Mastering Inequality Word Problems and Feasible Solutions

A local bakery sells cupcakes for $2 each and cookies for $1 each. If the bakery wants to make at least $50 in one day, write an inequality to represent the number of cupcakes (x) and cookies (y) sold. Graph the inequality and shade the feasible region.

• 2x + y ≤ 50

• 3x + y ≥ 50

• 2x + y ≥ 50

• x + 2y ≥ 50

A school is planning a field trip and has a budget of $300. Each student ticket costs $15 and each adult ticket costs $20. Write an inequality to represent the number of student tickets (x) and adult tickets (y) that can be purchased. Graph the inequality and identify the feasible solutions.

• 10x + 15y ≤ 300

• 20x + 15y ≤ 300

• 15x + 20y ≤ 300

• 15x + 25y ≤ 300

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 for the number of classes (x) they can attend. Graph the inequality and shade the feasible region.

• x ≤ 14

• x ≥ 15

• x = 12

• x < 10

A farmer has a total of 100 acres of land to plant corn and wheat. Each acre of corn requires 2 hours of labor, and each acre of wheat requires 1 hour of labor. 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 and identify the feasible solutions.

• x + y ≤ 100, 2x + y ≤ 120

• x + y = 100, 2x + y = 120

• x + y ≥ 100, 2x + y ≥ 120

• x + y ≤ 80, 2x + y ≤ 100

A concert venue has a seating capacity of 500. If tickets for adults cost $20 and tickets for children cost $10, and the venue wants to make at least $8000, write an inequality to represent the number of adult tickets (x) and child tickets (y) sold. Graph the inequality and shade the feasible region.

• x + y ≥ 500 and 20x + 10y ≤ 8000

• x + y ≤ 400 and 20x + 10y ≥ 10000

• x + y ≤ 500 and 20x + 10y ≥ 8000

• x + y = 500 and 20x + 10y = 8000

A clothing store has a sale on shirts and pants. Shirts are $15 each and pants are $25 each. If a customer wants to spend no more than $100, write an inequality for the number of shirts (x) and pants (y) they can buy. Graph the inequality and identify the feasible solutions.

• 20x + 15y ≤ 100

• 15x + 25y ≤ 100

• 5x + 30y ≤ 100

• 10x + 20y ≤ 100

A charity event is selling tickets for $10 each and donations are accepted at any amount. If the goal is to raise at least $2000, write an inequality to represent the number of tickets sold (x) and the total donations (y). Graph the inequality and shade the feasible region.

• 10x + 2y >= 2000

• 5x + y >= 2000

• 10x + y <= 2000

• 10x + y >= 2000

A restaurant has a special offer where a meal costs $12 and a drink costs $3. If a family wants to spend no more than $60, write an inequality for the number of meals (x) and drinks (y) they can order. Graph the inequality and identify the feasible solutions.

• x + y ≤ 20

• 12x + 3y = 60

• 12x + 3y ≤ 60

• 12x + 3y < 60

A pet store has a limit of 50 animals that can be adopted. If dogs (x) require 2 spaces and cats (y) require 1 space, write an inequality to represent the number of dogs and cats that can be adopted. Graph the inequality and shade the feasible region.

• 2x + 3y ≤ 50

• 3x + 2y ≤ 50

• 2x + y ≤ 50

• x + y ≤ 50

A tech company is producing two types of gadgets. Each gadget A requires 3 hours of labor and gadget B requires 2 hours. If the company has 60 hours of labor available, write an inequality for the number of gadget A (x) and gadget B (y) that can be produced. Graph the inequality and identify the feasible solutions.

• 2x + 3y ≤ 60

• 4x + y ≤ 60

• 3x + 2y ≤ 60

• x + 2y ≤ 60