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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. A = 3x + 0 B = 2x + 5. Let’s Walk! Who can cross the classroom first?

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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.

B = 2x + 5

Let’s 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.

B = 3x + 3

Let’s 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.

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 we’re 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 you’re trying to figure out 2 things.

2k + 1p = $20

3p + 1k = $35

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 we’re 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 you’re trying to figure out 2 things.

3k + 1p = $26

3p + 2k = $36

Make one for your neighbour.

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 we’re 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 you’re trying to figure out 2 things.

l

Step 1B:

Draw a picture!

2l + 2w = 10

w + 1 = l

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 we’re 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:

l

Step 1B:

Draw a picture!

2l + 2w = 12

w + 2 = l

Make one for your neighbour.

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 we’re 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:

To decide which

columns to add, look

for the variables!

Step 2B:

Make a table.

t + f = 100

0.10t + 0.05f = 70

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 we’re 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:

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.

End 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?

Start

Mrs. Lamoureux canoes to school. On the way to school, she paddles downstream for 1hr. The river’s 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 we’re 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:

Step 1B:

Draw a picture!

Distance = speed x time

Step 2B:

Make a table.

d = (s + 4) x 1

d = (s – 4) x 2

End 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?

Start

Mr. Marchildon also canoes to school. On the way to school, he paddles downstream for 0.5hr. The river’s 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 we’re 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:

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.

There you have it! 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?

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 don’t understand.

If you stay on task, you will be given the rest of today’s class and tomorrow’s class to complete the assignment. Then, you shouldn’t have much homework.

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