill A27 Glencoe Algebra 1
An
swer
s
Skil
ls P
ract
ice
Wei
gh
ted
Ave
rag
es
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-9
3-9
©G
lenc
oe/M
cGra
w-H
ill18
7G
lenc
oe A
lgeb
ra 1
Lesson 3-9
SEA
SON
ING
For
Exe
rcis
es 1
–4,u
se t
he
foll
owin
g in
form
atio
n.
A h
ealt
h f
ood
stor
e se
lls
seas
onin
g bl
ends
in
bu
lk.O
ne
blen
d co
nta
ins
20%
bas
il.S
hei
law
ants
to
add
pure
bas
il t
o so
me
20%
ble
nd
to m
ake
16 o
un
ces
of h
er o
wn
30%
ble
nd.
Let
bre
pres
ent
the
amou
nt
of b
asil
Sh
eila
sh
ould
add
to
the
20%
ble
nd.
1.C
ompl
ete
the
tabl
e re
pres
enti
ng
the
prob
lem
.
Ou
nce
sA
mo
un
t o
f B
asil
20%
Bas
il B
len
d16
�b
0.20
(16
�b
)
100%
Bas
ilb
1.00
b
30%
Bas
il B
len
d16
0.30
(16)
2.W
rite
an
equ
atio
n t
o re
pres
ent
the
prob
lem
.0.
20(1
6 �
b)
�1.
00b
�0.
30(1
6)
3.H
ow m
any
oun
ces
of b
asil
sh
ould
Sh
eila
use
to
mak
e th
e 30
% b
len
d?2
oz
4.H
ow m
any
oun
ces
of t
he
20%
ble
nd
shou
ld s
he
use
?14
oz
HIK
ING
For
Exe
rcis
es 5
–7,u
se t
he
foll
owin
g in
form
atio
n.
At
7:00
A.M
.,tw
o gr
oups
of
hik
ers
begi
n 2
1 m
iles
apa
rt a
nd
hea
d to
war
d ea
ch o
ther
.Th
e fi
rst
grou
p,h
ikin
g at
an
ave
rage
rat
e of
1.5
mil
es p
er h
our,
carr
ies
ten
ts,s
leep
ing
bags
,an
dco
okin
g eq
uip
men
t.T
he
seco
nd
grou
p,h
ikin
g at
an
ave
rage
rat
e of
2 m
iles
per
hou
r,ca
rrie
sfo
od a
nd
wat
er.L
et t
repr
esen
t th
e h
ikin
g ti
me.
5.C
opy
and
com
plet
e th
e ta
ble
repr
esen
tin
g th
e pr
oble
m.
rt
d�
rt
Fir
st g
rou
p o
f h
iker
s1.
5t
1.5t
Sec
on
d g
rou
p o
f h
iker
s2
t2t
6.W
rite
an
equ
atio
n u
sin
g t
that
des
crib
es t
he
dist
ance
s tr
avel
ed.
1.5t
�2t
�21
7.H
ow l
ong
wil
l it
be
un
til
the
two
grou
ps o
f h
iker
s m
eet?
6 h
SALE
SF
or E
xerc
ises
8 a
nd
9,u
se t
he
foll
owin
g in
form
atio
n.
Ser
gio
sell
s a
mix
ture
of V
irgi
nia
pea
nu
ts a
nd
Spa
nis
h p
ean
uts
for
$3.
40 p
er p
oun
d.T
om
ake
the
mix
ture
,he
use
s V
irgi
nia
pea
nu
ts t
hat
cos
t $3
.50
per
pou
nd
and
Spa
nis
h p
ean
uts
that
cos
t $3
.00
per
pou
nd.
He
mix
es 1
0 po
un
ds a
t a
tim
e.
8.H
ow m
any
pou
nds
of V
irgi
nia
pea
nu
ts d
oes
Ser
gio
use
?8
lb
9.H
ow m
any
pou
nds
of
Spa
nis
h p
ean
uts
doe
s S
ergi
o u
se?
