Algebra in Words Presents WORD PROBLEMS DECODED by Bullock, Gregory -- Read -- Imperial Library of Trantor

Index

INTRODUCTION

HOW TO USE THIS BOOK: The 4 Phases WHY WORD PROBLEMS MATTER THE CONCESSIONS CONTRACT

THE BASICS OF WORD PROBLEMS

THE CODE WORDS (DEFINITIONS)

The Components of Word Problems Geometry Words Money & Investment Words Time Cycle Words (used w/ Investments) Money: Profit & Expenses Words Rate-of-Speed Words

Unknown vs. a Variable The Importance of the Equal Sign The Importance of Units Equalities, Ratios, & Conversions The Real Order of Operations: GEMA

THE WORD PROBLEM PROCEDURE THE CATEGORIES DETAILED EXPLANATIONS & TEMPLATES

One Unknown, One Variable, One Equation One Variable, Multiple Unknowns, One Equation A Reference-to-a-Reference-to-the Variable Consecutive Integers Consecutive Even or Odd Integers Ratios & Proportions Percentage PERCENT INCREASE: Price or Salary Percent Increase: New Amount Unknown Percent Increase: Original Amount Unknown Percent Increase: Percent Unknown Percent Decrease MONEY RELATED Fees & Membership Costs = Total Bill Expenses & Profit A More Complicated Expenses & Profit Problem Simple Interest Investments (or Loans) Simple Interest: New Amount is Unknown GEOMETRY Perimeter of a Rectangle Triangle: Sum of Sides (Perimeter) or Sum of Angles Area of a Rectangle Area of a Triangle Areas of Two Squares Areas of Two Circles Perimeter of a Right Triangle & The Pythagorean Theorem Similar Right Triangles, Cast Shadow, Using Proportion/LCD The Area or Volume of the Shaded Region RATE OF SPEED Traveling Towards Each Other, When Will They Meet? Time is Unknown, Total Distance Given, Different Speeds Catch-Up: Traveling In The Same Direction, When Will They Meet? Two Different Roads: Rates are Unknown, Total Distance Given Two Different Roads: Rates are Unknown, Total Time Given Rate of Speed Unknown but Same; Distances Given, Time Not Given but Reference to Time Given Rate of Vehicle Unknown; Distance & Rate of Current Given; Same Time Rate of Speed of Vehicle & Current Unknown (Upstream/Downstream) Travel Times Unknown; References to Rate & Time Given SPLITTING A TASK MIXED ITEMS: Nuts, Candy, Coins, Tickets, Solutions, Investments Two Coins of Different Value (One Variable) Two Different Priced Tickets (One Variable) Buying Mixed Items at Two Different Unit Prices (One Variable) Mixing Two Chemicals to Make a Final Solution (One Variable) Investing in Two Simple Interest Investments (One Variable) TWO VARIABLES, TWO EQUATIONS THREE VARIABLES, THREE EQUATIONS

Procedure for solving a System of 3 Linear Equations with 3 Variables

IDENTIFY & MATCH Practice ANNOTATED EXAMPLES

WP1: An Unknown Among an Average WP2: Consecutive Integers WP3: Consecutive Odd Integers WP4: Consecutive Even Integers

MIXED ITEMS USING ONE VARIABLE & ONE EQUATION

WP5: Two Coins of Different Value (One Variable) WP6: Three Coins: A Reference-To-A-Reference-To One Variable WP7: Two Different Priced Tickets (One Variable) WP8: Buying Mixed Items at Two Different Unit Prices (One Variable) WP9: Mixing Two Chemicals to Make a Final Solution (One Variable)

MONEY RELATED

WP10: Fees & Membership Costs = Total Bill WP11: Expenses & Profit WP12: Expenses & Profit (More Complicated)

PERCENT

WP13: Percent: Part of Whole Unknown WP14: Percent: Size of Whole Unknown WP15: Percent: Percent Unknown WP16: Salary/Percent Increase, New Salary Unknown WP17: Percent Increase (Sales Tax), Original Amount Unknown WP18: Salary/Percent Increase; Percent is Unknown WP19: Percent Decrease

INVESTMENTS & LOANS

WP20: Simple Interest: Interest Unknown WP21: Simple Interest: Total Amount after Interest Unknown WP22: Investing in Two Simple Interest Investments (One Variable)

RATE OF SPEED

WP23: Meeting in Between: Time Unknown, Total Distance Given, Different Speeds WP24: Catch-Up: Times Unknown, Same Distance, Different Speeds WP25: Two Different Roads, Rates Unknown, Total Distance Given WP26: Two Different Roads, Rates Unknown, Total Time Given WP27: Rate of Speed Unknown but Same; Distances Given, Time Not Given but Reference to Time Given WP28: Rate of Vehicle Unknown; Distance & Rate of Current Given; Same Time WP29: Rate of Vehicle & Current Unknown: Upstream/Downstream (2 Variables) WP30: Travel Times Unknown; References to Rate & Time Given

SPLITTING A TASK

WP31: Time to Complete Task Together Unknown WP32: Time to Complete Task Alone Unknown WP33: Times for Each to Complete Task Unknown

WP34: PROPORTION & LCD GEOMETRY

WP35: Perimeter of a Rectangle WP36: Perimeter of a Triangle WP37: Area of a Rectangle WP38: Area of a Triangle WP39: Areas of Two Squares WP40: Perimeter of a Triangle & The Pythagorean Theorem WP41: Areas of Two Circles WP42: Similar Right Triangles, Cast Shadow, Proportion/LCD WP43: Finding the Area of the Shaded Region WP44: Finding the Volume of the Shaded Region

TWO VARIABLES, TWO EQUATIONS

WP45: Two Coins of Different Value (2 Variables) WP46: Two Different Priced Tickets (2 Variables) WP47: Manufacturing Two Different Items (2 Variables) WP48: Mixing Two Chemicals to Make a Final Solution (2 Variables) WP49: Investing in Two Simple Interest Investments (2 Variables) WP50: Buying Mixed Items at Two Different Unit Prices (2 Variables) WP51: Distances on Two Different Roads Unknown, Miles/Gallon Given, Total Miles & Total Gallons Given (2 Variables)

THREE VARIABLES, THREE EQUATIONS

WP52: Three Coins of Different Value (3 Variables)

CLOSING

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