1. 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
6x = 48
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

2. 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

3. 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
4) Solve Equation
2x = 36
5) Check Answer
x = 18
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

4. 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

5. 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
4) Solve Equation
23 = 2x
5) Check Answer
11.5 = x
Belt = $11.50
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

6. 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

7. 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
4) Solve Equation
39 = 3y
5) Check Answer
13 = y
Khufu covers 13 acres
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

8. 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
5x = 40
x = 8
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

9. 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
5x = 165
x = 33
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

10. 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

11. 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
3x = 72
x = 24
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

12. 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
4x = -52
x = -13
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

13. 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
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