2-6 Systems of Inequalities Word Problems

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.

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CCSS.HSA.REI.C.7

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

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CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

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

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CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

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

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CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

Write the system of inequalities
Eiko is drawing caricatures at a fair for 8 hours (480 minutes). She can complete a small drawing in 15 minutes and charges $10 for the drawing. She can complete a larger drawing in 45 minutes and charges $25 for the drawing. Eiko hopes to make at least $200 at the fair. 

• 10x+15y≤480
  45x+25y≥250
• 10x+25y≤200
  15x+45y≤480
• 10x+25y>200
  15x+45y<480
• 10x+25y≥200
  15x+45y≤480

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CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.D.12

Cullin needs to save at least $100 for homecoming.  He works 2 jobs earning $8/hour at Culvers and $25/hour mowing lawns.  He only has time to work 14 hours before homecoming. 

• x + y  ≥ 25
  x + y ≤ 8
• 100x + 25 y ≤ 100
  2x + 8y ≤ 14
• x + y ≥ 100
  8x + 25y ≤ 14
• 8x + 25y ≥ 100
  x + y ≤ 14

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CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.D.12

Cameron uses a laser range finder to determine distances on the golf course.  Her range finder is accurate to within 0.5 yard.  If Cameron measures the distance from the tee to the flag on a par 3 to be 136 yards, what is the minimum number of yards that the distance could actually be? 

• 133 ≤  x ≤ 139
• 136.5
• 135.5 ≤  x ≤ 136.5
• 135.5

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CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

CCSS.HSN.Q.A.3

Tyler has no more than $20 in his bank account.

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CCSS.6.EE.B.8

There are less than 180 days left of school.

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CCSS.6.EE.B.8

Haley hopes to make higher than a 90 in Math this quarter.

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CCSS.6.EE.B.8