Solving Real-Life Linear Inequalities: Variables & Symbols

A local gym charges a monthly fee of $30 plus $5 for each class attended. Write an inequality to represent the total cost (C) for attending x classes in a month if the total cost must be less than $100.

• 30 + 5x > 100

• 5x < 70

• 30 + 5x < 100

• 30 + 5x = 100

A school is planning a field trip and has a budget of $500. The cost per student is $20. Write an inequality to represent the number of students (s) that can attend the trip while staying within budget.

• s < 25

• s ≥ 20

• s ≤ 25

• s > 30

Maria is saving money to buy a new bike that costs $200. She saves $15 each week. Write an inequality to represent the number of weeks (w) she needs to save to afford the bike.

• 10w >= 200

• w <= 13.33

• 15w >= 200

• 15w < 200

A farmer has 120 acres of land and wants to plant corn and wheat. Each acre of corn requires 1 hour of labor, and each acre of wheat requires 2 hours. If the farmer has 100 hours of labor available, write an inequality to represent the acres of corn (c) and wheat (w) he can plant.

• c + w ≤ 120 and c + 2w ≤ 100

• c + w ≤ 100 and c + 2w ≤ 120

• c + w ≥ 120 and c + 2w ≥ 100

• c + w ≤ 150 and c + 2w ≤ 80

A concert hall can seat a maximum of 800 people. If tickets are sold for $15 each, write an inequality to represent the number of tickets (t) that can be sold without exceeding the seating capacity.

• t = 800

• t <= 800

• t >= 800

• t < 800

A bakery sells cupcakes for $3 each and cookies for $2 each. If the bakery wants to make at least $100 in one day, write an inequality to represent the number of cupcakes (c) and cookies (k) sold.

• 5c + k >= 100

• 3c + 2k <= 100

• c + k >= 50

• 3c + 2k >= 100

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write an inequality to represent the total cost (C) for renting a car and driving m miles if the total cost must be less than $100.

• 50 + 0.20m < 100

• 50 + 0.20m > 100

• 50 + 0.20m = 100

• 0.20m < 50

A student has a budget of $40 to spend on books. If each book costs $8, write an inequality to represent the number of books (b) the student can buy without exceeding the budget.

• b < 5

• b >= 6

• 5b <= 40

• 8b <= 40

A pet store has a limit of 50 animals. If they currently have 30 dogs and x cats, write an inequality to represent the number of cats (x) they can have without exceeding the limit.

• x < 10

• x = 30

• x ≤ 20

• x ≥ 25

A charity event aims to raise at least $1,000. If each ticket sold is $25, write an inequality to represent the number of tickets (t) that need to be sold to meet the goal.

• 25t >= 1000

• t > 50

• t <= 40

• 25t < 1000