Solving Real-Life Inequalities: Grade 8 Challenge

1. Sarah has at least $50 to spend on books. If each book costs $12, how many books can she buy? Write and solve the inequality.

• 5

• 4

• 3

• 6

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

• 30

• 20

• 25

• 15

3. Tom is saving money for a video game that costs $60. If he saves $5 each week, how many weeks will it take him to save enough? Write and solve the inequality.

• 12 weeks

• 10 weeks

• 15 weeks

• 8 weeks

4. A farmer has a maximum of 200 acres to plant crops. If he plants corn on x acres and wheat on y acres, write a system of inequalities to represent the situation and graph it.

• x + y = 200, x < 0, y ≥ 0

• x + y < 200, x > 0, y < 0

• x + y ≤ 200, x ≥ 0, y ≥ 0

• x + y ≥ 200, x ≤ 0, y ≤ 0

5. A concert hall can hold a maximum of 500 people. If tickets are sold for $20 each, how many tickets can be sold without exceeding the capacity? Write and solve the inequality.

• 450

• 400

• 500

• 600

6. Lisa wants to buy a new phone that costs $300. If she has $50 saved and can save $25 each week, write an inequality to find out how many weeks it will take her to afford the phone.

• w >= 10

• w < 10

• w <= 10

• w > 10

7. A gym has a maximum capacity of 100 members. If there are currently x members and y new members want to join, write a system of inequalities to represent the situation and graph it.

• x + y < 100, y ≤ 0

• x + y ≤ 100, y ≥ 0

• x + y ≥ 100, y < 0

• x + y = 100, y > 0

8. A store is having a sale where each item is at least 30% off. If an item originally costs $80, what is the lowest price it can be sold for? Write and solve the inequality.

• $72

• $40

• $60

• $56

9. A car rental company charges a base fee of $30 plus $0.20 per mile driven. If a customer wants to spend no more than $50, how many miles can they drive? Write and solve the inequality.

• 50 miles

• 75 miles

• 100 miles

• 120 miles

10. A charity event needs to raise at least $1,000. If each ticket sold is $25, how many tickets must be sold to meet the goal? Write the inequality and solve it.

• 30

• 40

• 20

• 50