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PROBLEM SOLVING Translating Problems Into Equations Steps to Solve Problems Lesson 1-6 to 1-7 Mrs. Crespo Algebra I 2012-2013

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TRANSLATING PROBLEMS INTO EQUATIONS Read the problem carefully. Choose a variable. Write an equation. Represent the unknown. Crespo 2012-2013

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TRANSLATE INTO AN EQUATION (1) Lynn has twice as much money as Jo. (2)Together they have $63. How much money does each have? Write an equation. Represent the unknown. Choose a variable. Let J = Jo’s money Find a variable for something you don’t have any info on. 2J = Lynn’s money J+2J= 63 Crespo 2012-2013

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TRANSLATE INTO AN EQUATION (1) A college has 620 students. (2)There are 20 more women than men. How many women are there? Write an equation. Represent the unknown. Choose a variable. Let m = number of men Find a variable for something you don’t have any info on. m+20 = number of women m+(m+20)=620 Crespo 2012-2013

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TRANSLATE INTO AN EQUATION (1)Bret drove three times as far as Jan. (2)Bret drove 24 miles more than Jan. How far did Jan drive? Write an equation. Represent the unknown. Choose a variable. Let J = Jan’s distance Find a variable for something you don’t have any info on. 3J = J+24 = Bret’s distance 3J = J+24 Crespo 2012-2013

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TRANSLATE INTO AN EQUATION (1)The Ravens won twice as many games as they lost. (2)They played 96 games. How many games did they win? Write an equation. Represent the unknown. Choose a variable. Let L = number of losses 2L= number of wins L+2L=96 (YOUR TURN) Crespo 2012-2013

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TRANSLATE INTO AN EQUATION (1)Skip had 8 fewer job interviews than Woody. (2)Together they had 20 interviews. How many interviews did each have? Write an equation. Represent the unknown. Choose a variable. Let w = Woody’s interviews w-8 = Skip’s interviews w + (w-8) =20 Crespo 2012-2013 (YOUR TURN)

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MORE TRANSLATE INTO AN EQUATION The height of a tower is three times the height of a certain building. If the tower is 50 m taller than the building, how tall is the tower? LLet b = height of building 33b = 50+b = height of tower 33b = 50+b BUILDING TOWER 50 m Crespo 2012-2013

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PROBLEM SOLVING Read the problem carefully. Choose a variable. Write an equation. Represent the unknown. Solve the equation. Check. Crespo 2012-2013

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SOLVE THE PROBLEM The gym is 21 years newer than the auditorium. The gym is also one fourth as old as the auditorium. How old is each building? Let a = age of auditorium Choose a variable. Write an equation. Represent the unknown. Solve the equation. Check. a-21 = a/4 = age of gym a-21 = a/4 4(a-21) = 4(a/4) 4a-84 = a 4a-a = 84 3a = 84 a = 84/3 = 28 years a-21 = age of gym = 28-21 = 7 years Crespo 2012-2013

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SOLVE THE PROBLEM One number is 4 times another number. The larger number is also 87 more than the smaller number. Find the numbers. Let s = smaller number Choose a variable. Write an equation. Represent the unknown. Solve the equation. Check. 4s = s+87 = larger number 4s = s+87 4s-s = 87 3s = 87 s = 87/3 = 29 4s = 4(29) = 116 =larger number Crespo 2012-2013

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A clown weighs 60 lb. more than a trapeze artist. The trapeze artist weighs two thirds as much as the clown. How much does each weigh? Let c = clown’s weight Choose a variable. Write an equation. Represent the unknown. Solve the equation. Check. c-60 = (2/3)c = trapeze’s weight c-60 = (2/3)c 3(c-60) = 3(2c/3) 3c-180 = 2c 3c-2c = 180 c = 180 lb. SOLVE THE PROBLEM c-60 = 180-60 = 120 lb. = trapeze’s weight Crespo 2012-2013 (YOUR TURN)

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The ninth grade class has 17 more girls than boys. There are 431 students in all. How many boys are there? How many girls are there? Choices for the number of boys: 191, 202, 207 Let b = number of boys Choose a variable. Write an equation. Represent the unknown. Solve the equation. Check. b+17 = number of girls b+(b+17) = 431 2b+17 = 431 2b = 431-17 2b = 414 b = 414/2=207 SOLVE THE PROBLEM b+17=207+17 = 224 = number of girls Crespo 2012-2013 (YOUR TURN)

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HOMEWORK Lesson 1-6 to 1-7 Page 24 1-17 odd Page 28 1-9 odd Crespo 2012-2013

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REFERENCE: Crespo 2012-2013 Word Problems from this PowerPoint are from the school textbook: McDougall Littell’s Algebra: Structure and Method, Book 1 by Brown, Dolciani, Sorgenfrey, and Cole. PowerPoint: Created by Mrs. Crespo for Algebra 1.

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Introduction to Algebra Chapter 1.6 Translating Problems into Equations.

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