Math word problems demystified 0071443169

MATH WORD PROBLEMS DEMYSTIFIED Demystified Series Advanced Statistics Demystified Algebra Demystified Anatomy Demystified Astronomy Demystified Biology Demystified Business Statistics Demystified Calculus Demystified Chemistry Demystified College Algebra Demystified Differential Equations Demystified Earth Science Demystified Electronics Demystified Everyday Math Demystified Geometry Demystified Math Word Problems Demystified Physics Demystified Physiology Demystified Pre-Algebra Demystified Pre-Calculus Demystified Project Management Demystified Robotics Demystified Statistics Demystified Trigonometry Demystified MATH WORD PROBLEMS DEMYSTIFIED ALLAN G BLUMAN McGRAW-HILL New York Chicago San Francisco Lisbon London Madrid Mexico City Milan New Delhi San Juan Seoul Singapore Sydney Toronto Copyright © 2005 by The McGraw-Hill Companies, Inc All rights reserved Manufactured in the United States of America Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written permission of the publisher 0-07-147115-4 The material in this eBook also appears in the print version of this title: 0-07-144316-9 All trademarks are trademarks of their respective owners Rather than put a trademark symbol after every occurrence of a trademarked name, we use names in an editorial fashion only, and to the benefit of the trademark owner, with no intention of infringement of the trademark Where such designations appear in this book, they have been printed with initial caps McGraw-Hill eBooks are available at special quantity discounts to use as premiums and sales promotions, or for use in corporate training programs For more information, please contact George Hoare, Special Sales, at george_hoare@mcgraw-hill.com or (212) 904-4069 TERMS OF USE This is a copyrighted work and The McGraw-Hill Companies, Inc (“McGraw-Hill”) and its licensors reserve all rights in and to the work Use of this work is subject to these terms Except as permitted under the Copyright Act of 1976 and the right to store and retrieve one copy of the work, you may not decompile, disassemble, reverse engineer, reproduce, modify, create derivative works based upon, transmit, distribute, disseminate, sell, publish or sublicense the work or any part of it without McGraw-Hill’s prior consent You may use the work for your own noncommercial and personal use; any other use of the work is strictly prohibited Your right to use the work may be terminated if you fail to comply with these terms THE WORK IS PROVIDED “AS IS.” McGRAW-HILL AND ITS LICENSORS MAKE NO GUARANTEES OR WARRANTIES AS TO THE ACCURACY, ADEQUACY OR COMPLETENESS OF OR RESULTS TO BE OBTAINED FROM USING THE WORK, INCLUDING ANY INFORMATION THAT CAN BE ACCESSED THROUGH THE WORK VIA HYPERLINK OR OTHERWISE, AND EXPRESSLY DISCLAIM ANY WARRANTY, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE McGraw-Hill and its licensors not warrant or guarantee that the functions contained in the work will meet your requirements or that its operation will be uninterrupted or error free Neither McGraw-Hill nor its licensors shall be liable to you or anyone else for any inaccuracy, error or omission, regardless of cause, in the work or for any damages resulting there from McGraw-Hill has no responsibility for the content of any information accessed through the work Under no circumstances shall McGraw-Hill and/or its licensors be liable for any indirect, incidental, special, punitive, consequential or similar damages that result from the use of or inability to use the work, even if any of them has been advised of the possibility of such damages This limitation of liability shall apply to any claim or cause whatsoever whether such claim or cause arises in contract, tort or otherwise DOI: 10.1036/0071443169 ������������ Want to learn more? 