Inequalities in Real Life: Combine & Interpret Solutions

1. Sarah has $50 to spend on school supplies. She wants to buy notebooks for $3 each and pens for $2 each. If she buys x notebooks and y pens, write an inequality to represent her spending limit. Combine like terms and solve for y in terms of x.

• y ≤ (50 - 5x) / 2

• y ≤ (50 - 2x) / 3

• y ≤ (50 - 3x) / 2

• y ≤ (50 + 3x) / 2

2. A concert venue can hold a maximum of 500 people. If 200 tickets have already been sold and each ticket costs $20, write an inequality to represent the maximum number of additional tickets that can be sold. Solve the inequality and interpret the result in context.

• x ≤ 300

• x ≤ 400

• x ≤ 200

• x ≤ 250

3. A gym charges a monthly fee of $30 plus $5 for each class attended. If a member wants to spend no more than $100 in a month, write an inequality to represent the number of classes they can attend. Solve the inequality and explain what the solution means.

• x ≤ 14

• x ≤ 5

• x ≤ 20

• x ≤ 10

4. A farmer has 120 acres of land. He wants to plant corn and wheat, where corn requires 2 acres per field and wheat requires 3 acres per field. Write an inequality to represent the maximum number of fields he can plant. Combine like terms and solve for the number of corn fields in terms of wheat fields.

• x ≤ (120 - 2y) / 4

• x ≤ (120 - 3y) / 2

• x ≤ (120 - 2y) / 3

• x ≤ (120 - 4y) / 2

6. A student is saving money for a new laptop that costs $600. If they save $50 a week, write an inequality to represent how many weeks it will take to save enough money. Solve the inequality and explain what the solution indicates about their savings plan.

• w < 12

• w <= 12

• w >= 12

• w > 12

7. A car rental company charges a flat fee of $40 plus $0.25 per mile driven. If a customer wants to spend no more than $100, write an inequality to represent the maximum number of miles they can drive. Solve the inequality and interpret the result in context.

• x <= 240

• x <= 180

• x <= 300

• x <= 200

8. A local charity is collecting cans for a food drive. They want to collect at least 500 cans. If they have already collected 250 cans and each donation adds x cans, write an inequality to represent the number of additional cans needed. Solve the inequality and explain the significance of the solution.

• x >= 250

• x = 500

• x <= 300

• x < 250

9. A school is planning a field trip and has a budget of $800. If the cost per student is $25, write an inequality to represent the maximum number of students that can attend. Solve the inequality and interpret the result in the context of the trip.

• 32

• 40

• 35

• 30

10. A restaurant offers a special deal where a meal costs $15 and a drink costs $3. If a family wants to spend no more than $60, write an inequality to represent the maximum number of meals and drinks they can order. Solve the inequality and explain what the solution means for their order.

• The family can order a maximum of 3 meals and 5 drinks.

• The family can order a maximum of 5 meals and 1 drink.

• The family can order a maximum of 4 meals and 0 drinks, or any combination of meals and drinks that does not exceed the total cost of $60.

• The family can order a maximum of 2 meals and 10 drinks.