Systems of Inequalities Word Problems

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

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

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

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

You can work a total of no more than 41 hours each week at your two jobs. Housecleaning pays $5 per hour and your sales job pays $8 per hour. You need to earn at least $254 each week to pay your bills. Write a system to represent the situation.

• x+y≤254
  5x+8y≥41
• x+41≤y
  5x+8y≥254
• x+y≤41
  5x+8y≥254
• x+y>41
  5x+8y<254

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

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

Christian had brochures printed for a new business venture. Christian originally ordered 4 boxes of black-and-white brochures and 3 boxes of color brochures, which cost a total of $134. After those ran out, Christian spent $120 on 3 boxes of black-and-white brochures and 3 boxes of color brochures. Which system represents this situation?

• x+y=134
  x+y=120
• 3x+3y=134
  4x+3y=120
• 4x+3y=134
  3x+3y=120
• 7xy=134
  6xy=120

If a system of equations has no solution, what does the graph look like? 

• intersecting lines
• parallel lines
• skew lines
• intersecting lines

Which system of inequality is shown?

• y ≥ -x - 1
  y < x + 4
• y < -x - 1
   y ≥ x + 4
• y > -x - 1
  y ≥ x + 4
• y = -x - 1
  y ≥ x + 4