Inequalities in Real Life: Write & Interpret Solutions

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 they can purchase. Interpret the solution contextually.

• 10x + 15y ≤ 500

• 15x + 25y ≤ 500

• 15x + 20y ≤ 500

• 20x + 15y ≤ 500

2. Maria is saving money to buy a new bike. She has $50 saved and plans to save $10 each week. If the bike costs $150, write an inequality to represent the number of weeks (x) she needs to save to afford the bike. Interpret the solution contextually.

• x >= 10

• x < 10

• x <= 10

• x > 10

3. A farmer has a total of 100 acres of land. He wants to plant corn (x) and wheat (y) but can only plant a maximum of 80 acres of corn. Write an inequality to represent the relationship between the corn and wheat planted. Interpret the solution contextually.

• x + y ≤ 80 and y ≤ 20

• x + y ≥ 100 and x ≤ 80

• x + y ≤ 100 and x ≤ 80

• x + y < 100 and x < 80

4. A concert hall has a seating capacity of 300. If tickets for adults (x) cost $25 and tickets for children (y) cost $15, write an inequality to represent the total number of tickets sold. Interpret the solution contextually.

• x + y = 300

• x + y < 300

• x + y ≥ 300

• x + y ≤ 300

5. A gym has a maximum capacity of 50 members at a time. If there are currently x adult members and y child members, write an inequality to represent the total number of members allowed. Interpret the solution contextually.

• x + y ≥ 50

• x + y ≤ 50

• x + y = 50

• x + y < 50

6. A bakery sells muffins for $2 each and cookies for $1 each. If the bakery wants to make at least $100 in one day, write an inequality to represent the number of muffins (x) and cookies (y) they need to sell. Interpret the solution contextually.

• 2x + y >= 100

• 2x + 3y > 100

• 3x + y <= 100

• x + 2y >= 100

7. A car rental company charges $30 per day for a car and $15 per day for a van. If a customer has a budget of $300, write an inequality to represent the number of days (x) they can rent a car and (y) a van. Interpret the solution contextually.

• 30x + 15y = 300

• 30x + 15y < 300

• 30x + 15y ≥ 300

• 30x + 15y ≤ 300

8. A charity event aims to raise at least $2000. If each ticket sold for adults (x) is $50 and for children (y) is $25, write an inequality to represent the total amount raised. Interpret the solution contextually.

• 50x + 25y <= 2000

• 50x + 25y >= 2000

• 25x + 50y >= 2000

• 50x + 25y = 2000

9. A local theater has a maximum of 200 seats. If adult tickets (x) are sold for $10 and child tickets (y) for $5, write an inequality to represent the total revenue generated if all seats are sold. Interpret the solution contextually.

• 10x + 5y >= 2000

• 10x + 5y <= 2000

• 10x + 10y <= 2000

• 15x + 5y <= 2000

10. A student is planning to spend no more than $100 on school supplies. If notebooks cost $3 each (x) and pens cost $2 each (y), write an inequality to represent the total amount spent. Interpret the solution contextually.

• 3x + 2y = 100

• 3x + 2y < 100

• 3x + 2y ≥ 100

• 3x + 2y ≤ 100