Solving Inequalities in Two Variables

Cullin needs to save at least $100 for homecoming. He works 2 jobs, earning $8/hour at Culver's Restaurant and $25/hour mowing lawns. He only has time to work 14 hours before homecoming. Which system of inequalities below correctly models Cullin's constraints?

• 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

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

Write a system of inequalities to model the following situation:
"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

Marsha is buying plants and soil for her garden. The soil cost $4 per bag, and the plants cost $10 each. She wants to buy at least 5 plants and can spend no more than $100. Write a system of inequalities to model the situation.

• 4s+10p≤100
  s+p≥5

• 4s+10p≤100
  p≥5

• s+p≤100
  4s+10p≥5

• 4+p≤10
  5+s≤100

• Lars meets both of his expectations

• Lars works for the expected number of days but doesn't earn the expected number of money

• Lars earns the expected amount of money but doesn't work for the expected number of days

• Lars doesn't meet either of his expectations

• Astrid meets both of her expectations

• Astrid buys the expected number of fruits, but she does beyond her budget

• Astrid stays within her budget, but she doesn't buy the expected number of fruits

• Astrid doesn't meet either of her expectations

10X + 2y ≤ 14

• y ≤ -5x + 7

• y ≥-5x +7

4x + 2y ≤ 20

• -y ≤ -2x +10

• y ≤ -2x + 10

Alexa is printing brochures for his new business and needs printer cartridges. Christian needs at least 50 cartridges. Black and white cartridges are $10 and color cartridges are $15. Alexa only budgeted $500 for the project. Which system represents this situation?

• x+y≥50

  10x+15y≤500

• x+y≤50

  10x+15y≥500

• 10x+15y≥50

  x+y≤500

• 10x+15y≤50

  x+1y≥500

Lorenzo has 46 cent stamps and 20 cent stamps. He needs to use stamps totaling at least $3.00 to mail a package. There is enough room for up to 9 stamps on the package. This situation can be represented by the following system of inequalities, where x = number of 46 cent, y = number of 20 cent. Which of the following is a true statement?  x+y≤9  46x+20y≥300

• Lorenzo can use four 46 cent stamps and six 20 cent stamps

• Lorenzo can use five 46 cent stamps and four 20 cent stamps.

• If Lorenzo uses six 46 cent stamps, he only needs to use one 20 cent stamp

• If Lorenzo uses twelve 20-cent stamps, he only needs to use one 46-cent stamp.