Inequalities in Action: Writing & 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 sheep. If the length of the pen is represented by x meters, write an inequality for the width (y) of the pen.

• y = 50 + x

• y < 200 - x

• y ≥ 100 - x

• y ≤ 100 - x

A school is planning a field trip and has a budget of $500. The cost per student is $20, and there are additional costs of $100 for transportation. Write an inequality to represent the maximum number of students (s) that can attend the trip.

• s <= 20

• s = 15

• s >= 25

• s < 20

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 24 hours of labor available, write an inequality to represent the number of gadgets A (x) and B (y) that can be produced.

• 2x + 3y ≤ 24

• x + y ≤ 8

• 2x + 3y < 24

• 4x + 2y ≤ 24

A concert venue can hold a maximum of 500 people. If tickets are sold for $15 each, write an inequality to represent the total revenue (R) generated from selling x tickets, ensuring it does not exceed the venue capacity.

• x <= 33.33

• 15x < 500

• 15x <= 500

• R >= 500

A restaurant has a special offer where a meal costs $12 and a drink costs $3. If a customer wants to spend no more than $60, write an inequality to represent the number of meals (m) and drinks (d) they can purchase.

• 10m + 5d ≤ 60

• 12m + 3d < 60

• 15m + 2d ≤ 60

• 12m + 3d ≤ 60

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.

• t > 50

• t <= 40

• 25t < 1000

• 25t >= 1000

A student is saving money for a new laptop that costs $800. If they save $50 each week, write an inequality to represent the number of weeks (w) they need to save to afford the laptop.

• 50w = 800

• 50w < 800

• 50w <= 800

• 50w >= 800

A factory produces two products, X and Y. Each product X requires 4 hours of machine time and product Y requires 2 hours. If the factory has 40 hours available, write an inequality to represent the production limits of X (x) and Y (y).

• 4x + 2y ≤ 40

• 4x + 3y ≤ 40

• 3x + 2y ≤ 40

• 4x + 2y ≥ 40

A local bakery can produce a maximum of 300 loaves of bread per day. If they produce x loaves of whole wheat and y loaves of sourdough, write an inequality to represent the total production limit.

• x + y = 300

• x + y ≤ 300

• x + y ≥ 300

• x + y < 300