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## SOLVING WORD PROBLEMS

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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**• 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.**Example 1**The sum of two numbers is 48. One number is three times as great as the other. Find the two numbers. 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 problem. 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 Check: 4x 4 48 4 x + 3x = 48 (12) + 3(12) = 48 12 + 36 = 48 48 = 48 = x = 12**Example 2**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. 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 problem. Equation: x + (x + 1) + (x + 2) = 114 x + (x + 1) + (x + 2) = 114 3x + 3 = 114 3x + 3 - 3 = 114 - 3 3x = 111 x = 37 x + 1 = 38 x + 2 = 39 3x 3 111 3 =**Example 3**A number is doubled and then decreased by 8. The result is 42. Find the number Let x represent the number. 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 problem. Equation: 2x - 8 = 42 2x - 8 + 8 = 42 + 8 2x = 50 2x 2 50 2 Check: 2x - 8 = 42 2(25) - 8 = 42 50 - 8 = 42 42 = 42 = x = 25**Example 4**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. 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 problem. Equation: x + (x + 2) = 110 x + (x + 2 ) = 110 2x + 2 = 110 2x + 2 - 2 = 110 - 2 2x = 108 Check: x + (x + 2) = 110 (54) + (56) = 110 110 = 110 2x 2 108 2 = x = 54 x + 2 = 56**Class work**• Check solutions to Lesson 2(3) - Page 147 - # 13, 14 • Copy down notes and examples • Do Lesson 3 Worksheet