One Variable Inequality Word Problems

Which inequality is represented by the words " more than"?

• <

• >

• ≤

• ≥

Which inequality is represented by the words " at least"?

• <

• >

• ≤

• ≥

Joan needed $100 to buy a graphing calculator for her math class. Her neighbor will pay her $5 per hour to babysit and her Father gave her $10 for mowing the lawn. Which inequality represents the minimum amount of hours she will need to babysit in order for her to buy her calculator?

• 5x + 10 ≥ 100

• 5x - 100 ≥ 10

• 10x + 5 ≤ 100

• 5x + 10 > 100

The dance committee hired a DJ for the fall dance. The DJ charges $125 per hour but offers a $55 discount for clients who pay ahead of time. 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 if the committee pays ahead of time?

• 125x + 55 < 600

• 125x - 55 > 600

• 125x + 55 > 600

• 125x - 55 < 600

The Rug store installs carpet for $80 plus $9.50 per square yard of carpet. The Magic Carpet charges $120 for installation and $7.50 per square yard of carpet. Write an inequality that could be used to determine the number of square yards of carpet that need to be installed for The Rug Store to charge more than The Magic Carpet.

• 80+9.50x > 120+7.50x

• 80+9.50x < 120+7.50x

• 80x+9.50 > 120x+7.50

• 80x+9.50 < 120x+7.50

Cody’s Gym charges a $18 fee to join and $30 per month. Tyler’s Gym charges a $50 fee to join and $20 per month. Write an inequality that could be used to determine how many months you will have to go to the gym before Tyler’s gym would be the better deal.

• 50 + 20x < 18 + 30x

• 50x + 20 < 18x + 30

• 50 + 20x > 18 + 30x

• 50x + 20 > 18x + 30

A rectangle has a length that is seven inches longer than its width (w). If the perimeter of this rectangle is at most 30 inches, which of the following inequalities gives the possible values of "w"?

The budget for a banquet is $1,900. If it costs $3.75 to serve a single meal at this banquet, which inequality describes the possible numbers of meals (m) that can be served?

Read each answer choice carefully!

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

Cole is doing a basketball challenge for charity. In order to win money for the charity, he needs to score at least 20 points in less than 10 shots. If x is the number of 2-point shots, and y is the number of three point shots, which inequalities below represent the situation?

• x + y < 10

  2x + 3y ≥ 20

• x + y ≤ 10

  2x + 3y ≥ 20

• x + y ≤ 10

  2x + 3y > 20

• x + y < 10

  2x + 3y > 20