Real-World Applications of Linear Inequalities for Grade 9

A local bakery sells muffins and cookies. Each muffin costs $2 and each cookie costs $1. If the bakery wants to make at least $50 in sales, write a linear inequality to represent the number of muffins (m) and cookies (c) they need to sell. Graph the inequality and interpret the solution.

• m + c <= 50

• m + 2c >= 50

• 3m + 2c >= 50

• 2m + c >= 50

A school is organizing 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 (s) that can attend. Graph the inequality and explain what the solution means in this context.

• 10s <= 300, s <= 30

• 5s <= 300, s <= 60

• 15s <= 300, s <= 20

• 20s <= 300, s <= 15

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 for the number of classes (c) they can attend. Graph the inequality and discuss the implications of the solution.

• c ≤ 10

• c ≤ 20

• c ≤ 5

• c ≤ 14

A farmer has 100 acres of land 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 situation. Graph the inequality and interpret the feasible region.

• 2x + y <= 100 and x + y <= 120

• 2x + y >= 120 and x + y >= 100

• The linear inequalities are: 2x + y <= 120 and x + y <= 100.

• x + 2y <= 120 and x + y <= 100

A concert hall has a seating capacity of 500. If tickets for adults cost $20 and tickets for children cost $10, and the total revenue must be at least $8000, write a linear inequality for the number of adult (a) and child (c) tickets sold. Graph the inequality and explain the significance of the solution.

• a + c = 500 and 20a + 10c = 8000

• The linear inequalities are: a + c ≤ 500 and 20a + 10c ≥ 8000.

• a + c ≤ 400 and 20a + 10c ≥ 6000

• a + c ≥ 500 and 20a + 10c ≤ 8000

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 (s) and pants (p) sold. Graph the inequality and interpret the solution in terms of sales strategy.

• 20s + 30p ≥ 800

• 25s + 40p ≥ 1000

• 30s + 50p ≤ 1200

• 15s + 25p = 1000

A charity event has a goal of raising at least $2000. If each ticket sold is $50 and each donation is $20, write a linear inequality to represent the number of tickets (t) and donations (d) needed. Graph the inequality and discuss the meaning of the solution.

• 50t + 20d = 2000

• 50t + 20d ≥ 2000

• 30t + 10d ≥ 2000

• 50t + 20d ≤ 2000

A restaurant has a seating limit of 150 people. If each table seats 5 people, write a linear inequality to represent the number of tables (t) that can be set up. Graph the inequality and interpret the solution in the context of restaurant operations.

• t >= 25

• t < 30

• t > 30

• t <= 30

A tech company produces laptops and tablets. Each laptop requires 3 hours of assembly and each tablet requires 2 hours. If the company has 60 hours available for assembly, write a linear inequality for the number of laptops (l) and tablets (t) that can be produced. Graph the inequality and explain the implications of the solution.

• 2l + 3t ≤ 60

• 4l + t ≤ 60

• l + 2t ≤ 60

• 3l + 2t ≤ 60

A community center offers art and music classes. Each art class costs $15 and each music class costs $10. If a student can spend no more than $100 on classes, write a linear inequality for the number of art (a) and music (m) classes they can take. Graph the inequality and interpret the solution in terms of class selection.

• 15a + 10m ≤ 100

• 5a + 20m ≤ 100

• 15a + 10m ≥ 100

• 20a + 5m ≤ 100