Linear Inequalities Word Problems (& Systems)

Multiple Choice

The dance committee hired a DJ for the fall dance. The DJ charges $125 per hour in addition to $55 for an assistant. The committee wants to keep the total cost under $600. Which inequality represents the maximum amount of hours the DJ will play at the dance?

• 125x + 55 ≤ 600
• 125x + 55 ≥ 600
• 125x + 55 > 600
• 125x + 55 < 600

Multiple Choice

The Bombetta Company wants to send a team of three representatives to a conference.  Their budget is $700.00 plus $125.00 per day for expenses.  If their total budget cannot exceed $1,400.00, which of the following inequalities expresses this situation?

• 125x + 700 ≥1,400
• 700 + 125x ≤1,400
• 700x + 125 ≤1,400
• 125x - 700 ≤ 1,400

Multiple Choice

At the Big Bear video rental store, blank CDs cost $1.50 each and blank DVDs cost $3.25 each.  Which of the following statements best describes the number of CDs (c) and DVDs (d) that can be purchased for less than $65.00?

• 1.50c + 3.25d < 65.00

• 3.25c + 1.50d <65.00

• 1.50c + 3.25d ≤ 65.00

• 3.25c + 1.50d ≤ 65.00

Multiple Choice

Sam make $10.25 per hour working at Cheddars.  He plans to buy a laptop for $550.  Write and solve an inequality describing how many hours h Sam will have to work to be able to buy the laptop. (Round to the next higher hour)

• 10.25h < 550

  less than 54 hours

• 10.25h > 550

  greater than 54 hours

• 10.25h ≤ 550

  at most 54 hours

• 10.25h ≥ 550

  at least 54 hours

Multiple Choice

Johnny earns $15 per hour dog walking. He wants to earn at least $105 to buy a new bike. Which inequality represents how long Johnny needs to work to afford his new bike?

• 15h ≤ 105

• 15h > 105

• 15h < 105

• 15h ≥ 105

Multiple Choice

The Starlight Bowling Alley charges $6 to rent shoes and $8 per game. Cameron has only $42 to spend. Which inequality represents this scenario if “x” represents the number of games Cameron can play?

• 6x + 8 ≥ 42

• 8x + 6 ≤ 42

• 6x + 8 > 42

• 8x + 6 < 42

Multiple Choice

A limo driver needs to make more than $450 in one day. He charges a rental fee of $375 plus $0.85 per mile. What inequality represents the number of miles, x, he would have to drive to reach his goal?

• 0.85x + 375 > 450

• 0.85x + 375 < 450

• 0.85 + 375x > 450

• 0.85 + 375x < 450

Multiple Choice

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, which system could be used to find how many of each type of ticket were sold?

• S + A = 530
  3S + 4A = 1740
• S + A = 530
  4S + 3A = 1740
• S + A = 1740
  3S + 4A = 530
• S + A = 1740
  4S + 3A = 530

Multiple Choice

Write the system of inequalities:
Carlos works at a movie theater selling tickets. The theater has 300 seats and charges $7.50 for adults and $5.50 for children. The theater expects to make at least $2000 for each showing

• x+y≤300
  7.5x+5.5y≥2000
• x+y<300
  7.5x+5.5y≥2000
• x+y≤300
  7.5x+5.5y≤2000
• x+y>2000
  7.5x+5.5y≤300

Multiple Choice

JoAnn likes her job as a baby-sitter, but it pays only $3 per hour. She has been offered a job as a tutor that pays $6 per hour. Because of school, her parents only allow her to work a maximum of 15 hours per week.

How many hours can JoAnn tutor and baby-sit and still make at least $66 per week?

• b + t < 15
  3b + 6t > 66
• b + t > 15
  3b + 6t < 66
• 3b + 6t > 15
  b + t < 66
• 3b + 6t < 15
  b + t < 66

Multiple Choice

Luka and Dana are making cookies for the Westland Pantry. They only have up to 6 hours to bake!

They can bake 32 chocolate chip cookies in an hour (x), and 20 snickerdoodle cookies in an hour (y).

They need to make at least 150 cookies.

Which inequalities represent the situation?

• x + y ≥ 6
  32x + 20y ≤ 150

• x + y ≥ 632
  x + 20y ≥ 150

• x + y ≤ 6
  32x + 20y ≤ 150

• x + y ≤ 6
  32x + 20y ≥ 150

Multiple Choice

Kate is selling bracelets and earrings on Etsy to make money for summer vacation. The bracelets (x) cost $2 and earrings (y) cost $3. She needs to make at least $100, but can only make up to 40 pieces of jewelry. Which inequalities represent this situation?

• 2x + 3y > 100

  x + y ≤ 40

• 100x + 2y > 3

  x + y ≤ 40

• 100x + 40y > 100

  3x + 2y ≤ 40

• 3x + 2y > 100

  x + y ≤ 40

Multiple Choice

Jonah is going to the store to buy candles. Small candles cost $3.50, and large candles cost $5.00.

He needs to buy at least 20 candles and cannot spend more than $80.

Write a system of linear inequalities that represents the situation.

• $$x+y\le20$$

  $$3.5x+5y\ge80$$

• $$xy\ge20$$
  $$3.5+5y\le80$$

• $$x-y\ge20$$
  $$3.5x+5y\le80$$

• $$x+y\ge20$$
  $$3.5x+5y\le80$$

Multiple Choice

Which of the following is not a solution to this system of inequalities?

• (0,-1)
• (0,3)
• (4,0)
• (6,-2)

Multiple Choice

Which system of inequalities matches the graph?

• y > 2x - 4
  y < 2
• y < 2x - 4
  y < 2
• y > 2x - 4
  y <  2 
• y < 2x - 4
  y <   -2