# PROBLEM SOLVING Translating Problems Into Equations Steps to

PROBLEM SOLVING Translating Problems Into Equations Steps to Solve Problems Lesson 1 -6 to 1 -7 Mrs. Crespo Algebra I 20122013

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

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

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

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

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

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

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? Let b = height of building 50 m 3 b = 50+b = height of tower BUILDING TOWER 3 b = 50+b Crespo 2012 -2013

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

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? Choose a variable. Let a = age of auditorium a-21 = a/4 = age of gym Represent the unknown. a-21 = a/4 Write an equation. Solve the equation. Check. 4(a-21) = 4(a/4) a-21 = age of gym 4 a-84 = a = 28 -21 4 a-a = 84 = 7 years 3 a = 84/3 = 28 years Crespo 2012 -2013

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

SOLVE THE (YOUR TURN) PROBLEM 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? Choose a variable. Represent the unknown. Write an equation. Solve the equation. Check. Let c = clown’s weight c-60 = (2/3)c = trapeze’s weight c-60 = (2/3)c c-60 = 180 -60 3(c-60) = 3(2 c/3) 3 c-180 = 2 c 3 c-2 c = 180 lb. = 120 lb. = trapeze’s weight Crespo 2012 -2013

SOLVE THE (YOUR TURN) PROBLEM 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. b+17 = number of girls Represent the b+(b+17) = 431 unknown. Write an equation. b+(b+17) = 431 b+17=207+17 Solve the equation. 2 b+17 = 431 = 224 2 b = 431 -17 = number of 2 b = 414 girls b = 414/2=207 Check. Crespo 2012 -2013

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

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

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