Solving and Graphing Linear Inequalities in Real Life

A local bakery sells cupcakes for $2 each and cookies for $1 each. If the bakery wants to make at least $50 in one day, write a linear inequality to represent the number of cupcakes (x) and cookies (y) they need to sell. Graph the inequality.

• 2x + 3y < 50

• x + 2y ≤ 50

• 3x + y ≥ 50

• 2x + y ≥ 50

A school is planning a field trip and has a budget of $300. The cost per student is $15 for the trip. Write a linear inequality to represent the maximum number of students (x) that can go on the trip. Interpret the graph of this inequality.

• 10x ≤ 300, x ≤ 30

• 20x ≤ 300, x ≤ 15

• 15x < 300, x < 20

• 15x ≤ 300, x ≤ 20

A farmer has 100 acres of land and wants to plant corn and wheat. Each acre of corn requires 2 hours of labor, and each acre of wheat requires 1 hour. If the farmer has 120 hours of labor available, write a linear inequality to represent the relationship between acres of corn (x) and acres of wheat (y). Graph the inequality.

• 2x + y ≤ 120, x + y ≤ 100

• 3x + y ≤ 100

• 2x + 3y ≤ 120

• x + 2y ≤ 120

A gym charges a monthly fee of $30 plus $5 for each class attended. If a member wants to spend no more than $100 in a month, write a linear inequality to represent the number of classes (x) they can attend. Interpret the graph of this inequality.

• x ≤ 12

• x ≤ 20

• x ≤ 10

• x ≤ 14

A concert hall has a seating capacity of 500. If tickets for adults cost $20 and tickets for children cost $10, write a linear inequality to represent the total revenue (R) generated from selling x adult tickets and y child tickets, if the revenue must be at least $8000. Graph the inequality.

• 20x + 10y = 8000, x + y = 500

• 15x + 5y >= 8000, x + y <= 600

• 20x + 10y >= 8000, x + y <= 500

• 20x + 10y <= 8000, x + y >= 500

A clothing store sells shirts for $25 and pants for $40. If the store wants to make at least $1000 in sales, write a linear inequality to represent the number of shirts (x) and pants (y) they need to sell. Interpret the graph of this inequality.

• 25x + 40y >= 1000

• 30x + 50y <= 1000

• 20x + 30y >= 1000

• 25x + 40y < 1000

A charity event aims to raise at least $2000. If each ticket sold is $50 and each donation is $20, write a linear inequality to represent the relationship between the number of tickets (x) sold and donations (y) received. Graph the inequality.

• 50x + 20y >= 2000

• 50x + 20y = 2000

• 50x + 20y < 2000

• 50x - 20y >= 2000

A restaurant has a seating capacity of 200. If each table seats 4 people, write a linear inequality to represent the maximum number of tables (x) that can be set up. Interpret the graph of this inequality in terms of seating arrangements.

• x ≤ 75

• x ≤ 50

• x ≤ 100

• x ≤ 25

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. If the company has 60 hours of labor available, write a linear inequality to represent the production of Type A (x) and Type B (y) gadgets. Graph the inequality.

• 3x + 3y ≤ 60

• 4x + y ≤ 60

• 3x + 2y ≤ 60

• 2x + 3y ≤ 60

A student is saving money for a new laptop that costs $800. If they save $50 a week from their allowance and also earn $20 from chores, write a linear inequality to represent the number of weeks (x) they need to save to afford the laptop. Interpret the graph of this inequality.

• x >= 12

• x < 12

• x > 15

• x <= 10