Systems of Inequalities Applications

Which system of inequalities matches the graph?

• y > 2x - 4

  y < 2

• y < 2x - 4

  y < 2

• y > 2x - 4

  y < 2

• y < 2x - 4

  y < -2

Carlos is working two summer jobs, making $6 per hour walking dogs and making $11 per hour clearing tables. In a given week, he can work no more than 14 total hours and must earn no less than $110. If x represents the number of hours walking dogs and y represents the number of hours clearing tables, which of the following systems could represent Carlos' situation?

• 6x + 11y ≥ 110

  x + y ≤ 14

• 6x + 11y < 14

  x + y < 110

• x + y = 14

  6x + 11y = 14

• x + y > 110

  6x + 11y < 14

Damian and his children went into a grocery store that sells apples for $1.75 each and mangos for $1.25 each. Damian has $20 to spend and must buy a minimum of 13 apples and mangos altogether. If x represents the number of apples purchased and y represents the number of mangos purchased, which of the following systems of inequalities represents the scenario?

• x + y > 20

  1.75x + 1.25y < 13

• 1.75x + 1.25y ≤ 20

  x + y ≥ 13

• 1.75x + 1.25y ≥ 20

  x + y ≤ 13

Savannah is working two summer jobs, making $10 per hour washing cars and making $22 per hour tutoring. In a given week, she can work at most 8 total hours and must earn no less than $110. If x represents the number of hours washing cars and y represents the number of hours tutoring, determine which of the following is a possible number of hours she is able to work.

• 15 hours washing cars and 2 hours tutoring

• 3 hours washing cars and 12 hours tutoring

• 1 hour washing cars and 6 hours tutoring

• 2 hours tutoring and 2 hours washing cars

Hudson owns a food truck that sells tacos and burritos. He only has enough supplies to make 100 tacos or burritos. He sells each taco for $3 and each burrito for $7. Hudson must sell at least $420 worth of tacos and burritos each day. If x represents the number of tacos sold and y represents the number of burritos sold, determine a possible combination of tacos and burritos sold.

• 5 tacos and 20 burritos

• 15 tacos and 80 burritos

• 60 tacos and 20 burritos

• 45 tacos and 80 burritos

Nigel wants to buy t-shirts and socks at a clothing store. T-shirts cost $10 and socks cost $5. Nigel has no more than $45 to spend. Let x represent the number of t-shirts and let y represent the number of socks. Write an inequality.

Mathematical Equivalence

ON

Sebastian has x nickels and y pennies. He has at least 20 coins worth at most $0.65 combined. Write a system of inequalities.

• x+y<20

  0.05x+0.01y≤0.65

• 0.05x+0.01y>20

  x+y≥0.65

• x+y<0.65

  0.05x+0.1y>0.65

• x+y≥20

  0.05x+0.01y≤0.65

An online furniture store sells chairs for $200 each and tables for $450 each. Every day, the store can ship at most 18 pieces of furniture and must sell no less than $5600 worth of chairs and tables. If x represents the number of tables sold and y represents the number of chairs sold, write a system of inequalities.

• 450y+200x>5600

  x+y>18

• 450x+200y≥5600

  x+y≤18

• 450x+200y<5600

  x+y<18

• x+y≥5600

  450x+200y<18