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Building Linear Equations from Word Problems

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Building Linear Equations from Word Problems. A family daycare center charges a $75 enrollment fee and $100 per week. Write an equation for the total cost over time. A family daycare center charges a $75 enrollment fee and $100 per week. Write an equation for the total cost over time. - PowerPoint PPT Presentation

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Page 1: Building Linear Equations  from Word Problems
Page 2: Building Linear Equations  from Word Problems

Step Things to rememberWhat to do in the

equation

Step 1:

Step 2:

Step 3:

Step 4:

Page 3: Building Linear Equations  from Word Problems

A family daycare center charges a $75 enrollment fee and $100

per week. Write an equation for the total cost over time.

Page 4: Building Linear Equations  from Word Problems

A family daycare center charges a $75 enrollment fee and $100 per week. Write an

equation for the total cost over time.

Step 1: Identify the variables• Variables represent values that can change.• There may be one, two or several in a word problem.

Page 5: Building Linear Equations  from Word Problems

A family daycare center charges a $75 enrollment fee and $100 per week. Write an

equation for the total cost over time.

W

Write letters for the variables that will help you

remember what they represent.

Page 6: Building Linear Equations  from Word Problems

A family daycare center charges a $75 enrollment fee and $100 per week. Write an

equation for the total cost over time.

W T

Write letters for the variables that will help you remember what they represent.

Page 7: Building Linear Equations  from Word Problems

A family daycare center charges a $75 enrollment fee and $100 per week. Write an

equation for the total cost over time.

Step 2: Identify the end result of the situation.• This may be a variable (if you don’t know the value) or a number (if the value is given).

Page 8: Building Linear Equations  from Word Problems

A family daycare center charges a $75 enrollment fee and $100 per week. Write an

equation for the total cost over time.

W T

Put the end result after the equal sign.

Page 9: Building Linear Equations  from Word Problems

A family daycare center charges a $75 enrollment fee and $100 per week. Write an

equation for the total cost over time.

W = T

Put the end result after the equal sign.

Page 10: Building Linear Equations  from Word Problems

A family daycare center charges a $75 enrollment fee and $100 per week. Write an

equation for the total cost over time.

Step 3: Identify any constants.• A constant is a value that will stay the same no matter what the variables are. • Figure out if the constant is being added to or subtracted from the total.

Page 11: Building Linear Equations  from Word Problems

A family daycare center charges a $75 enrollment fee and $100 per week. Write an

equation for the total cost over time.

W + 75 = T

Add or subtract the constant(s).

Page 12: Building Linear Equations  from Word Problems

A family daycare center charges a $75 enrollment fee and $100 per week. Write an

equation for the total cost over time.

Step 4: Identify the rate(s) of change.

• The rate of change is how much the total will change each time the variable changes.• In a linear equation, the rate of change will remain steady.

Page 13: Building Linear Equations  from Word Problems

A family daycare center charges a $75 enrollment fee and $100 per week. Write an

equation for the total cost over time.

100 * W + 75 = T

Multiply the rate of change by the variable(s).

Page 14: Building Linear Equations  from Word Problems

A family daycare center charges a $75 enrollment fee and $100 per week. Write an

equation for the total cost over time.

100 * W + 75 = T

Page 15: Building Linear Equations  from Word Problems

Next problem: The daycare center down the street charges no enrollment fee, but $110 per week. Write an equation for the

total cost over time.

Page 16: Building Linear Equations  from Word Problems

The daycare center down the street charges no enrollment fee, but $110 per week. Write an

equation for the total cost over time.

Step 1: Identify the variables

Page 17: Building Linear Equations  from Word Problems

The daycare center down the street charges no enrollment fee, but $110 per week. Write an

equation for the total cost over time.

W T

Step 1: Identify the variables

Page 18: Building Linear Equations  from Word Problems

The daycare center down the street charges no enrollment fee, but $110 per week. Write an

equation for the total cost over time.

W T

Step 1: Identify the variables.

Step 2: Identify the end result of the situation

Page 19: Building Linear Equations  from Word Problems

The daycare center down the street charges no enrollment fee, but $110 per week. Write an

equation for the total cost over time.

W = T

Step 1: Identify the variables.

Step 2: Identify the end result of the situation

Page 20: Building Linear Equations  from Word Problems

The daycare center down the street charges no enrollment fee, but $110 per week. Write an

equation for the total cost over time.

W = T

Step 1: Identify the variables.

Step 2: Identify the end result of the situation

Step 3: Identify any constants.

