Exploring Linear Inequalities: Real-Life Applications

A local 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, how many classes can they attend? Graph the inequality and solve it algebraically.

• 14

• 10

• 16

• 12

A school is planning a field trip and has a budget of $500. The cost per student is $15. Write an inequality to represent the maximum number of students that can attend the trip and solve it. Graph the inequality.

• x ≤ 30

• x ≤ 40

• x ≤ 25

• x ≤ 33

Maria is saving money to buy a new bike that costs $250. She saves $20 each week. Write an inequality to show how many weeks it will take her to save enough money and solve it. Graph the inequality.

• w < 13

• w >= 13

• w <= 12

• w > 13

A farmer has 120 acres of land and wants to plant corn and wheat. Each acre of corn requires 1.5 hours of labor, and each acre of wheat requires 2 hours. If the farmer has 200 hours of labor available, write an inequality to represent the situation and solve it. Graph the inequality.

• The inequalities are 1.5x + 2y ≤ 200 and x + y ≤ 120.

• 1.5x + 2y = 200 and x + y = 120

• 1.5x + 2y ≤ 150 and x + y ≤ 100

• 1.5x + 2y ≥ 200 and x + y ≥ 120

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If a customer wants to spend no more than $100, how many miles can they drive? Write and solve the inequality, then graph it.

• 200 miles

• 250 miles

• 150 miles

• 300 miles

A bookstore is having a sale where each book costs $12. If a customer wants to buy books without spending more than $60, how many books can they buy? Write the inequality, solve it, and graph it.

• 4

• 6

• 7

• 5

A factory produces gadgets and has a maximum production capacity of 500 units per day. If each gadget requires 3 hours of labor to produce, how many hours of labor can be used if the factory operates for 8 hours a day? Write and solve the inequality, then graph it.

• The factory can use 16 hours of labor per day.

• The factory can use 24 hours of labor per day.

• The factory can use 8 hours of labor per day.

• The factory can use 12 hours of labor per day.

A pizza shop sells large pizzas for $15 each. If a customer has $75 to spend, how many pizzas can they buy? Write the inequality, solve it, and graph it.

• 5

• 6

• 4

• 3

A charity event aims to raise at least $1,000. If each ticket sold is $20, write an inequality to represent the number of tickets that need to be sold to meet the goal. Solve the inequality and graph it.

• x > 50

• x < 50

• x <= 50

• x >= 50