Inequalities in Action: Writing and Analyzing Solutions

1. Sarah has $50 to spend on school supplies. Each notebook costs $5. Write an inequality to represent how many notebooks she can buy. Graph the inequality and analyze the solution.

• n <= 10

• n <= 5

• n < 10

• n >= 10

2. A local gym charges a monthly fee of $30 plus $5 for each class attended. Write an inequality to show the maximum number of classes a member can attend if they want to spend no more than $100. Graph the inequality and interpret the results.

• x ≤ 5

• x ≤ 20

• x ≤ 14

• x ≤ 10

3. A farmer has 120 acres of land. He wants to plant corn and wheat, with each corn field taking 10 acres and each wheat field taking 5 acres. Write an inequality to represent the number of corn (c) and wheat (w) fields he can plant. Graph the inequality and analyze the feasible solutions.

• 10c + 5w ≤ 120

• 8c + 4w ≤ 120

• 15c + 3w ≤ 120

• 5c + 10w ≤ 120

4. A concert hall has a seating capacity of 500. If each ticket costs $20, write an inequality to represent the maximum number of tickets that can be sold if the total revenue must be at least $8000. Graph the inequality and discuss the implications.

• 300 <= x <= 400

• 0 <= x <= 500

• 400 <= x <= 500

• 400 <= x <= 600

5. A school is planning a field trip and has a budget of $300. Each student ticket costs $15 and each adult ticket costs $20. Write an inequality to represent the number of student (s) and adult (a) tickets they can purchase. Graph the inequality and analyze the possible combinations.

• 15s + 20a ≤ 300

• 20s + 10a ≤ 300

• 5s + 25a ≤ 300

• 10s + 15a ≤ 300

6. A car rental company charges a flat fee of $40 plus $0.25 per mile driven. Write an inequality to represent the maximum number of miles (m) a customer can drive if they want to spend no more than $100. Graph the inequality and interpret the solution.

• m ≤ 240

• m ≤ 180

• m ≤ 200

• m ≤ 300

7. A bakery sells cupcakes for $2 each and cookies for $1 each. If they want to make at least $50 in sales, write an inequality to represent the number of cupcakes (c) and cookies (k) they need to sell. Graph the inequality and analyze the possible sales combinations.

• c + k ≥ 50

• 3c + k ≤ 50

• 2c + k ≥ 50

• 2c + 3k ≥ 50

8. A student has a part-time job and can work a maximum of 20 hours a week. If they earn $10 per hour, write an inequality to represent the total earnings (E) they can make in a week. Graph the inequality and discuss the implications of the solution.

• E <= 200

• E >= 200

• E < 200

• E = 200

9. A charity event aims to raise at least $2000. If each ticket sold is $25, write an inequality to represent the number of tickets (t) that need to be sold. Graph the inequality and analyze the minimum number of tickets required.

• t >= 80

• t <= 80

• t > 80

• t < 80

10. A restaurant has a special offer where each meal costs $15. If they want to keep the total cost under $300 for a group, write an inequality to represent the number of meals (m) they can order. Graph the inequality and interpret the results.

• m ≤ 20

• m > 20

• m < 15

• m < 20