Kinh tế học - Chapter 5: Solving for the unknown: A how - To approach for solving equations

Chapter 5Solving for the Unknown: A How-to Approach for Solving EquationsExplain the basic procedures used to solve equations for the unknownList the five rules and the mechanical steps used to solve for the unknown in seven situations; know how to check the answersSolving for the Unknown: A how-to Approach for Solving Equations#5Learning Unit ObjectivesSolving Equations for the UnknownLU5.1List the steps for solving word problemsComplete blueprint aids to solve word problems; check the solutionsSolving for the Unknown: A how-to Approach for Solving Equations#5Learning Unit ObjectivesSolving Word Problems for the UnknownLU5.2Expression – A meaningful combination of numbers and letters called terms.Equation – A mathematical statement with an equal sign showing that a mathematical expression on the left equals the mathematical expression on the right.Formula – An equation that expresses in symbols a general fact, rule, or principle. Variables and constants are terms of mathematical expressions.TerminologySolving Equations for the UnknownLeft side of equationRight side of equationEquality in equationsA + 858Dick’s age in 8 years will equal 58Variables and Constants Rules1. If no number is in front of a letter, it is a 1: B = 1B; C = 1C2. If no sign is in front of a letter or number, it is a +: C = +C; 4 = +4Solving for the Unknown RuleWhatever you do to one side of an equation, you must do to the other side.Opposite Process RuleIf an equation indicates a process such as addition, subtraction, multiplication, or division, solve for the unknown or variable by using the opposite process.Opposite Process RuleA + 8 = 58 - 8 - 8A = 50Check 50 + 8 = 58Equation Equality RuleYou can add the same quantity or number to both sides of the equation and subtract the same quantity or number from both sides of the equation without affecting the equality of the equation. You can also divide or multiply both sides of the equation by the same quantity or number (except 0) without affecting the equality of the equation.Equation Equality Rule7G = 357G = 357 7G = 5Check7(5) = 35Multiple Processes RuleWhen solving for an unknown that involves more than one process, do the addition and subtraction before the multiplication and division.Multiple Process RuleH + 2 = 5 4H + 2 = 5 4 -2 -2H = 3 4H = 4(3) 4H = 12()(4)Check12 + 2 = 5 43 + 2= 5Parentheses RuleWhen equations contain parentheses (which indicates grouping together, you solve for the unknown by first multiplying each item inside the parentheses by the number or letter just outside the parentheses. Then you continue to solve for the unknown with the opposite process used in the equation. Do the addition and subtractions first; then the multiplication and division.Parentheses Rule5(P - 4) = 205P – 20 = 20 +20 +205P = 405P = 405 5P =8Check5(8-4) = 20 5(4) = 20 20 = 20Like Unknown RuleTo solve equations with like unknowns, you first combine the unknowns and then solve with the opposite process used in the equation.Like Unknown Rule4A + A = 205A = 205A = 205 5A = 4Check4(4) +4 = 20 16 + 4 = 20Solving Word Problems for Unknowns1) Read the entire Problem2) Ask: “What is the problem looking for?”3) Let a variable represent the unknown4) Visualize the relationship between the unknowns and variables. Then set up an equation to solve for unknown(s)5) Check your results to ensure accuracyY = Computers4Y + Y = 600Read again if necessarySolving Word Problems for the UnknownBlueprint aidSolving Word Problems for the UnknownICM Company sold 4 times as many computers as Ring Company. The difference in their sales is 27. How many computers of each company were sold?4C - C = 273C = 27 3 3C = 9Ring = 9 computersICM = 4(9) = 36 ComputersCars SoldICM 4C 4CRing C -C 27Check 36 - 9 = 27