Objective - To use the five-step plan for solving word problems Lesson 2.5 Five Step Plan for Solving Word Problems Objective - To use the five-step plan for solving word problems The length of a rectangle is 3cm more than twice its width. If the perimeter is 60 cm, find its length. 2x + 6 Let x = width = 8 cm 2x + 6 = length = 2(8) + 6 = 24 cm x 2(x) + 2(2x + 6) = 60 2x + 4x + 12 = 60 -12 -12 6x = 48 6 6 x = 8 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series Algebra 1 by James Wenk © 2003 published by TEACHINGpoint

Five-Step Plan 1) Read the problem. Draw a picture. Make a chart. 2) Determine the unknowns. Define an unknown with a variable. Define all other unknowns in terms of first variable. 3) Write an equation involving the variable. 4) Solve the equation. 5) Check your answer. Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

1) Five less than twice a number x is 31. Find the number. 1) Read Problem Let x = the number 2) Define Unknown 2x - 5 = 31 3) Write Equation +5 +5 4) Solve Equation 2x = 36 5) Check Answer 2 2 x = 18 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

2) A shirt cost $28. This is $5 more than twice the cost of a belt. Find the cost of the belt. 1) Read Problem Let x = the cost of the belt 2) Define Unknown 3) Write Equation Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

2) A shirt cost $28. This is $5 more than twice the cost of a belt. Find the cost of the belt. 1) Read Problem Let x = the cost of the belt 2) Define Unknown 28 = 2x + 5 3) Write Equation -5 -5 4) Solve Equation 23 = 2x 5) Check Answer 2 2 11.5 = x Belt = $11.50 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

3) The largest pyramid in the world is Quetzalcoatl in Mexico. It’s base covers an area of 45 acres. This is 6 acres more than 3 times that covered by the Great Pyramid of Khufu in Egypt. How many acres does the Egyptian pyramid cover? 1) Read Problem Let y = the size of Khufu 2) Define Unknown 3) Write Equation Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Let y = the size of Khufu 45 = 3y + 6 -6 -6 39 = 3y 3 3 13 = y 3) The largest pyramid in the world is Quetzalcoatl in Mexico. It’s base covers an area of 45 acres. This is 6 acres more than 3 times that covered by the Great Pyramid of Khufu in Egypt. How many acres does the Egyptian pyramid cover? 1) Read Problem Let y = the size of Khufu 2) Define Unknown 45 = 3y + 6 3) Write Equation -6 -6 4) Solve Equation 39 = 3y 5) Check Answer 3 3 13 = y Khufu covers 13 acres Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Multiple Unknowns 4) There are 6 more gum drops than 4 times the number of jelly beans in a bag. Find how many of each are in the bag if there are 46 pieces? Let x = the # of jelly beans = 8 4x + 6 = the # of gum drops = 4(8) + 6 = 38 (x) + (4x + 6) = 46 5x + 6 = 46 -6 -6 5x = 40 5 5 x = 8 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

5) Mark has $13 more than Patty. Patty has twice the money Jim has. If together they have $178, find how much Mark has? Let x = Jim’s money = 33 2x = Patty’s money = 2(33) = 66 2x + 13 = Mark’s money = 2(33) + 13 = 79 x + 2x + 2x + 13 = 178 5x + 13 = 178 Mark has $79 -13 -13 5x = 165 5 5 x = 33 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Consecutive Integer Problems Integers Even Integers Odd Integers x - 3 x - 6 x - 6 x - 2 x - 4 x - 4 x - 1 x - 2 x - 2 any integer any even integer any odd integer Let x = Let x = Let x = x + 1 x + 2 x + 2 x + 2 x + 4 x + 4 x + 3 x + 6 x + 6 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

6) The sum of three consecutive integers is 75. Find the integers. Let x = 1st integer x + 1 = 2nd integer x + 2 = 3rd integer = 24 = 25 = 26 x + (x + 1) + (x + 2) = 75 3x + 3 = 75 -3 -3 3x = 72 3 3 x = 24 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

7) The sum of four consecutive odd integers is -40. Find the integers. Let x = 1st odd integer x + 2 = 2nd odd integer x + 4 = 3rd odd integer x + 6 = 4th odd integer = -13 = -11 = -9 = -7 x + (x + 2) + (x + 4) + (x + 6) = -40 4x + 12 = -40 -12 -12 4x = -52 4 4 x = -13 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

8) The smallest of three consecutive even integers is 18 less than twice the largest. Find the integers. Let x = 1st even integer x + 2 = 2nd even integer x + 4 = 3rd even integer = 10 = 12 = 14 x = 2(x + 4) - 18 x = 2x + 8 - 18 x = 2x - 10 -2x -2x -x = -10 (-1)(-x) = -10(-1) x = 10 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series