Exploring Real-Life Linear Inequalities and Solutions

A school is planning a field trip and can take no more than 120 students. If each bus can hold 30 students, how many buses are needed? Write an inequality to represent the situation and find the feasible solutions.

• The school needs at most 3 buses.

• The school needs at most 5 buses.

• The school needs at most 6 buses.

• The school needs at most 4 buses.

A bakery sells cookies for $2 each and brownies for $3 each. If a customer has $20 to spend, write an inequality to represent the maximum number of cookies and brownies they can buy. What are the feasible combinations?

• (7, 0)

• (2, 3)

• (0, 8)

• Feasible combinations include (0, 6), (1, 5), (2, 4), (3, 3), (4, 2), (5, 1), (6, 0) for (cookies, brownies).

A farmer has 150 feet of fencing to enclose a rectangular garden. If the length of the garden must be at least 20 feet, write an inequality for the width of the garden. What are the possible widths?

• 20 ≤ W ≤ 70

• 10 ≤ W ≤ 50

• 0 ≤ W ≤ 30

• 0 ≤ W ≤ 55

A concert hall has a seating capacity of 500. If tickets are sold for $15 each, how many tickets can be sold to ensure that the total revenue does not exceed $6000? Write an inequality and find the feasible solutions.

• x ≤ 300

• x ≤ 450

• x ≤ 400

• x ≤ 500

A gym has a maximum capacity of 200 members. If 75 members are currently enrolled, how many new members can join? Write an inequality to represent this situation and find the feasible solutions.

• New members can join: 0 to 100.

• New members can join: 0 to 50.

• New members can join: 0 to 175.

• New members can join: 0 to 125.

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 represent the maximum number of miles they can drive. What are the feasible solutions?

• m ≤ 300

• m ≤ 150

• m ≤ 200

• m ≤ 250

A local pool can accommodate a maximum of 80 people at a time. If there are currently 45 people in the pool, how many more can enter? Write an inequality to represent this situation and find the feasible solutions.

• 40

• 35

• 50

• 30

A charity event aims to raise at least $5000. If each ticket sold is $25, how many tickets must be sold to meet the goal? Write an inequality and find the feasible solutions.

• 250 tickets must be sold.

• At least 200 tickets must be sold.

• 100 tickets must be sold.

• 150 tickets must be sold.

A restaurant has a special offer where a family can order a maximum of 5 pizzas and 10 drinks. If they have already ordered 3 pizzas, how many more pizzas can they order? Write an inequality to represent this situation and find the feasible solutions.

• 1

• 3

• 4

• 2

A student has a budget of $50 to spend on school supplies. If notebooks cost $3 each and pens cost $2 each, write an inequality to represent the maximum number of notebooks and pens the student can buy. What are the feasible combinations?

• (5, 20)

• (10, 15)

• Feasible combinations include: (0, 25), (1, 23), (2, 22), (3, 20), (4, 18), (5, 17), (6, 15), (7, 13), (8, 12), (9, 10), (10, 8), (11, 7), (12, 5), (13, 3), (14, 1).

• (0, 30)