Writing and Solving Linear Equations - Real World Application

​Writing and Solving Linear Equations –
Real World Applications

By James Shiring

Open Ended

Where have you used math outside of school?

Many real-world scenarios can be solved using algebra. We can write equations and solve for the unknown variable.

Example 1: Savings

Bonnie is saving to purchase a new cell phone that costs $450. She is saving $30 per week. How many weeks will it take for Bonnie to save enough money to afford the cellphone?

Let x = ???

Bonnie is saving to purchase a new cell phone that costs $450. She is saving $30 per week. How many weeks will it take for Bonnie to save enough money to afford the cellphone?

Example 1:

Let x = number of weeks

Bonnie is saving to purchase a new cell phone that costs $450. She is saving $30 per week. How many weeks will it take for Bonnie to save enough money to afford the cellphone?

Example 1

Let x = number of weeks

Equation:

Bonnie is saving to purchase a new cell phone that costs $450. She is saving $30 per week. How many weeks will it take for Bonnie to save enough money to afford the cellphone?

Example 1

Let x = number of weeks

Equation: 30x = 450

Bonnie is saving to purchase a new cell phone that costs $450. She is saving $30 per week. How many weeks will it take for Bonnie to save enough money to afford the cellphone?

Example 1

Now Let's solve!

Bonnie is saving to purchase a new cell phone that costs $450. She is saving $30 per week. How many weeks will it take for Bonnie to save enough money to afford the cellphone?

Example 1

Now Let's solve!

Bonnie is saving to purchase a new cell phone that costs $450. She is saving $30 per week. How many weeks will it take for Bonnie to save enough money to afford the cellphone?

Example 1

x = 15

It will take 15 weeks for Bonnie to save enough money

Now Let's solve!

Bonnie is saving to purchase a new cell phone that costs $450. She is saving $30 per week. How many weeks will it take for Bonnie to save enough money to afford the cellphone?

Example 1

Discussion

What if Bonnie already had $60 saved? How does this change the equation?

30x = 450

What if Bonnie already had $60 saved? How does this change the equation?

Example 1: Continued

30x + 60 = 450

Now let's solve!

What if Bonnie already had $60 saved? How does this change the equation?

Example 1: Continued

30x + 60 = 450
- 60 -60

Now let's solve!

What if Bonnie already had $60 saved? How does this change the equation?

Example 1: Continued

30x + 60 = 450
- 60 -60

30x = 390

Now let's solve!

What if Bonnie already had $60 saved? How does this change the equation?

Example 1: Continued

Now let's solve!

What if Bonnie already had $60 saved? How does this change the equation?

Example 1: Continued

Now let's solve!

What if Bonnie already had $60 saved? How does this change the equation?

Example 1: Continued

x = 13

It will take 13 weeks for Bonnie to save enough money

Solution

What if Bonnie already had $60 saved? How does this change the equation?

Example 1: Continued

Example 2

Evan wants to fence in a rectangular region in his yard for a garden. He wants the length of the garden to be 4 times the width. If he has 180 feet of fencing, what are the dimensions of the garden?

Identify what we are looking for.

Evan wants to fence in a rectangular region in his yard for a garden. He wants the length of the garden to be 4 times the width. If he has 180 feet of fencing, what are the dimensions of the garden?

Example 2

Identify what we are looking for.

Length = ?

Width = ?

Evan wants to fence in a rectangular region in his yard for a garden. He wants the length of the garden to be 4 times the width. If he has 180 feet of fencing, what are the dimensions of the garden?

Example 2

Identify what we are looking for.

Length = 4x

Width = x

Evan wants to fence in a rectangular region in his yard for a garden. He wants the length of the garden to be 4 times the width. If he has 180 feet of fencing, what are the dimensions of the garden?

Example 2

How do we find the Perimeter?

Evan wants to fence in a rectangular region in his yard for a garden. He wants the length of the garden to be 4 times the width. If he has 180 feet of fencing, what are the dimensions of the garden?

Example 2

How do we find the Perimeter?


Equation: L + L + W + W

Evan wants to fence in a rectangular region in his yard for a garden. He wants the length of the garden to be 4 times the width. If he has 180 feet of fencing, what are the dimensions of the garden?

