Translating & Graphing Inequalities in Real Life Scenarios

1. A school is planning a field trip and needs to collect at least $300 from students. If each student pays $15, how many students must participate? Write the inequality and graph it.

• At least 15 students must participate.

• At least 30 students must participate.

• At least 25 students must participate.

• At least 20 students must participate.

2. A farmer has a budget of $500 to buy seeds and fertilizer. If seeds cost $20 per bag and fertilizer costs $30 per bag, write an inequality to represent the number of bags he can buy and graph it.

• 5x + 10y ≤ 500

• 15x + 25y ≤ 500

• 20x + 30y ≤ 500

• 10x + 20y ≤ 500

3. A concert hall can seat a maximum of 800 people. If tickets are sold for $25 each, how many tickets must be sold to make at least $15,000? Write the inequality and graph it.

• At least 500 tickets must be sold.

• At least 400 tickets must be sold.

• At least 800 tickets must be sold.

• At least 600 tickets must be sold.

4. A gym has a maximum capacity of 50 members. If 30 members are currently enrolled, how many new members can join while staying within the limit? Write the inequality and graph it.

• 10

• 25

• 15

• 20

5. A store sells pencils for $2 each and erasers for $3 each. If a student has $20 to spend, write an inequality to represent the number of pencils and erasers they can buy and graph it.

• 2x + 3y < 20

• 2x + 3y ≥ 20

• 2x + 3y ≤ 20

• 2x + 3y = 20

6. 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, write an inequality and graph it to show the maximum miles they can drive.

• m ≤ 300

• m ≤ 250

• m ≤ 150

• m ≤ 200

7. A bakery makes cakes and cookies. Each cake requires 3 eggs and each cookie requires 1 egg. If the bakery has 24 eggs, write an inequality to represent the number of cakes and cookies they can make and graph it.

• 3x + y ≤ 24

• x + y ≤ 24

• 2x + y ≤ 24

• 3x + 2y ≤ 24

8. A charity event aims to raise at least $1,000. If each ticket sold is $10, how many tickets must be sold? Write the inequality and graph it.

• At least 50 tickets must be sold.

• At least 75 tickets must be sold.

• At least 200 tickets must be sold.

• At least 100 tickets must be sold.

9. A student has a part-time job and earns $12 per hour. If they want to save at least $200 for a new bike, how many hours must they work? Write the inequality and graph it.

• The student must work at least 15 hours.

• The student must work at least 17 hours.

• The student must work at least 25 hours.

• The student must work at least 10 hours.

10. A local theater can accommodate a maximum of 200 people. If 120 tickets have already been sold, how many more tickets can be sold? Write the inequality and graph it.

• 60

• 40

• 100

• 80