Real-Life Inequalities: Interpreting and Applying Scenarios

1. Sarah has at least 3 times as many marbles as Tom. If Tom has x marbles, write an inequality to represent the situation and interpret the solution.

• S < 3x

• S > 3x

• S >= 3x

• S = 3x

2. A store sells notebooks for $2 each. If you want to spend no more than $20, write an inequality to represent the maximum number of notebooks you can buy and solve it.

• 12

• 10

• 15

• 5

3. A recipe requires at least 4 cups of flour. If you have y cups of flour, write an inequality to show how much more flour you need and interpret the solution.

• You need at least 4 - y cups more flour.

• You need 4 + y cups more flour.

• You need exactly 4y cups more flour.

• You need at least 2 - y cups more flour.

4. A car can travel at a speed of at least 50 miles per hour. If you want to reach your destination in less than 3 hours, write an inequality to represent the distance you can travel and solve it.

• d < 150

• d < 100

• d = 120

• d > 150

5. A gardener needs to plant at least 12 flowers in each row. If he has z rows, write an inequality to represent the minimum number of flowers he needs and interpret the solution.

• 12z > f

• f >= 12z + 1

• 12z <= f

• z <= 12f

6. A school has a budget of $500 for a field trip. If each student pays $25, write an inequality to find the maximum number of students that can go on the trip and solve it.

• 15

• 25

• 30

• 20

7. A box can hold no more than 30 pounds of items. If you have x pounds of items, write an inequality to represent how much more you can add and interpret the solution.

• y < 30 + x

• y ≥ 30 - x

• y ≤ 30 - x

• y = 30 - x

8. A movie theater has at least 100 seats available. If y is the number of seats sold, write an inequality to represent the maximum number of seats that can still be sold and solve it.

• y = 100

• y <= 100

• y >= 100

• y < 100

9. A runner wants to complete a marathon in less than 4 hours. If she runs at a pace of x minutes per mile, write an inequality to represent the maximum pace she can maintain and interpret the solution.

• x < 8.5

• x < 9.16

• x < 9.75

• x < 10.5

10. A student needs to score at least 75% on a test to pass. If there are 40 questions on the test, write an inequality to represent the minimum number of questions she must answer correctly and solve it.

• 25

• 40

• 30

• 35