Writing and Analyzing Linear Inequalities in Real Life

1. A local gym charges a monthly fee of $30 plus $5 for each class attended. Write an inequality to represent the maximum number of classes (x) a member can attend if they want to spend no more than $100 in a month.

• x ≤ 20

• x ≤ 14

• x ≤ 5

• x ≤ 10

2. If a student can study for a maximum of 15 hours a week, write an inequality to represent the number of hours (h) they can spend on math homework and science homework combined if they want to allocate at least 5 hours to math.

• 5 <= h <= 15

• h = 10

• h > 15

• h < 5

3. A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write an inequality to express the maximum number of miles (m) a customer can drive if they want to keep their total cost under $100.

• m < 250

• m < 150

• m < 300

• m < 200

4. A factory produces widgets and has a maximum production capacity of 500 units per day. If the factory produces x units of widgets, write an inequality to represent the production limit.

• x ≤ 500

• x = 500

• x < 500

• x ≥ 500

5. A school is planning a field trip and has a budget of $1,200. If each student pays $20 and there are s students attending, write an inequality to represent the maximum number of students that can attend the trip.

• s > 60

• 20s < 1200

• s ≤ 60

• 20s ≤ 1200

6. A store sells notebooks for $2 each and pens for $1 each. If a student has $15 to spend, write an inequality to represent the number of notebooks (n) and pens (p) they can buy.

• 2n + p ≤ 15

• n + p ≤ 15

• 3n + 2p ≤ 15

• n + 2p ≤ 15

7. A gardener has a budget of $200 to spend on plants. If each flower costs $15 and each shrub costs $25, write an inequality to represent the maximum number of flowers (f) and shrubs (s) the gardener can buy.

• 15f + 25s ≤ 200

• 5f + 30s ≤ 200

• 15f + 15s ≤ 200

• 10f + 20s ≤ 200

8. A concert venue has a seating capacity of 1,000. If x is the number of tickets sold, write an inequality to represent the maximum number of tickets that can be sold without exceeding capacity.

• x = 1000

• x ≥ 1000

• x ≤ 1000

• x < 1000

9. A charity event aims to raise at least $5,000. If each ticket sold is $50, write an inequality to represent the minimum number of tickets (t) that must be sold to meet the goal.

• 50t >= 5000

• t <= 100

• t >= 100

• 50t < 5000

10. A student is saving money for a new laptop that costs $800. If they save $50 each week, write an inequality to represent the number of weeks (w) they need to save to afford the laptop.

• 50w <= 800

• 50w >= 800

• 50w < 800

• 50w = 800