2 lb
©G
lenc
oe/M
cGra
w-H
ill18
8G
lenc
oe A
lgeb
ra 1
GR
ASS
SEE
DF
or E
xerc
ises
1–4
,use
th
e fo
llow
ing
info
rmat
ion
.
A n
urs
ery
sell
s K
entu
cky
Blu
e G
rass
see
d fo
r $5
.75
per
pou
nd
and
Tal
l F
escu
e se
ed f
or$4
.50
per
pou
nd.
Th
e n
urs
ery
sell
s a
mix
ture
of
the
two
kin
ds o
f se
ed f
or $
5.25
per
pou
nd.
Let
kre
pres
ent
the
amou
nt
of K
entu
cky
Blu
e G
rass
see
d th
e n
urs
ery
use
s in
5 p
oun
ds o
fth
e m
ixtu
re.
1.C
ompl
ete
the
tabl
e re
pres
enti
ng
the
prob
lem
.
Nu
mb
er o
f P
ou
nd
sP
rice
per
Po
un
dC
ost
Ken
tuck
y B
lue
Gra
ssk
$5.7
55.
75k
Tall
Fes
cue
5 �
k$4
.50
4.50
(5 �
k)
Mix
ture
5$5
.25
5.25
(5)
2.W
rite
an
equ
atio
n t
o re
pres
ent
the
prob
lem
.5.
75k
�4.
50(5
�k)
�5.
25(5
)
3.H
ow m
uch
Ken
tuck
y B
lue
Gra
ss d
oes
the
nu
rser
y u
se i
n 5
pou
nds
of
the
mix
ture
?3
lb
4.H
ow m
uch
Tal
l F
escu
e do
es t
he
nu
rser
y u
se i
n 5
pou
nds
of
the
mix
ture
?2
lb
TRA
VEL
For
Exe
rcis
es 5
–7,u
se t
he
foll
owin
g in
form
atio
n.
Tw
o co
mm
ute
r tr
ain
s ca
rry
pass
enge
rs b
etw
een
tw
o ci
ties
,on
e tr
avel
ing
east
,an
d th
e ot
her
wes
t,on
dif
fere
nt
trac
ks.T
hei
r re
spec
tive
sta
tion
s ar
e 15
0 m
iles
apa
rt.B
oth
tra
ins
leav
e at
the
sam
e ti
me,
one
trav
elin
g at
an
ave
rage
spe
ed o
f 55
mil
es p
er h
our
and
the
oth
er a
t an
aver
age
spee
d of
65
mil
es p
er h
our.
Let
tre
pres
ent
the
tim
e u
nti
l th
e tr
ain
s pa
ss e
ach
oth
er.
5.C
opy
and
com
plet
e th
e ta
ble
repr
esen
tin
g th
e pr
oble
m.
rt
d�
rt
Fir
st T
rain
55t
55t
Sec
on
d T
rain
65t
65t
6.W
rite
an
equ
atio
n u
sin
g t
that
des
crib
es t
he
dist
ance
s tr
avel
ed.
55t
�65
t�
150
7.H
ow l
ong
afte
r de
part
ing
wil
l th
e tr
ain
s pa
ss e
ach
oth
er?
1.25
h
8.TR
AV
ELT
wo
trai
ns
leav
e R
alei
gh a
t th
e sa
me
tim
e,on
e tr
avel
ing
nor
th,a
nd
the
oth
erso
uth
.Th
e fi
rst
trai
n t
rave
ls a
t 50
mil
es p
er h
our
and
the
seco
nd
at 6
0 m
iles
per
hou
r.In
how
man
y h
ours
wil
l th
e tr
ain
s be
275
mil
es a
part
?2.
5 h
9.JU
ICE
A p
inea
pple
dri
nk
con
tain
s 15
% p
inea
pple
juic
e.H
ow m
uch
pu
re p
inea
pple
juic
esh
ould
be
adde
d to
8 q
uar
ts o
f th
e dr
ink
to o
btai
n a
mix
ture
con
tain
ing
50%
pin
eapp
leju
ice?
