Inequalities in Action: Writing and Analyzing Solutions

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 if you want to spend no more than $100.

• 30 + 5x < 100

• 30 + 5x ≤ 100

• 30 + 5x ≥ 100

• 30 + 5x = 100

A farmer has 200 meters of fencing to create a rectangular pen for his sheep. If the length of the pen is represented by x meters, write an inequality to express the relationship between the length and width (y) of the pen.

• y = 200 - x

• y ≤ 100 - x

• y < 50 + x

• y ≥ 100 - x

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 maximum number of students (s) that can attend the trip within the budget.

• 15s ≤ 500

• 20s ≤ 500

• s < 25

• s ≤ 10

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) if a customer wants to spend no more than $100 on the rental.

• 50 + 0.20m = 100

• 50 + 0.20m ≤ 100

• 50 + 0.20m < 100

• 50 + 0.20m ≥ 100

A concert venue has a seating capacity of 500. If each ticket costs $15, write an inequality to represent the maximum number of tickets (t) that can be sold without exceeding the capacity.

• t < 500

• t <= 500

• t >= 500

• t = 500

A bakery sells cupcakes for $2 each and cookies for $1 each. If a customer wants to spend no more than $30, write an inequality to represent the number of cupcakes (c) and cookies (k) they can buy.

• c + 2k <= 30

• c + k <= 30

• 3c + 2k <= 30

• 2c + k <= 30

A student has a part-time job and earns $10 per hour. If they want to save at least $200 for a new laptop, write an inequality to express the number of hours (h) they need to work.

• h <= 20

• 5h >= 200

• 15h > 200

• 10h >= 200

A company produces two types of gadgets, A and B. Each gadget A requires 2 hours of labor and gadget B requires 3 hours. If the company has 60 hours of labor available, write an inequality to represent the production of gadgets A (a) and B (b).

• 2a + 3b = 60

• 2a + 3b < 60

• 2a + 3b ≤ 60

• 2a + 3b ≥ 60

A restaurant has a special offer where a meal costs $15 and a drink costs $5. If a family wants to spend no more than $60, write an inequality to represent the number of meals (m) and drinks (d) they can order.

• 10m + 5d ≤ 50

• 20m + 5d ≤ 80

• 15m + 10d ≤ 60

• 15m + 5d ≤ 60

A student is saving money for a new phone that costs $300. If they save $25 each week, write an inequality to express the number of weeks (w) they need to save to afford the phone.

• 25w < 300

• 25w = 300

• 25w >= 300

• 25w <= 300