Real-Life Inequalities: Modeling and Combining Scenarios

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.

• 0.50p + 0.75e = 10

• 0.50p + 0.75e ≥ 10

• 0.50p + 0.75e < 10

• 0.50p + 0.75e ≤ 10

A class has 30 students, and at least 10 of them must be present for a group project to start. If x represents the number of students present, write an inequality to show this situation.

• x = 10

• x < 10

• x >= 10

• x <= 10

A concert hall can hold a maximum of 500 people. If 200 tickets have already been sold, write an inequality to represent the number of additional tickets (t) that can still be sold.

• t ≤ 300

• t = 500

• t ≥ 400

• t < 200

A farmer has 120 apples and wants to pack them into boxes. Each box can hold 8 apples. Write an inequality to represent the maximum number of boxes (b) he can fill.

• 8b <= 120

• 5b <= 120

• b >= 10

• b < 15

A gym has a policy that no more than 50 members can be in the gym at the same time. If y represents the number of members currently in the gym, write an inequality to show how many more members can enter.

• y < 50

• y ≤ 50

• y = 50

• y > 50

A school is planning a field trip and has a budget of $1,200. If each student pays $30, write an inequality to represent the maximum number of students (s) that can go on the trip.

• s ≤ 50

• s ≤ 30

• s ≤ 20

• s ≤ 40

A recipe requires at least 2 cups of flour and no more than 5 cups. Write an inequality to represent the possible amounts of flour (f) that can be used in the recipe.

• f = 3

• f > 5

• f < 2

• 2 <= f <= 5

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If you want to spend no more than $100, write an inequality to represent the maximum number of miles (m) you can drive.

• m ≤ 150

• m ≤ 300

• m ≤ 250

• m ≤ 200

A local library has a limit of 15 books that a member can borrow at one time. If b represents the number of books borrowed, write an inequality to show this borrowing limit.

• b <= 15

• b < 15

• b >= 15

• b = 15

A student needs to score at least 75% on a test to pass. If the test has 40 questions, write an inequality to represent the minimum number of questions (q) the student must answer correctly to pass.

• q = 25

• q >= 30

• q >= 35

• q < 30