Inequalties in Context

1. Under her cell phone plan, Mayerlin pays a flat cost of $55 per month and $5 per gigabyte. She wants to keep her bill under $70 per month. Write an inequality which can be used to determine x, the number of gigabytes Mayerlin can use while staying within her budget.

• 55x+5 >70

• 55x+5<70

What symbol means at most?

• <

• >

What symbol means at least?

• <

• >

1. Violet needs to order some new supplies for the restaurant where she works. The restaurant needs at least 800 glasses. There are currently 164 glasses. If each set on sale contains 6 glasses, write an inequality which can be used to determine x, the number of sets of glasses Violet could buy for the restaurant to have enough glasses.

What symbol means under?

• <

• >

1. A group of friends wants to go to the amusement park. They have no more than $190 to spend on parking and admission. Parking is $7, and tickets cost $15.25 per person, including tax. Write an inequality which can be used to determine p, the number of people who can go to the amusement park.

1. Owen has a points card for a movie theater.

• He receives 30 rewards points just for signing up.

• He earns 12.5 points for each visit to the movie theater.

• He needs at least 115 points for a free movie ticket.

Write an inequality which can be used to determine x, the number of visits Owen can make to earn his first free movie ticket.

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

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

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