5.6
qt
Pra
ctic
e (
Ave
rag
e)
Wei
gh
ted
Ave
rag
es
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-9
3-9
Answers (Lesson 3-9)
© Glencoe/McGraw-Hill A28 Glencoe Algebra 1
Readin
g t
o L
earn
Math
em
ati
csW
eig
hte
d A
vera
ges
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-9
3-9
©G
lenc
oe/M
cGra
w-H
ill18
9G
lenc
oe A
lgeb
ra 1
Lesson 3-9
Pre-
Act
ivit
yH
ow a
re s
core
s ca
lcu
late
d i
n a
fig
ure
sk
atin
g co
mp
etit
ion
?
Rea
d th
e in
trod
uct
ion
to
Les
son
3-9
at
the
top
of p
age
171
in y
our
text
book
.
Wh
y is
th
e su
m o
f Il
ia K
uli
k’s
scor
es d
ivid
ed b
y 3?
Her
fir
st s
core
is c
ou
nte
d o
nce
an
d h
er s
eco
nd
sco
re is
cou
nte
d t
wic
e.
Rea
din
g t
he
Less
on
1.R
ead
the
defi
nit
ion
of
wei
ghte
d a
vera
geon
pag
e 17
1 of
you
r te
xtbo
ok.W
hat
is
mea
nt
byth
e w
eigh
t of
a n
um
ber
in a
set
of
data
?
the
nu
mb
er o
f ti
mes
th
e n
um
ber
occ
urs
in t
he
set
of
dat
a
2.L
inda
’s q
uiz
sco
res
in s
cien
ce a
re 9
0,85
,85,
75,8
5,an
d 90
.Wh
at i
s th
e w
eigh
t of
th
esc
ore
85?
3
3.S
upp
ose
Cli
nt
driv
es a
t 50
mil
es p
er h
our
for
2 h
ours
.Th
en h
e dr
ives
at
60 m
iles
per
hou
r fo
r 3
hou
rs.
a.W
rite
his
spe
ed f
or e
ach
hou
r of
th
e tr
ip.
Sp
eed
5050
6060
60H
ou
r1
23
45
b.
Wh
at i
s th
e w
eigh
t of
eac
h o
f th
e tw
o sp
eeds
?50
mp
h:
2;60
mp
h:
3
Hel
pin
g Y
ou
Rem
emb
er
4.M
akin
g a
tabl
e ca
n b
e h
elpf
ul
in s
olvi
ng
mix
ture
pro
blem
s.In
you
r ow
n w
ords
,exp
lain
how
you
use
a t
able
to
solv
e m
ixtu
re p
robl
ems.
Co
mp
lete
eac
h r
ow
to
wri
te a
n e
xpre
ssio
n in
th
e la
st c
olu
mn
fo
r ea
chp
art
of
the
pro
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m a
nd
fo
r th
e co
mb
inat
ion
,th
en w
rite
an
eq
uat
ion
usi
ng
th
ose
exp
ress
ion
s fr
om
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e la
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ill19
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ph
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sT
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(ab
out
A.D
.300
),de
vote
d m
uch
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his
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th
e so
lvin
g of
in
dete
rmin
ate
equ
atio
ns.
An
in
dete
rmin
ate
equ
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n h
as m
ore
than
on
e va
riab
le a
nd
anu
nli
mit
ed n
um
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of s
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tion
s.A
n e
xam
ple
is x
�2y
�4.
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en t
he
coef
fici
ents
of
an i
nde
term
inat
e eq
uat
ion
are
in
tege
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nd
you
are
ask
ed t
o fi
nd
solu
tion
s th
at m
ust
be
inte
gers
,th
e eq
uat
ion
is
call
ed d
ioph
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ne.
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ch e
quat
ion
s ca
n b
e qu
ite
diff
icu
lt t
o so
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g tr
ial
and
erro
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me
luck
!
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ve e
ach
dio
ph
anti
ne
equ
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n b
y fi
nd
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at l
east
on
e p
air
of p
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ive
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gers
th
at m
akes
th
e eq
uat
ion
tru
e.S
ome
hin
ts a
re g
iven
to
hel
p y
ou.
