Systems of Inequalities Applications

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

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

Which point is part of the solution?

• (4,0)

• (0,4)

• (10,5)

• (5,10)

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

• (2,3)

• Solution

• (4, -5)

• Not a solution

• (0,0)

• Solution

• (5,6)

• Not a solution

• (2,-2)

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

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

In the previous question you wrote a system for the following situation.  Smithfield High School is having a cookie dough fundraiser. Customers can buy packages of sugar cookie dough and packages of double chocolate cookie dough.  Sugar cookie dough sells for $5 per package and a package of double chocolate cookie dough sells for $8.  The school hopes to sell at least $1000 in cookie dough and they want to sell at least 150 packages.  The correct answer is in the image.  Now create a graph. When you are done with your graph click "done". 

• click here when you are done with your graph.  

• don't click here. 

The correct graph for the story below is provided in the image. Smithfield High School is having a cookie dough fundraiser. Customers can buy packages of sugar cookie dough and packages of double chocolate cookie dough.  Sugar cookie dough sells for $5 per package and a package of double chocolate cookie dough sells for $8.  The school hopes to sell at least $1000 in cookie dough and they want to sell at least 150 packages. Which of the following is NOT a solution to the problem?

• 60 sugar and 120 chocolate 

• 120 sugar and 60 chocolate 

• 140 sugar and 20 chocolate 

• 100 sugar and 100 chocolate 

In the previous question you wrote a system for the following situation.  Jill and Jack want to improve their yards by planting hostas and ivy.  The cost of one hosta is $8 and the cost of one pot of ivy is $12.  They do not want to spend more than  $60 and they want to buy at least 6 plants.  Write a system that represents the possible number of hosta x, and ivy plants y, that could be sold to meet these conditions. The correct answer is in the image.  Now create a graph. When you are done with your graph click "done". 

• click here when you are done with your graph.  

• don't click here. 

Now you have a graph for the story: Jill and Jack want to improve their yards by planting hostas and ivy. The cost of one hosta is $8 and the cost of one pot of ivy is $12. They do not want to spend more than $60 and they want to buy at least 6 plants.Is the following graph correct?

• yes 

• no