Systems of Inequalities word Problems

Luka and Dana are making cookies for the Westland Pantry. They only have up to 8 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 ≥ 8
  32x + 20y ≤ 150

• 20x + 32y ≥ 8
  x + 20y ≥ 150

• x + y ≤ 8
  32x + 20y ≤ 150

• x + y ≤ 8
  32x + 20y ≥ 150

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

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

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

What's the difference between systems of equations and systems of inequalities?

• Systems of equations have 1 solution, no solution, or infinite solutions while systems of inequalities can have a range of solutions.

• Systems of equations use slope-intercept form only while systems of inequalities use standard form only.

• Systems of equations have a shaded region while systems of inequalities do not.

• There is no difference.

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.REI.D.12

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

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.D.12

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.

Which region represents less than 300 seats sold?

• Red

• Blue

• Purple (red and blue overlap)

• Non Shaded

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.D.12

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.

Which region represents more than 300 seats sold and less than $2000 made?

• Red

• Blue

• Purple (red and blue overlap)

• Non Shaded

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.D.12

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.

Which region represents more than $2000 made?

• Red

• Blue

• Purple (red and blue overlap)

• Non Shaded

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.D.12

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.

Which region represents more than $2000 made and less than 30 tickets sold?

• Red

• Blue

• Purple (red and blue overlap)

• Non Shaded

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.D.12

Luka and Dana are making cookies for the Westland Pantry. They only have up to 8 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 region represents less than 8 hours baking?

• Red

• Blue

• Purple (overlap of red and blue)

• Non- Shaded

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.12

Luka and Dana are making cookies for the Westland Pantry. They only have up to 8 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 region represents less than 8 hours baking and over 150 cookies made?

• Red

• Blue

• Purple (overlap of red and blue)

• Non- Shaded

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.C.6

CCSS.HSA.REI.D.12