Inequalities in Action: Graphing and Writing Statements

1. A farmer has 100 meters of fencing to create a rectangular pen for his animals. Write an inequality to represent the relationship between the length (l) and width (w) of the pen. Graph the inequality on a coordinate plane.

• l + w = 50

• l + w ≥ 100

• l + w ≤ 50

• l + w < 50

2. A school is planning a field trip and has a budget of $500. The cost per student is $20. Write an inequality to represent the maximum number of students (s) that can attend the trip. Graph the inequality on a coordinate plane.

• s ≤ 25

• s ≤ 20

• s ≤ 15

• s ≤ 30

3. A store sells two types of fruit baskets: small and large. The small basket costs $15 and the large basket costs $25. If a customer wants to spend no more than $200, write an inequality to represent the number of small (x) and large (y) baskets they can buy. Graph the inequality.

• 10x + 20y ≤ 200

• 15x + 30y ≤ 200

• 15x + 25y ≤ 200

• 20x + 25y ≤ 200

4. A gym has a maximum capacity of 150 members. If there are currently 80 members, write an inequality to represent the number of new members (n) that can join. Graph the inequality on a coordinate plane.

• n ≥ 80

• n < 70

• n ≤ 70

• n ≤ 50

5. A car rental company charges a flat fee of $30 plus $0.20 per mile driven. If a customer wants to spend no more than $100, write an inequality to represent the number of miles (m) they can drive. Graph the inequality.

• m ≤ 400

• m ≤ 250

• m ≤ 350

• m ≤ 300

6. A local bakery sells cupcakes for $2 each and cookies for $1 each. If a customer wants to spend no more than $30, write an inequality to represent the number of cupcakes (c) and cookies (k) they can buy. Graph the inequality on a coordinate plane.

• 2c + 2k ≤ 30

• 3c + k ≤ 30

• 2c + k ≤ 30

• c + k ≤ 30

7. A concert venue has a seating capacity of 500. If 200 tickets have already been sold, write an inequality to represent the number of additional tickets (t) that can be sold. Graph the inequality on a coordinate plane.

• t > 300

• t ≥ 500

• t ≤ 300

• t < 200

8. A charity event aims to raise at least $1,000. If each ticket sold is $25, write an inequality to represent the number of tickets (x) that need to be sold. Graph the inequality on a coordinate plane.

• 25x < 1000

• x < 40

• 25x = 1000

• 25x ≥ 1000, x ≥ 40

9. 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) it will take to save enough money. Graph the inequality on a coordinate plane.

• 50w <= 800

• 50w < 800

• 50w >= 800

• 50w = 800

10. A restaurant has a special offer where a meal costs $15 and a drink costs $5. If a customer wants to spend no more than $60, write an inequality to represent the number of meals (m) and drinks (d) they can order. Graph the inequality on a coordinate plane.

• 2m + d ≤ 10

• 4m + d ≤ 15

• 3m + d ≤ 12

• m + 2d ≤ 20