1.2x
�5y
�32
a.F
irst
sol
ve t
he
equ
atio
n f
or x
.x
�16
�
b.
Wh
y m
ust
ybe
an
eve
n n
um
ber?
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is o
dd
,th
en x
wo
n’t
be
an in
teg
er.
c.F
ind
at l
east
on
e so
luti
on.
Any
of
thes
e:(1
1,2)
,(6,
4),(
1,6)
2.5x
�2y
�42
a.F
irst
sol
ve t
he
equ
atio
n f
or x
.x
�
b.
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you
r an
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in
th
e fo
rm x
�8
�so
me
expr
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on.
x�
8 �
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hy
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st (
2 �
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be a
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ltip
le o
f 5?
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ise,
xw
on
’t b
e an
inte
ger
.
d.
Fin
d at
lea
st o
ne
solu
tion
.A
ny o
f th
ese:
(8,1
),(6
,6),
(4,1
1),(
2,16
)
3.2x
�7y
�29
4.7x
�5y
�11
8
(11,
1) o
r (4
,3)
Any
of
thes
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4,4)
,(9,
11),
(4,1
8)
5.8x
�13
y �
100
6.3x
�4y
�22
(19,
4),(
32,1
2) o
r an
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air
(6
,1)
or
(2,4
)w
hen
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od
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um
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7.5x
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y�
118.
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3y�
40
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or
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5m�
4 an
d m
is
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mb
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42 �
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5y � 2
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
3-9
3-9
Answers (Lesson 3-9)
© Glencoe/McGraw-Hill A29 Glencoe Algebra 1
Chapter 3 Assessment Answer Key Form 1 Form 2APage 191 Page 192 Page 193
An
swer
s
(continued on the next page)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10. B
C
D
C
A
D
B
C
A
B
45
A
B
D
B
C
C
D
A
C
B
D
A
B
B
A
C
D
B
D
D
© Glencoe/McGraw-Hill A30 Glencoe Algebra 1
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B: 21
C
A
A
B
D
B
A
C
D
B
B
A
C
B
D
A
B
C
C
A
3.6 L
C
B
A
D
B
C
B
C
A
B
Chapter 3 Assessment Answer Key Form 2A (continued) Form 2BPage 194 Page 195 Page 196
© Glencoe/McGraw-Hill A31 Glencoe Algebra 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
B: 8
h � ��Vr 2�; 10.5 in.
2.5 h
3 L
$12.84
decrease; 20%
x � �bac�
13
all numbers
�1
22.5
1�13
�
yes
$134.40
5n � 12 � �3; �3
n � 3.5 � 12.7;16.2
Three times the sumof x and y equals two
times y minus x.
36 � x � 3(4 � x)
6
45
14�25
�
�186
5
�5
�35
�
�9
Chapter 3 Assessment Answer Key Form 2CPage 197 Page 198
An
swer
s
© Glencoe/McGraw-Hill A32 Glencoe Algebra 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
B: $9.60
h � ��Vr 2�; 18.67 in.
4 h
7.5 lb of nuts,2.5 lb of dried fruit
$13.50
increase; 25%
r � s(4v � t)
11
no solution
3
20
1�45
�
no
$176.80
6n � 15 � 9; �1
n � 8.1 � 4.9; 13
Three divided by y minusfive equals x times thesum of y and 7.
18 � n � 7(n � 3)
7
50
7�57
�
�70
7
7
�23
�
4
Chapter 3 Assessment Answer Key Form 2DPage 199 Page 200
© Glencoe/McGraw-Hill A33 Glencoe Algebra 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
B: 12 mi
3 ft/s
510 mph, 540 mph
$7000
$63.60
increase; 12%
x � �rs
4� t�
x � �r �
an
�
2
all numbers
��79
�
10 ft
�6
yes
$4000
(x � 2)10 � 8x � 36; 8
�35
�x � 1; �53
�
�x �
1245� � 20 � 5(32 � x)
8
126
�1�123�
52
�2�23
�
�13
�27
Chapter 3 Assessment Answer Key Form 3Page 201 Page 202
An
swer
sA
nsw
ers
Five times the sum oftwo times x and threetimes y equals thesquare of y minus twotimes the cube of x.
