Inequality Challenges: Isolate Variables & Validate Solutions

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. Solve for x and check your solution.

• x > 10

• x = 7

• x >= 5

• x < 5

2. A concert hall can hold a maximum of 500 people. If tickets are sold for $15 each and the hall is already filled with y people, write an inequality to find the maximum number of tickets that can still be sold. Solve for y and verify your answer.

• 500 - y

• 500 + y

• 15y

• y - 500

3. A store sells pencils for $2 each and erasers for $3 each. If a student spends no more than $20, write an inequality to represent the number of pencils (x) and erasers (y) they can buy. Solve for y in terms of x and check your solution.

• y ≤ (20 - 3x) / 2

• y ≤ (20 - 5x) / 3

• y ≤ (20 - 2x) / 4

• y ≤ (20 - 2x) / 3

4. A car rental company charges a flat fee of $30 plus $0.50 per mile driven. If a customer wants to spend no more than $100, write an inequality to represent the miles driven (m). Solve for m and confirm your solution is valid.

• m ≤ 140

• m ≥ 140

• m ≤ 100

• m < 120

5. A gym has a membership fee of $50 and charges $10 per class. If a member wants to spend less than $200 in a month, write an inequality for the number of classes (c) they can attend. Solve for c and check your work.

• c < 15

• c < 12

• c < 20

• c < 10

6. A farmer has x acres of land and wants to plant at least 200 trees. If each acre can hold 50 trees, write an inequality to represent the situation. Solve for x and verify your solution.

• x < 4

• x <= 5

• x >= 4

• x > 3

7. A school is planning a field trip and has a budget of $300. If each student pays $15 and there are y students, write an inequality to find the maximum number of students that can attend. Solve for y and check your answer.

• 25

• 30

• 20

• 15

8. A baker makes cookies and sells them for $1 each. If she wants to earn at least $100 in a day, write an inequality to represent the number of cookies (c) she needs to sell. Solve for c and confirm your solution is correct.

• c <= 100

• c > 100

• c >= 100

• c < 100

9. A video game costs $60, and a player has saved x dollars. If they want to buy the game and still have at least $10 left, write an inequality to represent the situation. Solve for x and check your solution for validity.

• x = 60

• x >= 70

• x < 50

• x > 80

10. A charity event has a goal of raising at least $500. If each ticket sold is $25 and y tickets are sold, write an inequality to represent the situation. Solve for y and verify your answer.

• y < 20

• y >= 20

• y <= 25

• y > 20