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If you’d like more information about this book, its author, or related books and websites, please click here To Betty Claire, Allan, Mark, and all my students who have made my teaching career an enjoyable experience This page intentionally left blank For more information about this title, click here CONTENTS Preface ix Introduction to Solving Word Problems Solving Word Problems Using Whole Numbers REFRESHER I LESSON Decimals Solving Word Problems Using Decimals 11 14 REFRESHER II LESSON Fractions Solving Word Problems Using Fractions Quiz 18 27 31 LESSON LESSON REFRESHER III Percents LESSON Solving Word Problems Using Percents LESSON Solving Word Problems Using Proportions LESSON Solving Word Problems Using Formulas Quiz 35 43 51 60 66 REFRESHER IV LESSON LESSON LESSON 10 69 82 88 98 Equations Algebraic Representation Solving Number Problems Solving Digit Problems vii CONTENTS viii LESSON 11 Solving Coin Problems Quiz 108 118 LESSON LESSON LESSON LESSON LESSON LESSON Solving Solving Solving Solving Solving Solving Quiz 121 131 147 160 172 181 194 12 13 14 15 16 17 REFRESHER V LESSON 18 REFRESHER VI LESSON 19 LESSON 20 LESSON 21 LESSON 22 LESSON 23 Age Problems Distance Problems Mixture Problems Finance Problems Lever Problems Work Problems Systems of Equations Solving Word Problems Using Two Equations 197 Quadratic Equations Solving Word Problems Using Quadratic Equations Solving Word Problems in Geometry Quiz 226 207 232 240 252 Solving Word Problems Using Other Strategies Solving Word Problems in Probability Solving Word Problems in Statistics Quiz Final Exam 255 267 276 283 285 Answers to Quizzes and Final Exam 293 Supplement: Suggestions for Success in Mathematics 295 Index 299 Final Exam 20 A child’s bank contains 89 coins consisting of dimes and quarters only Find the number of dimes it contains if the total amount in the bank is $16.70 (a) 41 (b) 37 (c) 34 (d) 52 21 The sum of the digits of a two-digit number is 15 If the digits are reversed, the new number is more than the original number Find the number (a) 87 (b) 69 (c) 96 (d) 78 22 A person in a motorboat traveled 48 miles upstream in hours The same trip downstream took hours Find the rate of the current (a) miles per hour (b) miles per hour (c) 10 miles per hour (d) 12 miles per hour 23 In a two-digit number, the ten’s digit is more than the unit’s digit If the digits are reversed, the new number is 27 less than the original number Find the number (a) 63 (b) 74 (c) 97 (d) 52 24 An airplane took 20 hours to fly a distance of 1500 miles, flying against the wind If the return trip took 12 hours flying with the wind, find the speed of the wind (a) 15 miles per hour (b) 20 miles per hour (c) 25 miles per hour (d) 35 miles per hour 289 Final Exam 290 25 How far will an automobile travel in 234 hours at a speed of 42 miles per hour? Use D ¼ RT (a) 11034 miles (b) 11212 miles (c) 11512 miles (d) 12114 miles 26 Find the interest on a loan of $8000 at 6% for years Use I ¼ PRT (a) $4800 (b) $2400 (c) $3200 (d) $3000 27 Find the perimeter of a rectangle whose length is 27 feet and whose width is feet Use P ẳ 2l ỵ 2w (a) 36 feet (b) 243 square feet (c) 80 feet (d) 72 feet 28 Find the distance an object falls in seconds Use d ¼ 12(32)t2 (a) 1296 feet (b) 144 feet (c) 96 feet (d) 960 feet 29 One angle of a triangle is 408 If another angle is 58 more than the third angle, find the measure of the third angle The sum of the measures of the angles of a triangle is 1808 (a) 67.58 (b) 72.58 (c) 87.58 (d) 82.58 30 A factory has 352 employees If there are 16 more males than females, find the number of females employed by the factory (a) 192 (b) 184 (c) 168 (d) 176 Final Exam 31 When three coins are tossed, the probability of getting tails is (a) (b) (c) (d) 32 When a single die is rolled, the probability of getting a seven is (a) (b) (c) (d) 33 When a card is selected from a deck, the probability of getting a or a club is (a) 13 (b) 17 (c) 52 (d) 13 34 In a meeting, there are six faculty members and two principals If a person is selected at random to be the group leader, the probability that the leader is a principal is (a) (b) (c) (d) 291 Final Exam 292 35 When a die is rolled, the probability of getting a number less than seven is (a) (b) (c) (d) 