Solving Inequalities: Contextual Interpretations & Solutions

A school is planning a field trip and needs to collect at least $300 from students. If each student pays $15, how many students must participate? Write and solve the inequality, then interpret the solution in context.

• 20

• 15

• 30

• 25

Maria has $50 to spend on supplies for a project. If she buys notebooks for $3 each and markers for $2 each, how many notebooks can she buy if she wants to spend no more than her budget? Set up the inequality and solve it, checking for extraneous solutions.

• 20

• 10

• 12

• 16

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, how many classes can they attend? Write the inequality, solve it, and explain the result in context.

• 12

• 10

• 14

• 16

Tom is saving money to buy a new bike that costs $250. He saves $20 each week. Write an inequality to represent how many weeks it will take him to save enough money, and solve it. Discuss the meaning of your solution.

• w >= 13

• w <= 12

• w > 15

• w < 13

A concert venue can hold a maximum of 500 people. If 200 tickets have already been sold and each ticket costs $25, how many more tickets can be sold without exceeding the capacity? Formulate and solve the inequality, then interpret the solution.

• 250

• 150

• 400

• 300

A recipe requires at least 2 cups of flour and 1 cup of sugar. If you have 5 cups of flour and 3 cups of sugar, how many batches of the recipe can you make? Set up the inequalities and solve them, checking for any extraneous solutions.

• 4

• 1

• 2

• 3

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, how many miles can they drive? Write the inequality, solve it, and explain the context of your solution.

• 100 miles

• 240 miles

• 300 miles

• 180 miles

Lily is buying books for her book club. Each book costs $12, and she wants to buy at least 5 books but not spend more than $100. Write and solve the inequality, then interpret the solution in the context of her budget.

• Lily can buy 4 to 6 books.

• Lily can buy between 5 and 8 books.

• Lily can buy 9 to 12 books.

• Lily can buy 1 to 3 books.

A farmer has a budget of $200 to buy seeds. If each packet of seeds costs $15, how many packets can he buy? Set up the inequality, solve it, and discuss the implications of your solution.

• 13

• 20

• 10

• 15

A video game costs $60, and a store is offering a discount of $10 for every game purchased. If a customer wants to buy multiple games but spend no more than $150, how many games can they buy? Write the inequality, solve it, and interpret the result in context.

• 3 games

• 2 games

• 4 games

• 5 games