Graphing and Writing Inequalities: Real-World Challenges

A local gym offers a membership for $30 per month. If you want to spend no more than $300 on memberships, write an inequality to represent this situation and shade the solution region on a graph.

• 30m < 300

• 30m = 300

• 30m ≤ 300

• 30m + 300 ≤ 0

Tags

CCSS.6.EE.B.8

A school is planning a field trip and has a budget of $500. Each bus costs $150 to rent. Write an inequality to show how many buses can be rented without exceeding the budget and graph the solution region.

• b <= 3

• b = 5

• b < 2

• b >= 4

Tags

CCSS.6.EE.B.8

Maria has at most 20 hours to volunteer at the animal shelter this month. If she has already volunteered for 8 hours, write an inequality to represent the remaining hours she can volunteer and shade the solution region.

• x >= 12

• x < 12

• x <= 12

• x <= 8

Tags

CCSS.6.EE.B.8

A farmer has 100 acres of land and wants to plant corn and wheat. If he plants at least 30 acres of corn, write an inequality to represent the maximum acres of wheat he can plant and graph the solution region.

• y ≤ 100

• y ≤ 70

• y ≤ 80

• y ≤ 50

A concert hall 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 and shade the solution region on a graph.

• x <= 500

• x >= 500

• x = 500

• x < 500

Tags

CCSS.6.EE.B.8

A store sells notebooks for $2 each and pens for $1 each. If you want to spend no more than $15, write an inequality to represent the number of notebooks and pens you can buy and graph the solution region.

• 2x + y ≤ 15

• 2x + 3y ≤ 15

• 3x + y ≤ 15

• 2x + y < 15

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 that need to be sold and shade the solution region on a graph.

• 25x <= 1000, x <= 40

• 25x = 1000, x = 40

• 25x >= 1000, x >= 40

• 25x < 1000, x < 40

Tags

CCSS.6.EE.B.8

A recipe requires at least 3 cups of flour and no more than 5 cups of sugar. Write a system of inequalities to represent this situation and graph the solution region.

• x >= 5, y <= 3

• x < 3, y < 5

• x >= 3, y <= 5

• x <= 3, y >= 5

Tags

CCSS.HSA.REI.D.12

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If you want to spend no more than $100, write an inequality to represent the miles you can drive and shade the solution region.

• m ≤ 200

• m ≤ 150

• m ≤ 300

• m ≤ 250

Tags

CCSS.7.EE.B.4B

A student can study for a maximum of 15 hours a week. If they have already studied for 5 hours, write an inequality to represent the remaining hours available for studying and graph the solution region.

• x = 10

• x < 5

• x <= 10

• x >= 15

Tags

CCSS.6.EE.B.8