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SOLVING WORD PROBLEMS LESSON 3 Think, Plan and Do, Look Back ► When solving word problems this approach will help you through the process of gathering information to solve word problems. ► THINK - What information is important? ► PLAN - Identify the unknowns with a variable ► DO - Make an equation by translating. ► LOOK BACK - Check your answer in the original problem. Are all the conditions satisfied? Can the problem to solved differently? Steps to Solving Word Problems 1. 2. 3. 4. 5. Use a variable to represent the unknown quantity Express any other unknown quantities in terms of this variable, if possible. Write an equation, and solve it. State the answer to the problem. Check your answer by substituting in the problem. The sum of two numbers is 48. One number is three times as great as the other. Find the two numbers. Let the 1st number be represent by x Let the 2nd number be represent by 3x Equation: x + 3x = 48 x + 3x = 48 4x = 48 4x = 48 4 4 x = 12 Check: x + 3x = 48 (12) + 3(12) = 48 12 + 36 = 48 48 = 48 Things to Remember: Use a variable to represent the unknown quantity Express any other unknown quantities in terms of this variable, if possible. Write an equation, and solve it. State the answer to the problem. Check your answer by substituting in the The sum of three consecutive numbers is 114. Find the numbers. Let x represent the 1st number. Let (x + 1) represent the 2nd number. Let (x + 2) represent the 3rd number. Equation: x + (x + 1) + (x + 2) = 114 x + (x + 1) + (x + 2) = 114 Things to Remember: Use a variable to represent the unknown quantity Express any other unknown quantities in terms of this variable, if possible. Write an equation, and solve it. 3x + 3 = 114 State the answer to the problem. 3x + 3 - 3 = 114 - 3 3x = 111 x = 37 3x = 111 3 3 x + 1 = 38 x + 2 = 39 Check your answer by substituting in the problem. A number is doubled and then decreased by 8. The result is 42. Find the number Let x represent the number. Things to Remember: Equation: 2x - 8 = 42 Use a variable to represent the unknown quantity 2x - 8 + 8 = 42 + 8 Express any other unknown quantities in terms of this variable, if possible. 2x = 50 Write an equation, and solve it. 2x = 50 2 2 Check: x = 25 2(25) - 8 = 42 2x - 8 = 42 50 - 8 = 42 42 = 42 State the answer to the problem. Check your answer by substituting in the problem. The sum of two consecutive even numbers is 110. Find the numbers Let x represent the 1st number. Let (x + 2) represent the 2nd number. Equation: x + (x + 2) = 110 x + (x + 2 ) = 110 2x + 2 - 2 = 110 - 2 x + 2 = 56 Use a variable to represent the unknown quantity Express any other unknown quantities in terms of this variable, if possible. 2x + 2 = 110 2x = 108 2x 108 = 2 2 x = 54 Things to Remember: Check: x + (x + 2) = 110 Write an equation, and solve it. State the answer to the problem. (54) + (56) = 110 110 = 110 Check your answer by substituting in the problem. Class work ► Check solutions to Lesson 2(3) - Page 147 # 13, 14 ► Copy down notes and examples ► Do Lesson 3 Worksheet