Graphing and Solving Inequalities in Real Life Scenarios

1. Sarah has twice as many apples as Tom. If Tom has x apples, write an inequality to represent the situation if Sarah has at least 10 apples. Graph the inequality on a number line.

• x <= 10

• 2x < 10

• 2x >= 10, or x >= 5

• x < 5

Tags

CCSS.6.EE.B.8

2. A store sells notebooks for $2 each and pens for $1 each. If you want to spend no more than $20, write an inequality involving x (notebooks) and y (pens) and identify the solutions.

• 2x + 3y ≤ 20

• 3x + y ≤ 20

• x + 2y ≤ 20

• 2x + y ≤ 20

3. A car rental company charges a flat fee of $30 plus $0.50 per mile driven. If you want to spend less than $100, write an inequality and graph it on a number line to find the maximum miles you can drive.

• m < 140

• m < 160

• m < 120

• m < 100

Tags

CCSS.6.EE.B.8

4. In a school, the number of students in the 8th grade is at least 150. If the number of students in the 7th grade is represented by y, write an inequality involving y and graph it.

• y = 150

• y > 200

• y < 150

• y >= 0

Tags

CCSS.6.EE.B.8

5. A gardener has 50 feet of fencing to create a rectangular garden. If the length is represented by x and the width by y, write an inequality for the perimeter and identify possible dimensions.

• x + y = 50; Possible dimensions include (0, 50), (25, 25), (40, 10), etc.

• x + y < 25; Possible dimensions include (0, 24), (5, 10), (15, 5), etc.

• x + y ≥ 25; Possible dimensions include (10, 15), (20, 5), (30, 0), etc.

• x + y ≤ 25; Possible dimensions include (0, 25), (10, 15), (12, 13), etc.

6. A movie theater charges $8 per ticket. If you want to spend less than $50 on tickets for a group, write an inequality involving t (number of tickets) and graph it on a number line.

• t <= 6

• t > 6

• t >= 7

• t < 5

Tags

CCSS.6.EE.B.8

7. A school is planning a field trip and has a budget of $500. If each student pays $15, write an inequality to represent the maximum number of students (s) that can go on the trip and identify the solutions.

• s ≤ 30

• s ≤ 25

• s ≤ 33

• s ≤ 40

8. A bakery sells cupcakes for $3 each and cookies for $2 each. If you want to spend no more than $30, write an inequality involving c (cupcakes) and k (cookies) and graph the solutions.

• 4c + k ≤ 30

• c + 3k ≤ 30

• 3c + 2k < 30

• 3c + 2k ≤ 30

9. A fitness center has a membership fee of $50 and charges $10 per class. If you want to spend less than $200, write an inequality involving m (number of classes) and graph it on a number line.

• m < 15

• m < 10

• m < 20

• m < 5

Tags

CCSS.6.EE.B.8

10. A charity event aims to raise at least $1,000. If each ticket sold is $20, write an inequality to represent the number of tickets (t) that need to be sold and identify the solutions.

• t > 50

• t >= 50

• t <= 50

• t < 50

Tags

CCSS.6.EE.B.8