Inequalities on Number Lines: Real-World Applications

1. Sarah has at least $50 to spend on books. If each book costs $12, how many books can she buy? Represent this situation with an inequality and graph it on a number line.

• 5

• 4

• 3

• 6

2. A school is planning a field trip and needs at least 30 students to sign up. If x represents the number of students signed up, write an inequality and graph it. How many more students are needed?

• 30 + x

• 30 - x (where x is the current number of students signed up)

• x - 30

• x > 30

3. A car rental company charges a base fee of $20 plus $0.50 per mile driven. If you want to spend no more than $50, write an inequality to represent the miles you can drive and graph it.

• m ≤ 80

• m ≤ 40

• m ≤ 50

• m ≤ 60

4. Tom is saving money for a new video game that costs $60. If he saves $5 each week, write an inequality to show how many weeks it will take him to save enough money. Graph the solution on a number line.

• w < 12

• w >= 12

• w <= 10

• w = 15

5. A local gym has a membership fee of $30 and charges $10 per class. If you want to spend no more than $100, write an inequality for the number of classes you can attend and graph it.

• x ≤ 3

• x ≤ 7

• x ≤ 5

• x ≤ 10

6. The temperature in a city must be below 75°F for a picnic to be held. If x represents the temperature, write an inequality and graph it. What temperatures are acceptable for the picnic?

• x < 75, acceptable temperatures are all values less than 75°F.

• x = 75, acceptable temperatures are exactly 75°F.

• x > 75, acceptable temperatures are all values greater than 75°F.

• x ≤ 75, acceptable temperatures are all values less than or equal to 75°F.

7. A farmer has a budget of $200 to buy seeds. If each packet of seeds costs $15, write an inequality to represent how many packets he can buy and graph the solution on a number line.

• x <= 10

• x < 13

• x >= 14

• x <= 13

8. A concert venue can hold a maximum of 500 people. If x represents the number of tickets sold, write an inequality to show how many tickets can still be sold and graph it.

• x < 500

• x > 500

• x ≤ 500

• x = 500

9. Lisa wants to buy a new phone that costs $300. If she saves $20 a week, write an inequality to determine how many weeks it will take her to save enough money. Graph the solution on a number line.

• w < 15

• w >= 15

• w > 15

• w <= 15

10. A recipe requires at least 2 cups of sugar. If you have x cups of sugar, write an inequality to represent how much more sugar you need and graph it.

• x < 2

• x > 2

• x = 2

• x ≤ 2