Inequalities in Action: Writing & Graphing Scenarios

1. A school is planning a field trip and has a budget of $500. Each student ticket costs $15 and each adult ticket costs $20. Write an inequality to represent the number of student (x) and adult (y) tickets that can be purchased. Graph the inequality on a coordinate plane.

• 15x + 20y ≤ 500

• 10x + 15y ≤ 500

• 20x + 15y ≤ 500

• 15x + 25y ≤ 500

2. 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 3 hours of labor. If the farmer has a total of 240 hours of labor available, write an inequality to represent the relationship between the acres of corn (x) and wheat (y). Graph the inequality.

• x + y ≥ 100, 2x + 3y ≥ 240

• x + y ≤ 80, 2x + 3y ≤ 200

• x + y = 100, 2x + 3y = 240

• x + y ≤ 100, 2x + 3y ≤ 240

3. A local gym has a maximum capacity of 200 members. If the number of adult members is represented by x and the number of youth members by y, write an inequality to express the maximum number of members allowed. Graph the inequality on a coordinate plane.

• x + y < 200

• x + y = 200

• x + y ≥ 200

• x + y ≤ 200

4. A concert venue can hold a maximum of 300 people. If tickets for adults cost $25 and tickets for children cost $15, and the total revenue must be at least $5000, write an inequality to represent the situation. Graph the inequality.

• x + y < 300, 25x + 15y < 5000

• x + y ≥ 300, 25x + 15y ≤ 5000

• x + y ≤ 300, 25x + 15y ≥ 5000

• x + y ≤ 250, 25x + 15y ≥ 6000

5. A bakery sells muffins and cookies. Each muffin costs $2 and each cookie costs $1. If the bakery wants to make at least $100 in sales, write an inequality to represent the number of muffins (x) and cookies (y) sold. Graph the inequality on a coordinate plane.

• 2x + y >= 100

• 3x + y >= 100

• 2x + 3y > 100

• x + 2y <= 100

6. A car rental company charges a flat fee of $30 plus $0.50 per mile driven. If a customer wants to spend no more than $100, write an inequality to represent the miles driven (x). Graph the inequality.

• x = 150

• x ≥ 140

• x < 100

• x ≤ 140

7. A charity event aims to raise at least $2000. If each ticket sold is $50 and each donation is $20, write an inequality to represent the number of tickets (x) and donations (y) needed. Graph the inequality on a coordinate plane.

• 50x + 20y ≥ 2000

• 30x + 10y ≥ 2000

• 50x + 20y ≤ 2000

• 50x + 30y ≥ 2000

8. A restaurant has a seating capacity of 150. If the number of tables for two is represented by x and the number of tables for four is represented by y, write an inequality to express the seating capacity. Graph the inequality.

• x + 2y ≤ 150

• 2x + 4y ≤ 150

• 3x + 2y ≤ 150

• 2x + 3y ≤ 150

9. A school is organizing a fundraiser and needs to sell at least 300 items. If each item costs $10, write an inequality to represent the number of items (x) and the total amount raised (y). Graph the inequality on a coordinate plane.

• y < 10x and x < 300

• y <= 10x and x >= 250

• y > 10x and x <= 300

• y >= 10x and x >= 300

10. A pet store has a limit of 50 animals. If the number of dogs is represented by x and the number of cats by y, write an inequality to express the maximum number of animals allowed. Graph the inequality.

• x + y = 50

• x + y < 50

• x + y ≥ 50

• x + y ≤ 50