Real-Life Linear Inequalities: Graphing & Writing Skills

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 the system of inequalities that represents the situation and graph it.

• x + y ≤ 100, 2x + 2y ≤ 120, x ≥ 0, y ≥ 0

• x + y ≤ 120, 2x + 3y ≤ 120, x ≥ 0, y ≥ 0

• x + y ≤ 100, 2x + y ≤ 120, x ≥ 0, y ≥ 0

• x + y ≤ 80, 2x + y ≤ 100, x ≥ 0, y ≥ 0

A school is organizing 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 the inequality that represents the maximum number of students that can attend the trip and graph it.

• x ≤ 5

• x ≤ 10

• x ≤ 15

• x ≤ 20

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 30 hours of labor available. Write the system of inequalities and graph the feasible region.

• 3x + 2y ≤ 30, x ≥ 0, y ≥ 0

• 2x + 3y ≤ 30, x ≥ 0, y ≥ 0

• 4x + y ≤ 30, x ≥ 0, y ≥ 0

• 3x + 3y ≤ 30, x ≥ 0, y ≥ 0

A restaurant sells two types of sandwiches: vegetarian and meat. Each vegetarian sandwich requires $2 in ingredients, and each meat sandwich requires $3. If the restaurant has a budget of $60 for ingredients, write the inequality and graph the possible combinations of sandwiches they can make.

• 2x + 3y ≤ 60

• 2x + 3y = 60

• 2x + 3y ≥ 60

• x + y ≤ 20

A local theater has 300 seats. They charge $10 for adult tickets and $5 for children's tickets. If they want to make at least $2000 from ticket sales, write the system of inequalities and graph the solution set.

• x + y = 300, 10x + 5y = 2000

• x + y ≥ 300, 10x + 5y ≤ 2000

• x + y ≤ 250, 10x + 5y ≥ 1500

• x + y ≤ 300, 10x + 5y ≥ 2000

A charity event aims to raise at least $1000. They sell tickets for $15 each and accept donations. If they expect to sell at most 80 tickets, write the inequality that represents the situation and graph it.

• 15x + d ≥ 1000, x ≤ 60

• 15x + d ≥ 800, x ≤ 100

• 15x + d ≤ 1000, x ≤ 80

• 15x + d ≥ 1000, x ≤ 80

A clothing store has a sale on shirts and pants. Shirts cost $15 each and pants cost $25 each. If the store wants to spend no more than $300 on inventory, write the system of inequalities and graph the feasible combinations of shirts and pants they can buy.

• 15x + 20y ≤ 300, x ≥ 0, y ≥ 0

• 20x + 25y ≤ 300, x ≥ 0, y ≥ 0

• 10x + 30y ≤ 300, x ≥ 0, y ≥ 0

• The system of inequalities is: 15x + 25y ≤ 300, x ≥ 0, y ≥ 0.

A student is saving money for a laptop that costs $800. She saves $50 a week from her allowance and can also earn $20 per week from chores. Write the inequality that represents the number of weeks needed to save enough money and graph it.

• 70w >= 800

• 80w >= 800

• 70w <= 800

• 60w >= 800

A bakery makes two types of cakes: chocolate and vanilla. Each chocolate cake requires 4 eggs and each vanilla cake requires 2 eggs. If the bakery has 50 eggs, write the system of inequalities and graph the combinations of cakes they can make.

• 4x + 3y <= 50, x >= 0, y >= 0

• 4x + 2y >= 50, x >= 0, y >= 0

• 3x + 2y <= 50, x >= 0, y >= 0

• 4x + 2y <= 50, x >= 0, y >= 0