Example 2

How do we find the Perimeter?
Length = 4x
Width = x

Equation: P= L+ L + W + W

Evan wants to fence in a rectangular region in his yard for a garden. He wants the length of the garden to be 4 times the width. If he has 180 feet of fencing, what are the dimensions of the garden?

Example 2

How do we find the Perimeter?
Length = 4x
Width = x

Equation: 180 = 4x+ 4x + x + x

Evan wants to fence in a rectangular region in his yard for a garden. He wants the length of the garden to be 4 times the width. If he has 180 feet of fencing, what are the dimensions of the garden?

Example 2

Let's Solve

Equation: 180 = 4x+ 4x + x + x

Evan wants to fence in a rectangular region in his yard for a garden. He wants the length of the garden to be 4 times the width. If he has 180 feet of fencing, what are the dimensions of the garden?

Example 2

Let's Solve - Combine Like Terms!

Equation: 180 = 4x+ 4x + x + x

Evan wants to fence in a rectangular region in his yard for a garden. He wants the length of the garden to be 4 times the width. If he has 180 feet of fencing, what are the dimensions of the garden?

Example 2

Let's Solve - Combine Like Terms!

Equation: 180 = 10x

Evan wants to fence in a rectangular region in his yard for a garden. He wants the length of the garden to be 4 times the width. If he has 180 feet of fencing, what are the dimensions of the garden?

Example 2

Let's Solve

Equation: 180 = 10x

Evan wants to fence in a rectangular region in his yard for a garden. He wants the length of the garden to be 4 times the width. If he has 180 feet of fencing, what are the dimensions of the garden?

Example 2

Evan wants to fence in a rectangular region in his yard for a garden. He wants the length of the garden to be 4 times the width. If he has 180 feet of fencing, what are the dimensions of the garden?

Example 2

Solution

x = 18

Evan wants to fence in a rectangular region in his yard for a garden. He wants the length of the garden to be 4 times the width. If he has 180 feet of fencing, what are the dimensions of the garden?

Example 2

Remember, we need to find the length and width!

x = 18

Evan wants to fence in a rectangular region in his yard for a garden. He wants the length of the garden to be 4 times the width. If he has 180 feet of fencing, what are the dimensions of the garden?.

Example 2

Length = 4x
Width = x

Evan wants to fence in a rectangular region in his yard for a garden. He wants the length of the garden to be 4 times the width. If he has 180 feet of fencing, what are the dimensions of the garden?.

Example 2

Length = 4(18) = 72
Width = 18

Evan wants to fence in a rectangular region in his yard for a garden. He wants the length of the garden to be 4 times the width. If he has 180 feet of fencing, what are the dimensions of the garden?.

Example 2

Length = 72 feet

Width = 18 feet

Evan wants to fence in a rectangular region in his yard for a garden. He wants the length of the garden to be 4 times the width. If he has 180 feet of fencing, what are the dimensions of the garden?.

Example 2

Multiple Choice

The Roaming Cell Phone Company charges $15.00 per month plus $0.20 per minute of airtime usage.  If Juanita uses x minutes of airtime, what is an equation that can be used to determine her monthly cell phone bill (C)?

• C = 0.20x + 15
• C =15 (0.20x)
• C = 15 + x + 0.20
• C = 0.20 + 15x

Multiple Choice

The drama club sold tickets to a play for $5 each.  They also made $55 in soda and popcorn sales.  If the drama club made a total of $290, how many tickets were sold?

• 47
• 58
• 69
• 113

Multiple Choice

Which equation represents the total cost of a repair by an electrician after x hours?
An electrician charges $90 per hour plus a $50 travelling fee.

• y = 50 - 90x
• y = 90x + 50
• y = -50x + 90
• y = -90 - 50x

Multiple Choice

There is a daily fee for renting a moving truck, plus a charge of $0.50 per mile driven.  If driven 48 miles, it costs $64 to rent a truck.  Find the daily fee.

• $40
• $53
• $37
• $42

Multiple Choice

Henry goes bowling. It costs $6 to rent bowling shoes and each game costs $4.50. If Henry spent $33 at the bowling alley, how many games did he bowl?

• 4 games

• 5 games

• 6 games

• 7 games