Graphing and Interpreting Linear Inequalities in Context

A local gym charges a monthly fee of $30 plus $5 for each class attended. If a member wants to spend no more than $100 in a month, how many classes can they attend? Graph the inequality and interpret the solution.

• 16

• 10

• 12

• 14

A farmer has 120 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 a maximum of 180 hours of labor available, write and graph the inequality that represents the possible combinations of corn and wheat that can be planted.

• x + y <= 120, 2x + y <= 180

• x + y = 120, 2x + y = 200

• x + y <= 100, 2x + y <= 150

• x + y >= 120, 2x + y >= 180

A school is planning a field trip and has a budget of $500. The cost per student is $15. Write an inequality to represent the maximum number of students that can attend the trip and graph it. What does the graph indicate about the number of students?

• x ≤ 25

• x < 33

• x ≤ 33

• x ≥ 40

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If a customer wants to spend no more than $100, how many miles can they drive? Write the inequality and graph it to find the solution.

• 150 miles

• 300 miles

• 200 miles

• 250 miles

A bakery sells cupcakes for $2 each and cookies for $1 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 region.

• 3x + y ≤ 20

• x + 2y ≤ 20

• x + y ≤ 20

• 2x + y ≤ 20

A concert venue has a seating capacity of 500. If tickets are sold for $20 each, write an inequality to represent the maximum number of tickets that can be sold. Graph the inequality and explain what the graph shows about ticket sales.

• x <= 500

• x = 500

• x < 500

• x >= 500

A charity event aims to raise at least $1,000. If each ticket sold is $25, how many tickets must be sold to meet the goal? Write the inequality and graph it to visualize the solution.

• At least 50 tickets must be sold.

• At least 40 tickets must be sold.

• At least 20 tickets must be sold.

• At least 30 tickets must be sold.

A student has a budget of $50 to spend on school supplies. If notebooks cost $3 each and pens cost $2 each, write an inequality to represent the number of notebooks (x) and pens (y) they can buy. Graph the inequality and discuss the possible combinations.

• 3x + 2y = 50

• 3x + 2y ≥ 50

• 3x + 2y < 50

• 3x + 2y ≤ 50

A restaurant has a special where a meal costs $15 and a drink costs $3. If a customer wants to spend no more than $30, how many meals and drinks can they order? Write the inequality and graph it to find the solution.

• The customer can order a maximum of 2 meals and 0 drinks, or 1 meal and 5 drinks, or combinations that satisfy 5x + y ≤ 10.

• 1 meal and 3 drinks

• 0 meals and 10 drinks

• 3 meals and 1 drink

A clothing store is having a sale where each shirt costs $25 and each pair of pants costs $40. If a customer has $200 to spend, write an inequality to represent the maximum number of shirts (x) and pants (y) they can buy. Graph the inequality and interpret the results.

• 25x + 40y ≤ 200

• 20x + 50y ≤ 200

• 30x + 35y ≤ 200

• 25x + 40y < 200