© Glencoe/McGraw-Hill A34 Glencoe Algebra 1
Chapter 3 Assessment Answer KeyPage 203, Open-Ended Assessment
Scoring Rubric
Score General Description Specific Criteria
• Shows thorough understanding of the concepts oftranslating between verbal sentences and equations,solving equations, percents of increase and decrease,uniform motion problems, and proportions.
• Uses appropriate strategies to solve problems.• Computations are correct.• Written explanations are exemplary.• Goes beyond requirements of some or all problems.
• Shows an understanding of the concepts of translatingbetween verbal sentences and equations, solvingequations, percents of increase and decrease, uniformmotion problems, and proportions.
• Uses appropriate strategies to solve problems.• Computations are mostly correct.• Written explanations are effective.• Satisfies all requirements of problems.
• Shows an understanding of most of the concepts oftranslating between verbal sentences and equations,solving equations, percents of increase and decrease,uniform motion problems, and proportions.
• May not use appropriate strategies to solve problems.• Computations are mostly correct.• Written explanations are satisfactory.• Satisfies the requirements of most of the problems.
• Final computation is correct.• No written explanations or work is shown to substantiate
the final computation.• Satisfies minimal requirements of some of the problems.
• Shows little or no understanding of most of the concepts oftranslating between verbal sentences and equations,solving equations, percents of increase and decrease,uniform motion problems, and proportions.
• Does not use appropriate strategies to solve problems.• Computations are incorrect.• Written explanations are unsatisfactory.• Does not satisfy requirements of problems.• No answer may be given.
0 UnsatisfactoryAn incorrect solutionindicating no mathematicalunderstanding of theconcept or task, or nosolution is given
1 Nearly Unsatisfactory A correct solution with nosupporting evidence orexplanation
2 Nearly SatisfactoryA partially correctinterpretation and/orsolution to the problem
3 SatisfactoryA generally correct solution,but may contain minor flawsin reasoning or computation
4 SuperiorA correct solution that is supported by well-developed, accurateexplanations
Chapter 3 Assessment Answer Key Page 203, Open-Ended Assessment
Sample Answers
© Glencoe/McGraw-Hill A35 Glencoe Algebra 1
1a. The student should explain that thefirst phrase is a product of x and y andthen the addition of z, while the secondphrase is a product of x and thequantity y � z.
1b. Check that the student’s values for x,y, and z satisfy both xy � z andx(y � z). One example is x � 1, y � 2,and z � 3. Another example is x � 2,y � 3, and z � 0.
2a. �ry
m� s� � t � x
(Original equation)
�ry
m� s� � t � t � x � t
(Add t to each side.)
�ry
m� s� � x � t
(Simplify.)
m��rym� s�� � m(x � t)
(Multiply each side by m.)ry � s � mx � mt
(Simplify.)ry � s � s � mx � mt � s
(Subtract s from each side.)ry � mx � mt � s
(Simplify.)
�rry� � �
mx �rmt � s�
(Divide each side by r.)
y � �mx �
rmt � s�
(Simplify.)The value of y is �mx �
rmt � s�.
2b. Division by 0 is undefined, so in theoriginal equation m � 0, and in thefinal equation r � 0.
3a. The student should conclude that a10% decrease followed by a 10%increase results in a net decrease of1%. Thus, the final cost would be 99%of the original price.
3b. Since multiplication is commutative,multiplying by 1.1 and then 0.9 wouldyield the same result as multiplying by0.9 and then 1.1. The student shouldconclude that a 10% increase followedby a 10% decrease yields the sameresult as a 10% decrease followed by a 10% increase.
4a. Since the two people walked for thesame amount of time and time can becalculated as distance divided by rate,the proportion
�
can be used to solve this problem.4b. The length of Tony’s walk can be
calculated directly from his rate of 3 miles per hour and his distance of 6 miles. Ivia walked 1 mile per hourfaster, so her rate is 4 miles per hour.The length of Ivia’s walk can be calculated directly from her rate of 4 miles per hour and distance of 6 miles. Thus, a proportion would notbe used to solve this problem.
