Solving Real-Life Inequalities: Write & Interpret Solutions

1. A local gym charges a monthly fee of $30 plus $5 for each class attended. Write an inequality to represent the maximum number of classes a member can attend if they want to spend no more than $100 in a month.

• x ≤ 20

• x ≤ 5

• x ≤ 10

• x ≤ 14

2. Sarah is saving money to buy a new laptop that costs $800. If she saves $50 each week, write an inequality to show how many weeks it will take her to save enough money. Graph the solution on a number line.

• w > 16

• w <= 16

• w < 16

• w >= 16

3. A school is planning a field trip and has a budget of $1,200. If each student pays $15, write an inequality to represent the maximum number of students that can attend the trip. Interpret the solution.

• x < 80

• x <= 100

• x >= 80

• x <= 80

4. A car rental company charges a flat fee of $40 plus $0.20 per mile driven. If a customer wants to spend no more than $100, write an inequality and solve for the maximum number of miles they can drive.

• 350

• 300

• 250

• 400

5. A farmer has 200 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 300 hours of labor available, write an inequality to represent the planting options.

• x + y ≥ 200 and 2x + y ≥ 300

• x + y = 200 and 2x + y = 300

• x + y ≤ 200 and 2x + y ≤ 300

• x + y ≤ 150 and 2x + y ≤ 250

6. A concert venue can hold a maximum of 500 people. If tickets are sold for $20 each, write an inequality to represent the total revenue generated if the venue is at full capacity. Graph the inequality on a coordinate plane.

• R < 10000

• R >= 10000

• R <= 10000

• R = 5000

7. A student needs to score at least 70% on their final exam to pass the class. If the exam is worth 100 points, write an inequality to represent the minimum score needed. Interpret the solution in the context of passing the class.

• score >= 70

• score > 70

• score = 70

• score < 70

8. A company produces x units of a product at a cost of $5 per unit. If the company wants to keep production costs under $1,000, write an inequality to represent the maximum number of units they can produce. Graph the solution.

• x < 150

• x < 200

• x < 100

• x < 250

9. A restaurant has a seating capacity of 150 people. If they want to maintain a minimum of 30% of seats available for walk-in customers, write an inequality to represent the maximum number of reservations they can take. Interpret the solution.

• r <= 90

• r <= 75

• r <= 105

• r <= 120

10. A student is planning to spend no more than $200 on school supplies. If notebooks cost $3 each and pens cost $2 each, write an inequality to represent the maximum number of notebooks and pens they can buy. Graph the solution on a coordinate plane.

• 2x + 4y ≤ 200

• 3x + 2y ≤ 200

• 3x + 2y < 200

• 5x + 3y ≤ 200