36 Find the mean of 9, 15, 18, 14, 23, 32, 13, and 20 (a) 14 (b) 15 (c) 18 (d) 16.5 37 Find the median of 9, 15, 18, 14, 23, 32, 45, and (a) 10.5 (b) 16.5 (c) 18.5 (d) 14.5 38 Find the median of 21, 32, 26, 15, and 12 (a) 21.2 (b) 26 (c) 15 (d) 21 39 Find the range of 106, 112, 98, 143, 152, and 127 (a) 54 (b) 21 (c) 38 (d) 15 40 Find the standard deviation of 7, 19, 32, 15, and (a) 98.8 (b) 10.32 (c) 9.94 (d) 6.25 Answers to Quizzes and Final Exam ANSWERS TO QUIZZES Quiz Quiz Quiz Quiz Quiz Quiz (c) (d) (b) (c) (c) (b) (b) (b) (d) (a) (b) (d) (d) (a) (a) (d) (d) (a) (a) (c) (d) (b) (a) (d) (c) (d) (b) (c) (c) (a) (a) (c) (b) (a) (d) (b) (c) (a) (d) (d) (b) (d) (b) (b) (c) (b) (d) (a) (a) (d) (d) (b) (a) (b) 10 (d) 10 (c) 10 (b) 10 (d) 10 (c) 10 (d) 293 Copyright © 2005 by The McGraw-Hill Companies, Inc Click here for terms of use Answers 294 ANSWERS TO FINAL EXAM (a) 11 (d) 21 (d) 31 (c) (b) 12 (b) 22 (a) 32 (b) (d) 13 (a) 23 (d) 33 (d) (c) 14 (d) 24 (c) 34 (d) (c) 15 (c) 25 (c) 35 (d) (d) 16 (b) 26 (b) 36 (c) (b) 17 (c) 27 (d) 37 (b) (d) 18 (b) 28 (a) 38 (d) (a) 19 (b) 29 (a) 39 (a) 10 (b) 20 (b) 30 (b) 40 (c) Supplement: Suggestions for Success in Mathematics Be sure to attend every class If you know ahead of time that you will be absent, tell your instructor and get the assignment If it is an emergency absence, get the assignment from another student Try to the problems before the next class If possible, get the class notes from another student 295 Copyright © 2005 by The McGraw-Hill Companies, Inc Click here for terms of use 296 Supplement Read the material in the textbook several times Write down or underline all definitions, rules, and symbols Try to the sample problems Do all assigned homework as soon as possible before the next class Concentrate on mathematics only Get all of your materials before you start doing your homework Make sure you write the assignment on the top of your homework Read the directions Copy each problem on your homework paper Make sure that you have copied it correctly Do not use scratch paper Work out each problem in detail and not skip steps Write neatly and large enough Check the answer with the one in the back of the book or rework the problem again If you did not get the correct answer, try to find your mistake or start over Don’t look for shortcuts because they not always work Write down any questions you have and ask your instructor or another student at the next class period If you are having difficulty with the problem, consult your textbook and notes Don’t give up too quickly Always review before each exam You can usually find a review or chapter test at the end of each chapter in the book If not, you can make up your own review by selecting several problems from each section in the book to try If you can’t get the correct answer, ask the teacher or another student to help you before the exam If you have made study cards, review them On the day of the test, arrive early Look over your notes and study cards Bring all necessary materials such as pencils, protractor, calculator, textbook, etc., to class When you get the test, look over the entire test before you get started Read the directions Work the problems that you know how to first Do not spend too much time on any one problem After you have finished the test, if time allows, check each problem When you get the test back, check your mistakes and study the types of problems that you have missed because similar problems may be on the final exam If you have difficulty with mathematics, arrange for a tutor Some schools have learning centers where you can receive free tutoring Supplement Finally, make sure that you are in the correct class You cannot skip math classes Mathematics is sequential in nature What you learn today, you will use tomorrow What you learn in one course you will use in the next course Good luck! 297 This page intentionally left blank INDEX addition, age problems, 121–130 algebraic expression, 69 algebraic representation, 82–87 angle of a triangle, 241 area circle, 246 square, 