Solving Real-Life Inequalities and Graphing Solutions

1. Sarah has $50 to spend on books. Each book costs $12. Write an inequality to represent how many books she can buy. Graph the solution on a number line and interpret what it means in this context.

• b <= 4

• b < 4

• b <= 5

• b >= 4

3. A gym charges a $30 membership fee plus $10 per class. If a member wants to spend no more than $100, write an inequality to represent the number of classes they can attend. Graph the solution and interpret it.

• x < 5

• x ≤ 10

• x ≥ 7

• x ≤ 7

4. A school is planning a field trip and has a budget of $500. Each student’s ticket costs $15. Write an inequality to determine how many students can go. Graph the solution and explain what it means.

• x <= 33

• x = 40

• x >= 35

• x < 30

5. A farmer has 200 acres of land. He wants to plant corn and wheat, with corn taking 2 acres and wheat taking 3 acres. Write an inequality to represent the maximum number of crops he can plant. Graph the solution and interpret it in context.

• 2x + 3y ≥ 200

• x + y ≤ 100

• 2x + 3y < 200

• 2x + 3y ≤ 200

6. A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If a customer wants to spend no more than $100, write an inequality to find out how many miles they can drive. Graph the solution and explain its meaning.

• m ≤ 250

• m ≤ 300

• m ≤ 200

• m ≤ 150

7. A student has a budget of $40 for snacks for a party. If each snack costs $5, write an inequality to determine how many snacks they can buy. Graph the solution and interpret it in the context of the party.

• x < 8

• x >= 10

• x <= 8

• x = 5

8. A local bakery sells cupcakes for $3 each. If a customer wants to spend no more than $30, write an inequality to find out how many cupcakes they can buy. Graph the solution and explain its significance.

• x <= 5

• x >= 10

• x <= 10

• x < 10

10. A student is saving money for a new video game that costs $60. If they save $5 a week, write an inequality to find out how many weeks it will take to save enough money. Graph the solution and explain what it means in this scenario.

• w <= 12

• w > 12

• w < 12

• w >= 12