Writing and Analyzing Linear Inequalities: Grade 9 Quiz

1. A local gym charges a monthly fee of $30 plus $5 for each class attended. Write an inequality to represent the total cost (C) for attending x classes if you want to spend no more than $100.

• 30 + 5x ≤ 100

• 30 + 5x < 100

• 30 + 5x = 100

• 30 + 5x ≥ 100

2. Sarah is saving money to buy a new laptop that costs $800. She saves $50 each week. Write an inequality to represent the number of weeks (w) she needs to save to afford the laptop.

• 50w >= 800

• 50w < 800

• 50w = 800

• 50w <= 800

3. A farmer has 120 acres of land and wants to plant corn and wheat. Each acre of corn requires 2 hours of labor, and each acre of wheat requires 1 hour. If he has a maximum of 200 hours of labor available, write a system of inequalities to represent the situation.

• x + y ≥ 120, 2x + y ≤ 150

• x + 2y ≤ 120, 2x + y ≤ 200

• x + y ≤ 120, 2x + y ≤ 200

• x + y ≤ 100, 2x + 2y ≤ 200

4. A school is planning a field trip and can spend no more than $1,200. The cost per student is $30, and there is a fixed cost of $300 for the bus. Write an inequality to represent the maximum number of students (s) that can attend the trip.

• s <= 30

• s < 30

• s >= 40

• s = 25

5. A company produces two types of gadgets, A and B. Each gadget A requires 3 hours of labor, and each gadget B requires 2 hours. If the company has 24 hours of labor available, write a system of inequalities to represent the production limits for A and B.

• 3x + 2y ≤ 24, x ≥ 0, y ≥ 0

• x + y ≤ 12, x ≥ 0, y ≥ 0

• 3x + 2y ≥ 24, x ≥ 0, y ≥ 0

• 2x + 3y ≤ 24, x ≥ 0, y ≥ 0

6. Emily wants to buy a new phone and has a budget of $600. If the phone costs $450 and she also wants to buy a case for $25, write an inequality to represent how many cases (c) she can buy without exceeding her budget.

• 25c ≤ 300

• 25c ≤ 100

• 25c ≤ 150

• 25c ≤ 200

7. A concert hall can seat a maximum of 500 people. If tickets for adults cost $20 and tickets for children cost $10, write an inequality to represent the total number of adult (a) and child (c) tickets that can be sold without exceeding the seating capacity.

• a + c = 500

• a + c ≤ 500

• a + c ≥ 500

• a + c < 500

8. A restaurant sells burgers for $8 and salads for $5. If they want to make at least $200 in one day, write an inequality to represent the number of burgers (b) and salads (s) they need to sell.

• 8b + 5s <= 200

• 7b + 6s >= 200

• 8b + 5s >= 200

• 10b + 4s >= 200

9. A student has a total of 15 hours to study for two subjects, Math and Science. If she spends 2 hours on Math and 1 hour on Science, write a system of inequalities to represent the time she can allocate to each subject.

• x + y >= 15

• 2x + 3y <= 15

• x + y <= 15, 2x + y <= 15, x >= 0, y >= 0

• x + 2y <= 15

10. A charity event aims to raise at least $5,000. If each ticket sold is $50 and they have a fixed donation of $1,000, write an inequality to represent the number of tickets (t) that need to be sold to meet their goal.

• t > 50

• t >= 80

• t <= 100

• t < 80