246 triangle, 243 decimals to fractions, 23 denominator, 18 digit problems, 98–107 digits, 98 diluted solution, 150 distance, 60, 131 distance problems, 131–146 division, downstream, 140 draw a picture, 259–261 base 38, 40 Celsius temperature, 61 checking an equation, 72 classical probability, 271 clearing fractions, 78 coin problems, 108–117 conditional equation, 69 consecutive even integers, 91 consecutive integers, 91 consecutive odd integers, 91 cross multiplication, 52 current, 140 data set, 276 decimals, 11–17 addition, 11 division, 12 multiplication, 12 subtraction, 11 word problems, 14–17 empirical probability, 271 equation, 69 estimation, evaluation, factoring, 226 Fahrenheit temperature, 61 finance problems, 160–171 find a pattern, 2–5, 261–262 formula, 60 formulas problems, 60–65 fraction problems, 27–30 fractions, 18–30 addition, 20 division, 21 multiplication, 20–21 subtraction, 20 word problems, 27–30 fractions to decimals, 23 fractions to higher terms, 18 299 Copyright © 2005 by The McGraw-Hill Companies, Inc Click here for terms of use INDEX 300 frequency distribution, 271 fulcrum, 172 goal, grouping symbols, 69 guess and test, 258–259 headwind, 140 How To Solve It, implementation, improper fractions, 19 improper fractions to mixed numbers, 19 interest, 160 lever problems, 172–180 lowest common denominator (LCD), 19 make an organized list, 256–257 measures of average, 276–279 mean, 276 median, 277 mode, 278 measures of variation, 279–281 range, 279 standard deviation, 280–281 mixed numbers, 19, 21–23 addition, 21 division, 23 multiplication, 22–23 subtraction, 21–22 mixed numbers to improper fractions, 19 mixture problems, 147–159 multiplication, number problems, 88–97 numerator, 18 operations, 6, 69 part, 38–39 percent, 35–50 decimal to percent, 36 fraction to percent, 36–37 percent to decimal, 35 percent to fraction, 36 word problems, 43–50 percent decrease, 47–48 percent increase, 47–48 percent problems, 37–40 perimeter of a rectangle, 63, 242 Polya, principal, 160 probability experiment, 267 event, 268 outcome, 267 sample space, 268 proportion, 52 quadratic equations, 226–231 rate, 38–39, 60, 131, 160 ratio, 51 reducing fractions, 18 return, 160 reversing digits, 98 second degree equation, 226 solution, 69 solve a simpler problem, 262–263 solving an equation, 69–81 solving problems in geometry, 240–251 solving problems using proportions, 51–59 solving problems using quadratic equations, 232–239 solving problems using two equations, 207–225 standard deviation, 280–281 strategy, statistics average, 276 mean, 276 median, 277 mode, 278 range, 279 spread, 279 standard deviation, 280–281 INDEX substitution, 198 subtraction, systems of equations, 197–206 tailwind, 140 time, 60, 131, 160 upstream, 140 301 whole numbers, 6–10 addition, division, multiplication, subtraction, total, 6, word problems, 6–10 work backwards, 263–264 work problems, 62, 181–193 This page intentionally left blank ABOUT THE AUTHOR Allan G Bluman taught mathematics and statistics in high school, college, and graduate school for 39 years He received his Ed.D from the University of Pittsburgh and has written three mathematics textbooks published by McGraw-Hill Dr Bluman is the recipient of an ‘‘Apple for the Teacher’’ award for bringing excellence to the learning environment and the ‘‘Most Successful Revision of a Textbook’’ award from McGraw-Hill His biographical record appears in Who’s Who in American Education, 5th edition ... Problems Distance Problems Mixture Problems Finance Problems Lever Problems Work Problems Systems of Equations Solving Word Problems Using Two Equations 197 Quadratic Equations Solving Word Problems. .. this book MATH WORD PROBLEMS DEMYSTIFIED This page intentionally left blank LESSON Introduction to Solving Word Problems In every area of mathematics, you will encounter ‘ word ’ problems Some... Quadratic Equations Solving Word Problems in Geometry Quiz 226 207 232 240 252 Solving Word Problems Using Other Strategies Solving Word Problems in Probability Solving Word Problems in Statistics