5a. Sample answer: x � 2 � 10, x � 2 � 6,2x � 16, �2
x� � 4
5b. Sample answer: 2x � 1 � x � 95c. These two equations are equivalent.
The solution to both equations is 5.The student should recognize that thesolution to all equations in parts a andb is 8. Therefore neither of these twoequations could be equivalent to any of the equations created for parts aand b.
Ivia’s distance��Ivia’s rate
Tony’s distance��Tony’s rate
In addition to the scoring rubric found on page A34, the following sample answers may be used as guidance in evaluating open-ended assessment items.
An
swer
s
© Glencoe/McGraw-Hill A36 Glencoe Algebra 1
1. false; added to
2. true
3. true
4. false; more
5. false; true
6. false; division
7. true
8. true
9. false; percent ofdecrease
10. false; percent ofincrease
11. an equation statingthat two ratios areequal
12. an equation thatstates a rule for therelationshipbetween certainquantities
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Quiz (Lessons 3-4 and 3-5)
Page 205
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Quiz (Lessons 3-8 and 3-9)
Page 206
1.
2.
3.
4.
5.� � �
P �2
2w�; 14 m
2.4 mph
4 g
b � x � ac
x � �p �
nm
�
$75.60
$19.08
increase; 25%
decrease; 28%
99
27
15
no
no
yes
135
2
C
7
0
no solution
�5
�5�35
�
84
7
�40
40
�9
�9
�49
14
Two times b minus10 equals 4.
y2 � 12 � 5x
2n � 3(n � 9)
Chapter 3 Assessment Answer Key Vocabulary Test/Review Quiz (Lessons 3-1 through 3-3) Quiz (Lessons 3-6 and 3-7)
Page 204 Page 205 Page 206
The sum of y and the productof three and the square of xis five times x.
© Glencoe/McGraw-Hill A37 Glencoe Algebra 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
1.
2.
3. Sample answer:
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16. 7 L
m � n(q � p)
3
�3
7
31
85 � 9y � 7(4 � y)
1:3
115 120 125 130 135
� � � �� ��
���
����
�1.3
�13
�384
16.9
5u � 9v
22
Three times the sumof y and 5 equals theproduct of y and 7.
Four times nequals m timesthe difference offive and n.
$116.15
�2
all numbers
0
Part II
C
B
C
A
D
B
Part I
Chapter 3 Assessment Answer Key Mid-Chapter Test Cumulative ReviewPage 207 Page 208
An
swer
s
y
xO
© Glencoe/McGraw-Hill A38 Glencoe Algebra 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10. 11.
12. 13.
14.
15.
16. DCBA
DCBA
DCBA
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
52
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
1 / 4
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
1 1 2/
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
3 2/
DCBA
HGFE
DCBA
DCBA
DCBA
HGFE
DCBA
HGFE
DCBA
Chapter 3 Assessment Answer KeyStandardized Test Practice
Page 209 Page 210
© Glencoe/McGraw-Hill A39 Glencoe Algebra 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30. 8 lb
v � t � sr
$3.91
3�27
�
all real numbers
�2
56
42
�12
�18
�3.6�5�, ��158�, �
7251�, �13�
irrational, real
Median; most of thedata clusters near the
median.
0 5 10 15
�� �� ��
� � ��
� ���
��
5 : 1
�14
� or 25%
�4.7
��23
�
�47
�2�3 �1 0 1 2 4 5 6 7 83
40 peopleTime
Tem
per
atu
re (
F°)
H: a figure is a triangle;C: it is a polygon; If afigure is a triangle, thenit is a polygon.
23a � 6b
7r � 9t
7t2 � 3t
MultiplicativeInverse Property; �
16
�
{4}
71
5 � n3
Chapter 3 Assessment Answer Key Unit 1 TestPage 211 Page 212
An
swer
s