Linear Inequality Word Problems

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.3

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.12

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

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.12

JoAnn likes her job as a baby-sitter, but it pays only $3 per hour. She has been offered a job as a tutor that pays $6 per hour. Because of school, her parents only allow her to work a maximum of 15 hours per week. How many hours can JoAnn tutor and baby-sit and still make at least $66 per week? How much does she make?

• b + t < 15
  3b + 6t > 66
• b + t > 15
  3b + 6t < 66
• 3b + 6t > 15
  b + t < 66
• 3b + 6t < 15
  b + t < 66

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

CCSS.HSA.SSE.A.1

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

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.12

David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation?

• 1.5x+0.5y=78.5
  x+y=87
• 1.5x+0.5y=78.5
  1.5x+0.5y=87
• x+y=78.5
  1.5x+0.5y=87
• x+y=78.5
  x+y=87

Tags

CCSS.HSA.CED.A.3

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

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

CCSS.HSN.Q.A.3

When grilling steaks, Washington likes to keep the grill temperature at 425°, plus or minus 15°.  Within what range of temperatures does Washington like the grill to be when he cooks his steaks? 

• 440° <  x < 410°
• 410° ≤  x ≤ 440°
• 440° ≤  x ≤ 410°
• 440° ≤ x ≥410°

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

CCSS.HSA.SSE.A.1

Caitlin won a bag full of money! She has 49 bills in all. She counts $1,430. There are $20 dollar bills and $50 dollar bills. How many of each bill does Caitlin have?
WRITE a system where T= # of $20 and F = # of $50.

• T + F = 1430
  20T + 50F = 49
• T+ F = 49
  10T + 5F = 1430 
• T + F = 49
  20T + 50F  = 1430
• T + F = 49
  T + F = 1430

Tags

CCSS.8.EE.C.8C

It takes Sarah 2 hours to make small purses and 3 hours to make big purses. She has a maximum of 18 hours a week. Which inequality represents this situation?

• 2x + 3y ≤ 18

• x + y ≤ 6

• x + y ≤ 9

• 3x + 2y ≤ 18

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.CED.A.2

Fuel x costs $2 per gallon and fuel y costs $3 per gallon. You have at most $18 to spend on fuel. Your tank can hold 14 gallons at most. Write a system to represent this situation.

• x+y≤14
  2x+3y≤18
• 2x+3y≤14
  x+y≤18
• 2x+y<18
  x+3y<14
• x+14≤y
  2x+3y≤18

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.CED.A.2