Applications of Inequality Systems

Select the correct graph for each inequality.

• A

• B

• C

• D

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

• (0,-1)

• (0,3)

• (4,0)

• (6,-2)

Select the graph for y ≥ -3.

• A

• B

• C

• D

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

Justin wants to make some chocolate milk using whole milk and chocolate syrup. He wanted his chocolate milk to have less than 10 grams of fat and less than 30 grams of sugar. The first mixture was on the amount of fat. He combined x ounces of whole milk containing 1 gram of fat per ounce with y ounces of chocolate syrup containing 0.34 grams of fat per ounce. The second mixture was focused on sugar and consisted of x ounces of whole milk containing 1.4 grams of sugar per ounce and y ounces of chocolate syrup containing 16 grams of sugar per ounce. Use the dropdowns to write a system of inequalities to represent the constraints of this situation. x + 0.34y ​ (a)   1.4x + 16y ​ (b)  

• < 10

• < 30

• > 10

• >30

Justin wants to make some chocolate milk using whole milk and chocolate syrup. He wanted his chocolate milk to have less than 10 grams of fat and less than 30 grams of sugar. The first mixture was on the amount of fat. He combined x ounces of whole milk containing 1 gram of fat per ounce with y ounces of chocolate syrup containing 0.34 grams of fat per ounce. The second mixture was focused on sugar and consisted of x ounces of whole milk containing 1.4 grams of sugar per ounce and y ounces of chocolate syrup containing 16 grams of sugar per ounce. Use the dropdowns to write a system of inequalities to represent the constraints of this situation. x + 0.34y ​ (a)   1.4x + 16y ​ (b)  

• < 10

• < 30

• > 10

• >30

Determine whether each ordered pair is a solution or not a solution to this system of inequalities.

y ≥ −x ​

2x + y > 2

• Solution

• (2,3)

• Solution

• (5,6)

• Not a solution

• (2,-2)

• Not a solution

• (4, -5)

• Not a solution

• (0,0)

Determine whether each ordered pair is a solution or not a solution to this system of inequalities.

y≥−x ​

2x+y>2

• Not a solution

• (2,-2)

• Not a solution

• (2,3)

• Solution

• (5,6)

• Not a solution

• (4, -5)

• Solution

• (0,0)

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

Select the correct graph for each inequality.

• A

• B

• C

• D