Inequalities in Action: Graphing and Writing Systems

A farmer has 100 acres of land. He wants to plant corn and wheat. Each acre of corn requires 2 hours of labor, and each acre of wheat requires 1 hour of labor. If he has a total of 120 hours of labor available, write a system of inequalities to represent the situation and graph it.

• x + y >= 100, 2x + y >= 120

• x + y <= 100, 2x + y <= 150

• x + y <= 100, 2x + y <= 120

• x + y <= 80, 2x + y <= 100

A school is planning a field trip and has a budget of $500. The cost per student for the trip is $20, and the bus rental costs $200. Write a system of inequalities to represent the maximum number of students that can attend the trip and graph it.

• x <= 12, x >= -3

• x <= 10, x >= 0

• x <= 15, x >= 0

• x <= 20, x >= 5

A company produces two types of gadgets: Type A and Type B. Each Type A gadget requires 3 hours of labor and each Type B gadget requires 2 hours. The company has a maximum of 30 hours of labor available. Write a system of inequalities to represent the production limits and graph it.

• 2x + 3y ≤ 30, x ≥ 0, y ≥ 0

• 3x + 2y ≤ 30, x ≥ 0, y ≥ 0

• 3x + y ≤ 30, x ≥ 0, y ≥ 0

• x + y ≤ 30, x ≥ 0, y ≥ 0

A gym offers two types of memberships: basic and premium. The basic membership costs $30 per month, and the premium membership costs $50 per month. If the gym wants to earn at least $1,200 in a month, write a system of inequalities to represent the number of each type of membership sold and graph it.

• 30x + 50y = 1200, x >= 0, y >= 0

• 30x + 50y <= 1200, x >= 0, y >= 0

• 20x + 40y >= 1200, x >= 0, y >= 0

• System of inequalities: 30x + 50y >= 1200, x >= 0, y >= 0.

A bakery sells two types of cakes: chocolate and vanilla. Each chocolate cake requires 2 hours to bake, and each vanilla cake requires 1 hour. If the bakery has 10 hours available for baking, write a system of inequalities to represent the maximum number of cakes that can be baked and graph it.

• 3x + y ≤ 10, x ≥ 0, y ≥ 0

• x + 2y ≤ 10, x ≥ 0, y ≥ 0

• 2x + y ≤ 5, x ≥ 0, y ≥ 0

• The system of inequalities is: 2x + y ≤ 10, x ≥ 0, y ≥ 0.

A concert venue can hold a maximum of 500 people. Tickets for adults cost $15, and tickets for children cost $10. If the venue wants to earn at least $6,000 from ticket sales, write a system of inequalities to represent the number of adult and child tickets sold and graph it.

• x + y ≤ 500, 15x + 10y = 6000

• x + y ≤ 500, 15x + 10y ≥ 6000

• x + y ≥ 500, 15x + 10y ≤ 6000

• x + y ≤ 600, 15x + 10y ≥ 5000

A clothing store sells shirts and pants. Each shirt costs $20 and each pair of pants costs $30. The store has a budget of $600 for inventory. Write a system of inequalities to represent the maximum number of shirts and pants that can be purchased and graph it.

• The system of inequalities is: 20x + 30y ≤ 600, x ≥ 0, y ≥ 0.

• 10x + 15y ≤ 600, x ≥ 0, y ≤ 0

• 25x + 35y ≤ 600, x ≥ 0, y ≥ 0

• 20x + 30y ≥ 600, x ≤ 0, y ≤ 0

A charity organization is collecting donations. They want to collect at least $1,000. Each individual can donate $50 or $100. Write a system of inequalities to represent the number of $50 and $100 donations needed to meet their goal and graph it.

• 50x + 100y >= 1000, x >= 0, y >= 0

• 50x + 100y <= 1000, x >= 0, y >= 0

• 50x + 100y = 1000, x < 0, y < 0

• 50x + 100y >= 500, x >= 0, y >= 0

A local restaurant offers two types of meals: vegetarian and non-vegetarian. Each vegetarian meal costs $12 and each non-vegetarian meal costs $15. If the restaurant wants to earn at least $1,800 in a week, write a system of inequalities to represent the number of each type of meal sold and graph it.

• 10x + 15y ≥ 1800, x ≥ 0, y ≥ 0

• 12x + 10y ≥ 1800, x ≥ 0, y ≥ 0

• 12x + 15y ≥ 1800, x ≥ 0, y ≥ 0

• 12x + 15y ≤ 1800, x ≥ 0, y ≥ 0

A tech company is developing two products: a smartphone and a tablet. Each smartphone requires $200 in materials and each tablet requires $150. The company has a budget of $3,000 for materials. Write a system of inequalities to represent the maximum number of smartphones and tablets that can be produced and graph it.

• 250x + 100y ≤ 3000, x ≥ 0, y ≥ 0

• 200x + 150y ≥ 3000, x ≥ 0, y ≥ 0

• 100x + 200y ≤ 3000, x ≥ 0, y ≥ 0

• 200x + 150y ≤ 3000, x ≥ 0, y ≥ 0