Writing and Graphing Inequalities in Real-Life Scenarios

A farmer has 100 acres of land. He wants to plant corn and wheat. Each acre of corn requires 2 hours of labor, and each acre of wheat requires 3 hours of labor. If he has a total of 240 hours of labor available, write an inequality to represent the situation and graph it.

• x + y = 100, 2x + 3y = 240

• x + y ≥ 100, 2x + 3y ≥ 240

• x + y ≤ 50, 2x + 3y ≤ 300

• x + y ≤ 100, 2x + 3y ≤ 240

A school is planning a field trip and has a budget of $500. The cost per student is $20 for the trip. Write an inequality to represent the maximum number of students that can attend the trip and graph it.

• 20x < 500, x < 25

• 15x ≤ 500, x ≤ 20

• 20x ≤ 500, x ≤ 25

• 25x ≤ 500, x ≤ 20

Maria is making gift baskets. Each basket requires $5 worth of supplies. She has $150 to spend. Write an inequality to represent the number of baskets she can make and graph it.

• x ≤ 30

• x < 30

• x ≤ 25

• x ≤ 40

A gym has a maximum capacity of 200 members. Currently, there are 120 members. If each new member requires 1.5 times the space of an existing member, write an inequality to represent the number of new members that can join and graph it.

• x <= 30

• x <= 75

• x <= 100

• x <= 53

A concert hall has 300 seats. Tickets are sold for $15 each. If the total revenue must be at least $2000, write an inequality to represent the number of tickets that must be sold and graph it.

• x ≥ 134

• x > 150

• x < 134

• x ≤ 134

A bakery sells cookies for $2 each and cupcakes for $3 each. If the bakery wants to make at least $100 in sales, write an inequality to represent the number of cookies (x) and cupcakes (y) they need to sell and graph it.

• x + 2y ≥ 100

• 2x + 3y ≤ 100

• 2x + 3y ≥ 100

• x + y ≥ 50

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 miles driven and graph it.

• m < 250

• m ≤ 250

• m ≥ 200

• m > 300

A charity event aims to raise at least $3000. Each ticket sold contributes $25. Write an inequality to represent the number of tickets that need to be sold and graph it.

• 25x = 3000

• 25x ≥ 3000, x ≥ 120

• 25x < 3000

• x ≤ 120

A local restaurant can serve a maximum of 150 customers. If they have 80 customers already, write an inequality to represent the number of additional customers they can serve and graph it.

• x = 70

• x < 80

• x ≥ 150

• x ≤ 70

A student is saving money for a new laptop that costs $800. If he saves $50 each week, write an inequality to represent the number of weeks he needs to save and graph it.

• w >= 16

• w > 16

• w <= 16

• w < 16