Writing Inequalities: Real-Life Constraints and Solutions

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.

• 3x + y ≤ 50

• x + y ≥ 50

• 2x + y ≥ 50

• x + 2y ≥ 50

A school is organizing 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 if the cost for transportation (y) is included.

• 10x + y ≤ 300

• 15x + 2y ≤ 300

• 20x + y ≤ 300

• 15x + y ≤ 300

A gym charges a monthly fee of $30 and $5 per class. 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.

• x ≤ 10

• x ≤ 20

• x ≤ 14

• x ≤ 5

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.

• x + y ≥ 100 and 2x + y ≥ 120

• x + y ≤ 120 and 2x + y ≤ 100

• x + y ≤ 100 and 2x + y ≤ 120

• x + y ≤ 100 and 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 total number of regular tickets (x) and VIP tickets (y) that can be sold without exceeding the capacity.

• x + y < 500

• x + y ≥ 500

• x + y = 500

• x + y ≤ 500

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 to represent the number of shirts (x) and pants (y) they can buy.

• 15x + 25y < 100

• 15x + 25y ≤ 100

• 5x + 30y ≤ 100

• 10x + 20y ≤ 100

A charity event aims to raise at least $2000. 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 meet the goal.

• 20x + 50y >= 2000

• 25x + 50y = 2000

• 25x + 50y >= 2000

• 25x + 50y < 2000

A restaurant offers a special deal on meals. Each meal costs $10, and drinks cost $3. If a family wants to spend no more than $60, write an inequality to represent the number of meals (x) and drinks (y) they can order.

• 5x + 2y ≤ 60

• 15x + 3y ≤ 60

• 10x + 3y = 60

• 10x + 3y ≤ 60

A student is saving money for a new laptop that costs $800. If they save $50 a week from their allowance and also plan to earn $20 from a part-time job, write an inequality to represent the number of weeks (x) they need to save to afford the laptop.

• 50x - 20 >= 800

• 50x + 20 <= 800

• 50x + 20 = 800

• 50x + 20 >= 800

A community center has a budget of $500 for a summer camp. Each child costs $25 to enroll, and supplies cost $100. Write an inequality to represent the maximum number of children (x) that can be enrolled while staying within the budget.

• x ≤ 16

• x ≤ 12

• x ≤ 10

• x ≤ 20