1. Using linear
equations to
solve wor d
pr oblems
Usually deal with changes over
Usually deal with changes over
time.
PPT File Name: F:TeachingNorth East Carolina Prep SchoolLesson PlansMathAssigments8 -- Using Linear Equations to Solve Word Problems
PPT URL: http://www.slideshare.net/Anthony_Maiorano/8-using-linear-equations-to-solve-word-problems or http://bag.sh/26ku
Notes File Name: F:TeachingNorth East Carolina Prep SchoolLesson PlansMathAssigments8 – Using Linear Equations to Solve Word Problems
Notes URL: http://www.scribd.com/doc/134269678/8-%E2%80%93-Using-Linear-Equations-to-Solve-Word-Problems

2. Common Core
Common Core Common Core
 8.EE.B.6: Understand the  8.F.B.4: Use functions to model
connections between relationships between
proportional relationships, quantities. Construct a function to
lines, and linear equations. Use model a linear relationship
similar triangles to explain why the between two quantities. Determine
slope m is the same between any the rate of change and initial
two distinct points on a non- value of the function from a
vertical line in the coordinate description of a relationship or
plane; derive the equation y = mx from two (x, y) values, including
for a line through the origin and reading these from a table or from
the equation y = mx + b for a line a graph. Interpret the rate of
intercepting the vertical axis at b. change and initial value of a linear
function in terms of the situation it
models, and in terms of its graph
or a table of values.

3. ¿Essential Question?
 How can you utilize a linear
equation in two variables to
model and solve real life
problems?

4. Vocabulary
 Linear Equation: algebraic equation in
which each term is either a constant or the
product of a constant and the first power of
a single variable
 Functions: a mathematical relationship
between two values. The second value
determines the first. y = 2x
 Value: a numerical worth or amount
 Variable: a quantity that can change
represented by a letter. x or y

5. How do you
UNRAAVEL?
U nderline the question
N ow predict what you think you need to do to
 solve the problem
R ead the word problem
A re the important words circled?
 (especially clue words)
A pply the step(s) you chose to solve the problem
V erify your answer (is it reasonable; does it
 make sense?)
E liminate wrong answers
L et the answer stay or rework the problem
 Double check your work!

6. Y intercept does not
change
Slope does change 
 Example: Kim wants to rent a car on the
Big Island. Mr. Lee’s Rentals rents cars
for $99.00 for one week plus $0.11 per
mile over 100 miles. If Kim drives 400
miles, how much does she pay?

7. y=mx +/-b. y = .11x
+99
 The weekly rental rate does not change.
It is the y-intercept, and it’s $99.00.
 The amount of miles changes, so it is the
slope. The slope is the rate of change:
$.11 per mile over 100 miles.
 Let x = the number of miles she drives
over 100 miles.

8. Example #2: y=5x+10
 Bobby charges $10. per lawn he mows, and an
additional $5. per hour.
 What does not change? What is the y-
intercept? $10.00 per lawn
 What changes? What is the slope? The $5.
per hour depending on how many hours it
takes to mow the lawn
 Let x = the number of hours it takes to mow a
lawn.

9. Create a My Way
 Make up a word problem where
something is constant (does not change)
and something does change.
 State the y-intercept
 State the slope
 State what the variable (the “x”) is

10. Examples of Word
Problems for My Way
 Cell Phone: $50. monthly rate + .12
cents a minute over 300 minutes. Let x =
# of minutes over 300.
 T-shirt company charges $24. per order
plus $12.00 per shirt. Let x = the # of
shirts ordered.
Yoga classes: $10 for sign-up plus $5. per
class

11. STEPS IN SOLVING WORD
PROBLEMS WITH LINEAR
ALGEBRA
 1. Define the variable that you want to find with a let
statement. Let x = ….
 2. Create an equation that expresses the information
given in the problem’s scenario. Decide on the y-
intercept and the slope (rate of change)
 3. Solve your equation using algebraic methods.
 4. Consider if your answer is reasonable.
 5. Label your solution appropriately.
 6. Check your answer with the conditions given in the
problem.

12. Video
Khan Academy Video on “Basic Linear
“
Equation Word Problem” details
Constructing and solving a basic equation
based on a word problem.
URL: https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/basic-equation-practice/v/basic-linear-equation-word-problem

13. Problem 1a
To move up to the maestro level
in his piano school, Ishaan needs to
master at least 80 songs.Ishaan has
already mastered 16 songs. If Ishaan
can typically master 4 songs per
month, what is the minimum number
of months it will take him to move to
the maestro level?