Page 21: Building Linear Equations  from Word Problems

The daycare center down the street charges no enrollment fee, but $110 per week. Write an

equation for the total cost over time.

W = T

Step 1: Identify the variables.

Step 2: Identify the end result of the situation

Step 3: Identify any constants.

None!

Page 22: Building Linear Equations  from Word Problems

The daycare center down the street charges no enrollment fee, but $110 per week. Write an

equation for the total cost over time.

W = T

Step 1: Identify the variables.

Step 2: Identify the end result of the situation

Step 3: Identify any constants.

Step 4: Identify the rate(s) of change.

Page 23: Building Linear Equations  from Word Problems

The daycare center down the street charges no enrollment fee, but $110 per week. Write an

equation for the total cost over time.

110 * W = T

Step 1: Identify the variables.

Step 2: Identify the end result of the situation

Step 3: Identify any constants.

Step 4: Identify the rate(s) of change.

Page 24: Building Linear Equations  from Word Problems

The daycare center down the street charges no enrollment fee, but $110 per week. Write an

equation for the total cost over time.

110 * W = T

Page 25: Building Linear Equations  from Word Problems

Naima and her friends have $40 to spend at the movie theater. Each large popcorn costs $5 and each

small soda costs $2. Write an equation for the number of snacks

she can buy with the money she has.

Page 26: Building Linear Equations  from Word Problems

Naima and her friends have $40 to spend at the movie theater. Each large popcorn costs $5

and each small soda costs $2. Write an equation for the number of snacks she can buy

with the money she has.

Step 1: Identify the variables

Page 27: Building Linear Equations  from Word Problems

Naima and her friends have $40 to spend at the movie theater. Each large popcorn costs $5

and each small soda costs $2. Write an equation for the number of snacks she can buy

with the money she has.

P S

Step 1: Identify the variables

Page 28: Building Linear Equations  from Word Problems

Naima and her friends have $40 to spend at the movie theater. Each large popcorn costs $5

and each small soda costs $2. Write an equation for the number of snacks she can buy

with the money she has.

P S

Step 1: Identify the variables.

Step 2: Identify the end result of the situation

Page 29: Building Linear Equations  from Word Problems

Naima and her friends have $40 to spend at the movie theater. Each large popcorn costs $5

and each small soda costs $2. Write an equation for the number of snacks she can buy

with the money she has.

P S = 40

Step 1: Identify the variables.

Step 2: Identify the end result of the situation

Page 30: Building Linear Equations  from Word Problems

Naima and her friends have $40 to spend at the movie theater. Each large popcorn costs $5

and each small soda costs $2. Write an equation for the number of snacks she can buy

with the money she has.

P S = 40

Step 1: Identify the variables.

Step 2: Identify the end result of the situation

Step 3: Identify any constants.

None!

Page 31: Building Linear Equations  from Word Problems

Naima and her friends have $40 to spend at the movie theater. Each large popcorn costs $5

and each small soda costs $2. Write an equation for the number of snacks she can buy

with the money she has.

P S = 40

Step 1: Identify the variables.

Step 2: Identify the end result of the situation

Step 3: Identify any constants.

Step 4: Identify the rate(s) of change.

Page 32: Building Linear Equations  from Word Problems

Naima and her friends have $40 to spend at the movie theater. Each large popcorn costs $5

and each small soda costs $2. Write an equation for the number of snacks she can buy

with the money she has.

5 * P 2 * S = 40

Step 1: Identify the variables.

Step 2: Identify the end result of the situation

Step 3: Identify any constants.

Step 4: Identify the rate(s) of change.

Page 33: Building Linear Equations  from Word Problems

Naima and her friends have $40 to spend at the movie theater. Each large popcorn costs $5

and each small soda costs $2. Write an equation for the number of snacks she can buy

with the money she has.

5 * P + 2 * S = 40

Page 34: Building Linear Equations  from Word Problems

Step Things to rememberWhat to do in the

equation

Step 1: Identify the variables

Variables represent values that can change.

There may be one, two or several in a word problem.

Write letters for the variables that will help you

remember what they represent

Step 2: Identify the end result of

the situation.

The end result may be a variable (if you don’t know the value) or a

number (if the value is given).

Put the end result after the equal sign.

Step 3: Identify any constants.

A constant is a value that will stay the same no matter what the

variables are.

Figure out if the constant is being added to or subtracted from

the total.

Add or subtract the constant(s).

Step 4: Identify the rate(s) of

change.

The rate of change is how much the total will change each time the

variable changes.

In a linear equation, the rate of change will remain steady.

Multiply the rate of change by the variable(s).