Mastering Graphs: Solving Linear Inequalities in Context

A local gym has a maximum capacity of 50 members. If they currently have 30 members, how many more members can they accept? Graph the inequality and interpret the solution.

• 25

• 10

• 20

• 15

A farmer has 100 feet of fencing to create a rectangular pen for his sheep. If the length of the pen is represented by x, write an inequality for the perimeter and graph it. What are the possible dimensions?

• 0 < x ≤ 50, 0 < w ≤ 50 - x

• 0 < x < 50, 0 < w < 50 - x

• 0 < x ≤ 100, 0 < w ≤ 100 - x

• 0 < x < 100, 0 < w < 100 - x

A school is planning a field trip and has a budget of $500. If each student ticket costs $15, write an inequality to represent the maximum number of students that can attend. Graph the inequality and interpret the results.

• x ≤ 33

• x ≤ 40

• x ≤ 30

• x ≤ 25

A concert venue can hold a maximum of 200 people. If 120 tickets have already been sold, how many more tickets can be sold? Write and graph the inequality to show this situation.

• 150

• 80

• 100

• 60

A bakery sells cupcakes for $3 each and cookies for $2 each. If a customer has $20 to spend, write an inequality to represent the number of cupcakes (x) and cookies (y) they can buy. Graph the inequality and interpret the feasible combinations.

• 3x + 2y = 20

• 3x + 2y < 20

• x + y ≤ 20

• 3x + 2y ≤ 20

A car rental company charges a flat fee of $30 plus $0.50 per mile driven. If a customer has a budget of $100, write an inequality to represent the miles driven (m). Graph the inequality and determine the maximum miles they can drive.

• m ≤ 100

• m ≤ 200

• m ≤ 120

• m ≤ 140

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. Graph the inequality and interpret the solution.

• t >= 40

• t > 40

• t < 40

• t <= 40

A pizza shop offers a deal where a large pizza costs $15 and a medium pizza costs $10. If a customer has $50 to spend, write an inequality for the number of large (x) and medium (y) pizzas they can buy. Graph the inequality and analyze the results.

• 15x + 5y ≤ 50

• 20x + 10y ≤ 50

• 15x + 10y ≤ 50

• 10x + 15y ≤ 50

A student has a part-time job and earns $12 per hour. If they want to save at least $200 for a new bike, write an inequality to represent the number of hours (h) they need to work. Graph the inequality and interpret the solution.

• h < 17

• h > 20

• h <= 15

• h >= 17

A local library has a limit of 300 books that can be checked out at one time. If 150 books are currently checked out, how many more can be checked out? Write and graph the inequality to show this situation.

• 100

• 200

• 250

• 150