Modeling Real-Life Scenarios with Inequalities

A store sells pencils for $0.50 each and erasers for $0.75 each. If you want to spend no more than $10, write an inequality to represent the maximum number of pencils (p) and erasers (e) you can buy. Combine the inequalities to find the possible combinations.

• 0.50p + 0.75e = 10

• 0.50p + 0.75e < 10

• 0.50p + 0.75e ≤ 10

• 0.50p + 0.75e ≥ 10

A school has a budget of $500 for a field trip. The cost per student is $25. Write an inequality to represent the maximum number of students (s) that can go on the trip. How many students can attend if the school wants to reserve at least $100 for other expenses?

• 15

• 20

• 16

• 10

A concert hall can hold a maximum of 1,200 people. If 300 tickets have already been sold, write an inequality to represent the number of additional tickets (t) that can be sold. What is the maximum number of tickets that can still be sold?

• 1,200

• 1,000

• 900

• 600

A farmer has a total of 150 acres of land. He wants to plant corn on at least 60 acres and wheat on at least 40 acres. Write a system of inequalities to represent the situation and determine how many acres he can use for other crops.

• 100 acres

• 50 acres

• 30 acres

• 70 acres

A gym has a maximum capacity of 200 members. Currently, there are 150 members. If the gym wants to maintain at least 30 open spots for new members, write an inequality to represent the maximum number of new members (n) that can join.

• n <= 50

• n <= 10

• n <= 20

• n <= 30

A car rental company charges a flat fee of $30 plus $0.20 per mile driven. If a customer wants to spend no more than $100, write an inequality to represent the number of miles (m) they can drive. How many miles can they drive without exceeding their budget?

• 350 miles

• 250 miles

• 400 miles

• 300 miles

A bakery sells cupcakes for $2 each and cookies for $1 each. If a customer wants to buy at least 10 items but spend no more than $20, write a system of inequalities to represent the situation. What are the possible combinations of cupcakes (c) and cookies (k) they can buy?

• c + k = 10, 2c + k = 20

• c + k <= 10, 2c + k >= 20

• c + k >= 10, 2c + k <= 20

• c + k <= 5, 2c + k <= 15

A student has a total of 15 hours to study for three subjects. If they want to study at least 5 hours for math and at least 3 hours for science, write a system of inequalities to represent the study hours (m, s, h) for math, science, and history. How many hours can they allocate to history?

• 8 hours

• 7 hours

• 5 hours

• 10 hours

A local community center has a budget of $1,000 for a summer camp. If they plan to spend at least $300 on supplies and $200 on snacks, write an inequality to represent the maximum amount they can spend on activities (a). What is the maximum budget for activities?

• 700

• 400

• 600

• 500

A pet store has a limit of 50 animals. If they currently have 20 dogs and 15 cats, write an inequality to represent the maximum number of other animals (o) they can have. How many other animals can they add to their store?

• 15

• 30

• 25

• 10