Word Problems

1
Algebraic Modelling
Word Problems
Algebraic modelling is basically word problems in
disguise. In this lesson, we will see how to
turn word problems into linear systems. We will
SOLVE these systems in the next lesson.
2
A 3x 0 B 2x 5
Lets Walk! Who can cross the classroom
first? ________ starts at 0, and can step 3
blocks each time. ________ starts at 5, and can
step 2 blocks each time.
3
A 4x 0 B 3x 3
Lets Walk Again! Who can cross the classroom
first? ________ starts at 0, and can step 4
blocks each time. ________ starts at 3, and can
step 3 blocks each time.
4
The pet store is having a sale. You can buy 2
kittens and 1 puppy for 20. You can also buy 3
puppies and 1 kitten for 35. How much does each
animal cost?

• STEP 1
• What are the two things were trying to figure
  out?
• How much are kittens?
• How much are puppies?
• STEP 2
• Assign each of them a variable letter.
• Cost of kitten k
• Cost of puppy p
• STEP 3
• Create equations using these variable letters.
  You will always create 2 equations if youre
  trying to figure out 2 things.

2k 1p 20 3p 1k 35
5
The other pet store is having a sale. You can
buy 3 kittens and 1 puppy for 26. You can also
buy 3 puppies and 2 kittens for 36. How much
does each animal cost?
Practice

• STEP 1
• What are the two things were trying to figure
  out?
• How much are kittens?
• How much are puppies?
• STEP 2
• Assign each of them a variable letter.
• Cost of kitten k
• Cost of puppy p
• STEP 3
• Create equations using these variable letters.
  You will always create 2 equations if youre
  trying to figure out 2 things.

3k 1p 26 3p 2k 36
Make one for your neighbour.
6
A gardener has a rectangular garden. The fence
around it is 10 meters long. It is 1m longer
than it is wide. What are the length and width of
the garden?
l
w
w

• STEP 1
• What are the two things were trying to figure
  out?
• How long is the garden?
• How wide is the garden?
• STEP 2
• Assign each of them a variable letter.
• Length of garden l
• Width of garden w
• STEP 3
• Create equations using these variable letters.
  You will always create 2 equations if youre
  trying to figure out 2 things.

l
Step 1B Draw a picture!
2l 2w 10 w 1 l
7
A different gardener also has a rectangular
garden. The fence around it is 12 meters long.
It is 2m longer than it is wide. What are the
length and width of the garden?
Practice
l
w
w

• STEP 1
• What are the two things were trying to figure
  out?
• How long is the garden?
• How wide is the garden?
• STEP 2
• Assign each of them a variable letter.
• Length of garden l
• Width of garden w
• STEP 3
• Create equations using these variable letters.
  You will always create 2 equations if youre
  trying to figure out 2 things.

l
Step 1B Draw a picture!
2l 2w 12 w 2 l
Make one for your neighbour.
8
Nicole invested her birthday money - 100. She
invested some at 10 per year and some at 5 per
year. After one year, she had earned 7. How
much did she invest at each rate?

• STEP 1
• What are the two things were trying to figure
  out?
• How much did she invest at 10?
• How much did she invest at 5?
• STEP 2
• Assign each of them a variable letter.
• invested at 5 f
• invested at 10 t
• STEP 3
• Create equations using these variable letters.
  You will always create 2 equations if youre
  trying to figure out 2 things.

To decide which columns to add, look for the
variables!
Step 2B Make a table.
t f 100 0.10t 0.05f 70
9
Nicole invested her birthday money last year too
- 80. She invested some at 6 per year and some
at 3 per year. After one year, she had earned
4.20. How much did she invest at each rate?
Practice

• STEP 1
• What are the two things were trying to figure
  out?
• How much did she invest at 10?
• How much did she invest at 5?
• STEP 2
• Assign each of them a variable letter.
• invested at 5 f
• invested at 10 t
• STEP 3
• Create equations using these variable letters.
  You will always create 2 equations if youre
  trying to figure out 2 things.

To decide which columns to add, look for the
variables!
Step 2B Make a table.
t f 100 0.10t 0.05f 70
Make one for your neighbour.
10
End
Start
Mrs. Lamoureux canoes to school. On the way to
school, she paddles downstream for 1hr. The
rivers current is 4km/hr. Going home takes her
2hr. How fast would Mrs. Lamoureux paddle if
there were no current? (How far does she have to
paddle?)
Current (4 km/hr)

• STEP 1
• What are the two things were trying to figure
  out?
• How fast can she paddle?
• (How far does she go?)
• STEP 2
• Assign each of them a variable letter.
• Speed in still water s
• Distance d
• STEP 3
• Create equations using these variable letters.
  You will always create 2 equations if youre
  trying to figure out 2 things.

Step 1B Draw a picture!
Distance speed x time
Step 2B Make a table.
d (s 4) x 1 d (s 4) x 2
11
End
Start
Mr. Marchildon also canoes to school. On the way
to school, he paddles downstream for 0.5hr. The
rivers current is 4km/hr. Going home takes him
1.5hr. How fast would Mr. Marchildon paddle if
there were no current? (How far does he have to
paddle?)
Practice
Current (4 km/hr)

• STEP 1
• What are the two things were trying to figure
  out?
• How fast can he paddle?
• (How far does he go?)
• STEP 2
• Assign each of them a variable letter.
• Speed in still water s
• Distance d
• STEP 3
• Create equations using these variable letters.
  You will always create 2 equations if youre
  trying to figure out 2 things.

Step 1B Draw a picture!
Distance speed x time
Step 2B Make a table.
d (s 4) x 0.5 d (s 4) x 1.5
Make one for your neighbour.
12
There you have it!
Your mission, if you choose to accept it, and
also if not, is to complete Exercises 1-13 on
pages 129-130. DO NOT FIND THE ANSWERS. Just
find the equations and draw pictures. Mr. Plett
will select 3 questions from 1-11 that must be
handed in for marks on Wednesday at the beginning
of class. If you complete 12 and 13, you will
get a special prize! Stay on task move to a
different seat if you need to ask questions if
you dont understand. If you stay on task, you
will be given the rest of todays class and
tomorrows class to complete the assignment.
Then, you shouldnt have much homework.