Mastering Graphing Linear Inequalities and Word Problems

A local bakery sells cupcakes for $2 each and cookies for $1 each. If the bakery wants to make at least $50 in sales, write an inequality to represent the number of cupcakes (x) and cookies (y) they need to sell. Graph the inequality.

• 2x + y >= 50

• 3x + y >= 50

• 2x + 3y > 50

• x + 2y <= 50

A school is planning a field trip and has a budget of $300. The cost per student is $15 for the trip. Write an inequality to represent the maximum number of students (x) that can attend the trip. Graph the inequality.

• x ≤ 25

• x ≤ 10

• x ≤ 20

• x ≤ 15

A gym charges a monthly fee of $30 plus $5 for each class attended. If a member wants to spend no more than $100 in a month, write an inequality to represent the number of classes (x) they can attend. Graph the inequality.

• x ≤ 14

• x ≤ 10

• x ≤ 5

• x ≤ 20

A farmer has 100 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 the farmer has 120 hours of labor available, write an inequality to represent the acres of corn (x) and wheat (y) that can be planted. Graph the inequality.

• x + y ≥ 100, 2x + y ≥ 120

• x + y ≤ 120, 2x + y ≤ 100

• x + y ≤ 100, 2x + y = 120

• x + y ≤ 100, 2x + y ≤ 120

A concert venue has a seating capacity of 500. If tickets for the concert are sold at $20 each and VIP tickets at $50 each, write an inequality to represent the number of regular tickets (x) and VIP tickets (y) that can be sold without exceeding capacity. Graph the inequality.

• x + y ≤ 500

• x + 2y ≤ 500

• x + y ≥ 500

• x + y < 500

A clothing store has a sale where jeans cost $30 and shirts cost $20. If a customer wants to spend no more than $200, write an inequality to represent the number of jeans (x) and shirts (y) they can buy. Graph the inequality.

• 30x + 20y = 200

• 30x + 20y ≥ 200

• 10x + 15y ≤ 200

• 30x + 20y ≤ 200

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 to represent the number of miles (x) they can drive. Graph the inequality.

• x ≤ 150

• x ≤ 250

• x ≤ 200

• x ≤ 300

A charity event aims to raise at least $1,000. If each ticket sold is $25 and each donation is $50, write an inequality to represent the number of tickets (x) and donations (y) needed to reach the goal. Graph the inequality.

• 10x + 50y >= 1000

• 25x + 50y >= 1000

• 25x + 50y <= 1000

• 25x + 50y = 1000

A restaurant has a seating limit of 200 people. If they have 50 tables and each table seats 4 people, write an inequality to represent the number of tables (x) and the number of people (y) that can be seated. Graph the inequality.

• 4x <= 200, x <= 50

• y <= 4x

• x + y <= 200

• 2x <= 100

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

• 50x = 800

• 50x <= 800

• 50x >= 800

• 50x < 800