14. Problem 1b
To move up to the maestro To solve this, let's set
level in his piano
school, Ishaan needs to up an expression to
master at least 80 songs. show how many
Ishaan has already
mastered 16 songs. If Ishaan
songs Ishaan will have
can typically master 4 songs mastered after each
per month, what is the month.
minimum number of months it
will take him to move to the
maestro level?

15. Problem 1c
To move up to the maestro Number of songs
level in his piano
school, Ishaan needs to mastered
master at least 80 songs.
Ishaan has already
=
mastered 16 songs. If Ishaan Months at school
can typically master 4 songs
per month, what is the ×
minimum number of months it
will take him to move to the
Songs mastered per
maestro level? month
+
Songs already
mastered

16. Problem 1d
To move up to the maestro Since Ishaan needs to
level in his piano
school, Ishaan needs to have at least 80 songs
master at least 80 songs. mastered to move to
Ishaan has already
mastered 16 songs. If Ishaan
maestro level, we can
can typically master 4 songs set up an inequality to
per month, what is the find the number of
minimum number of months it
will take him to move to the months needed
maestro level?

17. Problem 1e
To move up to the maestro  Number of songs
level in his piano
school, Ishaan needs to mastered ≥80
master at least 80 songs.
Ishaan has already Number of songs mastered
mastered 16 songs. If Ishaan
can typically master 4 songs =
per month, what is the Months at school
minimum number of months it ×
will take him to move to the Songs mastered per month
maestro level?
+
Songs already mastered

18. Problem 1f
To move up to the maestro We are solving for the
level in his piano
school, Ishaan needs to months spent at
master at least 80 songs. school, so let the
Ishaan has already
mastered 16 songs. If Ishaan
number of months be
can typically master 4 songs represented by the
per month, what is the variable x.
minimum number of months it
will take him to move to the
maestro level?
y = mx+b
y = mx+b

19. Problem 1g
To move up to the maestro y = mx+b
level in his piano
school, Ishaan needs to y = mx+b
master at least 80 songs.
Ishaan has already
mastered 16 songs. If Ishaan We can now plug in:
can typically master 4 songs
per month, what is the 80 = 4x +16
minimum number of months it
will take him to move to the
maestro level?

20. Problem 1h Two step
Equation
To move up to the maestro  We can now plug in:
level in his piano
school, Ishaan needs to 80 = 4x +16
master at least 80 songs.
Ishaan has already
mastered 16 songs. If Ishaan
can typically master 4 songs
per month, what is the 80 = 4x +16
minimum number of months it
will take him to move to the -16 = 4x -16
maestro level?
64 = 4x

21. Problem 1i
To move up to the maestro
level in his piano
school, Ishaan needs to
master at least 80 songs.
Ishaan has already
mastered 16 songs. If Ishaan
can typically master 4 songs
per month, what is the
minimum number of months it
will take him to move to the
maestro level?

22. Problem 1j
To move up to the maestro
level in his piano
school, Ishaan needs to Ishaan must work 16
master at least 80 songs.
Ishaan has already
months
mastered 16 songs. If Ishaan
can typically master 4 songs
per month, what is the
minimum number of months it
will take him to move to the
maestro level?

23. Problem 2a
For every level Kevin completes in his favorite
game, he earns 800 points. Kev already has 450
points in the game and wants to end up with at
least 3,390 points before he goes to bed. What is
the minimum number of complete levels
that Kevin needs to complete to reach his goal?

24. Problem 2a
For every level Kevin completes  To solve this, let's set
in his favorite up an expression to
game, he earns 800 points. Kev
show how many
in already has 450points in the
game and wants to end up with points Kevin will
at least 3390 points have after each level.
before he goes to bed. What is
the minimum number of
complete levels
that Kevin needs to complete to
reach his goal?

25. Problem 2a
For every level Kevin completes Number of points
in his favorite
game, he earns 800 points. Kev
=
already has 450 points in the Levels completed
game and wants to end up with ×
at least 3390 points
before he goes to bed. What is Points per level
the minimum number of +
complete levels
that Kevin needs to complete to Starting points
reach his goal?

26. Problem 2a
For every level Kevin completes Since Kevin wants to
in his favorite have at
game, he earns 800 points. Kev
least 3390 points
already has 450 points in the
game and wants to end up with before going to bed, we
at least 3390 points can set up an
before he goes to bed. What is inequality.
the minimum number of
complete levels
that Kevin needs to complete to
reach his goal?

27. Problem 2a
For every level Kevin completes  Number of
in his favorite points ≥3390
game, he earns 800 points. Kev
already has 450 points in the  Levels
game and wants to end up with completed × Points
at least 3390 points per level + Starting
before he goes to bed. What is points ≥3390
the minimum number of
complete levels

that Kevin needs to complete to
reach his goal?

28. statistics
 http://bag.sh/26ku+