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Solving for the Unknown

Solving for the Unknown. Kirkwood Community College February 9, 2009 Presented by Sanh Tran, MBA, CPIM, CTL . Chapter 5. Solving for the Unknown: A How-to Approach for Solving Equations. #5. Solving for the Unknown: A how-to Approach for Solving Equations. Learning Unit Objectives.

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Solving for the Unknown

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  1. Solving for the Unknown Kirkwood Community College February 9, 2009 Presented by Sanh Tran, MBA, CPIM, CTL

  2. Chapter 5 Solving for the Unknown: A How-to Approach for Solving Equations

  3. #5 Solving for the Unknown: A how-to Approach for Solving Equations Learning Unit Objectives Solving Equations for the Unknown LU5.1 • Explain the basic procedures used to solve equations for the unknown • List the five rules and the mechanical steps used to solve for the unknown in seven situations; know how to check the answers

  4. #5 Solving for the Unknown: A how-to Approach for Solving Equations Learning Unit Objectives LU5.2 Solving Word Problems for the Unknown • List the steps for solving word problems • Complete blueprint aids to solve word problems; check the solutions

  5. Terminology Expression – 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.

  6. Solving Equations for the Unknown Equality in equations A + 8 58 Right side of equation Left side of equation Dick’s age in 8 years will equal 58

  7. Variables and Constants Rules 1. If no number is in front of a letter, it is a 1: B = 1B; C = 1C 2. If no sign is in front of a letter or number, it is a +: C = +C; 4 = +4

  8. Solving for the Unknown Rule Whatever you do to one side of an equation, you must do to the other side.

  9. Opposite Process Rule If an equation indicates a process such as addition, subtraction, multiplication, or division, solve for the unknown or variable by using the opposite process.

  10. Opposite Process Rule A + 8 = 58 - 8 - 8 A = 50 Check 50 + 8 = 58

  11. Equation Equality Rule You 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.

  12. Equation Equality Rule 7G = 35 7G = 35 7 7 G = 5 Check 7(5) = 35

  13. Practice

  14. Multiple Processes Rule When solving for an unknown that involves more than one process, do the addition and subtraction before the multiplication and division.

  15. Multiple Process Rule H + 2 = 5 4 H + 2 = 5 4 -2 -2 H = 3 4 H = 4(3) 4 H = 12 ( ) (4) Check 12 + 2 = 5 4 3 + 2= 5

  16. Practice

  17. Parentheses Rule When 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.

  18. Parentheses Rule 5(P - 4) = 20 5P – 20 = 20 +20 +20 5P = 40 5P = 40 5 5 P =8 Check 5(8-4) = 20 5(4) = 20 20 = 20

  19. Practice

  20. Like Unknown Rule To solve equations with like unknowns, you first combine the unknowns and then solve with the opposite process used in the equation.

  21. Like Unknown Rule 4A + A = 20 5A = 20 5A = 20 5 5 A = 4 Check 4(4) +4 = 20 16 + 4 = 20

  22. Practice

  23. Solving Word Problems for Unknowns 1) Read the entire Problem 3) Let a variable represent the unknown Y = Computers 4) Visualize the relationship between the unknowns and variables. Then set up an equation to solve for unknown(s) Read again if necessary 2) Ask: “What is the problem looking for?” 4Y + Y = 600 5) Check your results to ensure accuracy

  24. Solving Word Problems for the Unknown Blueprint aid

  25. Solving Word Problems for the Unknown ICM 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? Cars Sold ICM 4C 4C Ring C -C 27 Ring = 9 computers ICM = 4(9) = 36 Computers 4C - C = 27 3C = 27 3 3 C = 9 Check 36 - 9 = 27

  26. Problem 5-34: 4S + S = 5,500 = 5,500 S = 1,100 4S = 4,400 Unknown(s) Variable(s) Relationship Shift 1 4S 4S (4,400) Shift 2 S + S (1,100) 5,500 5S 5 Solution:

  27. Problem 5-36: T + 3T = $40,000 = $40,000 4 T = $10,000 3T = $30,000 4T 4 Unknown(s) Variable(s) Relationship Jim T T ($10,000) Phyllis 3T + 3T ($30,000) $40,000 Solution:

  28. Problem 5-37: 1.5L + L = 5,600 = L = 2,240 1.5L = 3,360 2.5L 2.5 5,600 2.5 Unknown(s) Variable(s) Relationship Shift 1 1.5L 1.5L (3,360) Shift 2 L +L (2,240) 5,600 Solution:

  29. Problem 5-38: Check: 14B + 6B = 1,200 = B = 60 bottles 7B = 420 thermometers 20B 20 60($6) + 420($2) = $1,200 $360 + $840 = $1,200 $1,200 = $1,200 Unknown(s) Variable(s) Price Relationship Thermometers 7B $2 14B Hot-water Bottles B 6 +6B Total = $1,200 1,200 20 Solution:

  30. Reference • Slater, J. (2008). Practical business math procedures (9th ed.). New York: McGraw-Hill/Irwin

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