Linear Equations and Inequalities Word Problems

Identify the equation that represents this real-world problem:
A1 Plumbing service charges $35 per hour plus a $25 travel charge for a service call.  Good Guys Plumbing Repair charges $40 per hour for a service call with no travel charge.  How long must a service call be for the two companies to charge the same amount? 

• 25x + 35x = 40x
• 35x + 25 = 40x
• 35 + 25x = 40
• 35 + 25 = 40x

Identify the equation that represents this real-world situation:

All-Day Fitness Club charges $22 per month plus an $80 initiation fee for a membership. If a member paid $168, how many months did they pay for?

• 168 = 22x + 80

• 168 - 22x = 80

• 80x + 22 = 168

• 80x + 22x = 168x

Identify the equation that represents the real-world situation:

Discount Shipping Company charges $20 plus $1.50 a pound to ship an overnight package. If the company charged a total of $150, what was the weight of the package?

• 20x + 1.5 = 150

• 150x = 20x + 1.5x

• 150 = 20 + 1.5x

• 20 - 1.5x = 150

Identify the inequality that represents the real-world situation:

The Moore family budgets to spend less than $200 a month for cell phone services. Phones R Us charges $75 per line and offers a one-time sign up discount of $100. Write an inequality that can be used to determine the number of phone lines they can use while meeting their budget.

• 75x + 100 < 200

• 75x - 100 > 200

• 75x - 100 < 200

• 75x - 100 = 200

Which situation can be represented by the inequality 15x > 12x + 100? 

• Juanita saves $15 each week.  Dan has already saved $100 and saves $12 each week.  When will Juanita have less money saved than Dan?
• Juanita saves $12 each week.  Dan has already saved $100 and saves $15 each week.  When will Juanita have less money saved than Dan? 
• Juanita saves $15 each week.  Dan has already saved $100 and saves $12 each week.  When will Juanita have more money saved than Dan?
• Juanita saves $12 each week.  Dan has already saved $100 and saves $15 each week.  When will Juanita have more money saved than Dan?

Solve the equation and identify which value correctly represents n.

15 - 1/6n = 5

• 60

• -60

• -120

• -160

Solve the equation and identify which value correctly represents x.

12.1x + 10 = 34 .2

• about 3.65

• 2

• 2.21

• 4

Solve the equation and identify which value correctly represents c.
35c + 25 = 40c

• 5
• 10
• 15
• 3

Solve the equation and identify which value correctly represents m.

30 = 25m + 80

• -55

• 2

• -2

• 25

Lea needs at least $240 to buy new headphones. She has already saved $30. She earns $14 per car that she washes.

What is the least number of cars she can wash to buy the headphones?

Define the variable.

• x = Lea

• x = the number of cars she needs to wash

• x = the number of headphones she wants to buy

• x = the money she already saved