Systems of Linear Inequalities Word Problems

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

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

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

Yellow Cab Taxi charges a $1.75 flat rate in addition to $0.65 per mile.  Katie has no more than $10 to spend on the taxi ride.

• 1.75 + 0.65m < 10

• 1.75 + 0.65m > 10

• 1.75m + 0.65 < 10

• 1.75m + 0.65 > 10

• A

• B

• C

• D

• (8,4)

• (10,2)

• (7,9)

• (5,9)

Which is a solution to the system of inequalities?

• (4, -2)

• (4, 6)

• (-4, 2)

• (6, -2)

Select two solutions to this system of inequalities.

• (6,-2)

• (4,-6)

• (6,-8)

• (-4,0)

• (1,3)

• (2,1)

• (3,4)

• (6,2)

Which of the following is a solution to the systems of inequalities?

• (0, 0)

• (-3, 0)

• (2, -5)

• (3, -1)