Inequalities in Action: Graphing Real-World Scenarios

A local bakery sells cupcakes for $2 each and cookies for $1 each. If a customer spends no more than $20, write an inequality to represent the number of cupcakes (x) and cookies (y) they can buy. Graph the inequality.

• x + 2y ≤ 20

• x + y ≤ 20

• 2x + y ≤ 20

• 3x + y ≤ 20

A school is planning a field trip and has a budget of $500. If each student ticket costs $15 and each adult ticket costs $25, write an inequality to represent the number of student tickets (x) and adult tickets (y) that can be purchased. Analyze the solution set.

• 10x + 20y ≤ 500

• 15x + 30y ≤ 500

• 20x + 25y ≤ 500

• 15x + 25y ≤ 500

Maria has a budget of $100 to spend on supplies for her art project. If she buys paint for $10 per can and brushes for $5 each, write an inequality to represent the number of cans of paint (x) and brushes (y) she can buy. Graph the inequality and identify possible combinations.

• 10x + 5y < 100

• 10x + 5y = 100

• 5x + 10y ≤ 100

• 10x + 5y ≤ 100

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. Analyze the solution set and graph the inequality.

• x ≤ 10

• x ≤ 20

• x ≤ 14

• x ≤ 12

A farmer has 200 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 300 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 discuss the feasible region.

• x + y ≥ 200 and 2x + y ≥ 300

• x + y ≤ 300 and 2x + y ≤ 200

• x + y ≤ 200 and 2x + y ≤ 400

• x + y ≤ 200 and 2x + y ≤ 300

A concert venue has a maximum capacity of 500 people. If tickets are sold for $20 each and VIP tickets for $50 each, write an inequality to represent the number of regular tickets (x) and VIP tickets (y) that can be sold. Graph the inequality and analyze the solution set.

• x + y ≤ 500

• x + y < 500

• x + 2y ≤ 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 $150, write an inequality to represent the number of jeans (x) and shirts (y) they can buy. Graph the inequality and identify possible combinations.

• 30x + 20y ≤ 150

• 30x + 20y = 150

• 15x + 10y ≤ 150

• 30x + 20y < 150

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. Graph the inequality and analyze the solution set.

• 25x + 25y ≥ 1000

• 10x + 50y ≥ 1000

• 25x + 50y ≥ 1000

• 25x + 50y ≤ 1000

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 for the number of miles (x) they can drive. Graph the inequality and discuss the feasible region.

• x ≤ 300

• x ≤ 150

• x ≤ 200

• x ≤ 250

A restaurant offers a special where each burger costs $8 and each drink costs $2. If a family wants to spend no more than $40, write an inequality to represent the number of burgers (x) and drinks (y) they can order. Graph the inequality and analyze the solution set.

• 6x + 3y ≤ 40

• 10x + 2y ≤ 40

• 8x + 2y ≤ 40

• 8x + 5y ≤ 40