Solving Inequalities: Real-Life Applications for 8th Graders

1. Sarah has twice as many apples as Tom. If Tom has x apples, write an inequality to show that Sarah has more than 10 apples. Solve for x.

• x < 5

• x > 15

• x = 10

• x > 5

2. A store sells notebooks for $2 each and pens for $1 each. If the total cost of buying x notebooks and y pens is less than $20, write an inequality and solve for y in terms of x.

• y < 20 + 2x

• y > 20 - 2x

• y < 20 - 2x

• y = 20 - 2x

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 to represent the miles driven and solve for the maximum miles.

• 150

• 120

• 200

• 139

4. In a school, the number of students in the 8th grade is 5 more than twice the number of students in the 7th grade. If there are at least 30 students in the 7th grade, write and solve an inequality for the number of 8th graders.

• The number of 8th graders is at least 70.

• The number of 8th graders is at least 50.

• The number of 8th graders is at least 65.

• The number of 8th graders is at least 40.

5. A gardener has x square feet of garden space. If he wants to plant flowers that require 3 square feet each and vegetables that require 2 square feet each, write an inequality for the total number of plants he can grow if he wants to use less than 50 square feet.

• 3f + 2v > 50

• 3f + 2v < 50

• 3f + 2v = 50

• 3f + 2v ≤ 50

6. A concert hall has a seating capacity of 500. If tickets are sold for $15 each and the total revenue must exceed $6000, write an inequality to represent the number of tickets sold and solve for the minimum number of tickets.

• 450

• 300

• 600

• 401

7. A recipe requires 2 cups of flour and 3 cups of sugar. If you have x cups of flour and y cups of sugar, write an inequality to show that you can make the recipe if you have at least 10 cups of ingredients combined. Solve for y in terms of x.

• y <= 10 - x

• y > 10 - x

• y >= 10 - x

• y < 10 - x

8. A bike shop sells mountain bikes for $300 and road bikes for $400. If the total sales from x mountain bikes and y road bikes must be at least $2000, write and solve the inequality for y in terms of x.

• y ≥ 6 - (2/3)x

• y < 5 - (1/4)x

• y ≤ 4 - (1/2)x

• y ≥ 5 - (3/4)x

9. A student scored 75% on a test with x questions. If the student answered more than 60 questions correctly, write an inequality to represent the situation and solve for x.

• x ≤ 80

• x > 80

• x = 75

• x < 60

10. A factory produces x toys per hour. If the factory needs to produce more than 500 toys in a day (8 hours), write an inequality and solve for the minimum number of toys produced per hour.

• 63

• 80

• 100

• 50