Inequalities in Action: Finding Boundary Points (Grade 8)

A store sells notebooks for $2 each and pens for $1 each. If you want to spend no more than $20 on notebooks and pens combined, write an inequality to represent this situation and identify the boundary point for the number of notebooks you can buy if you buy 5 pens.

• x ≤ 3

• x ≤ 10

• x ≤ 5

• x ≤ 7 (maximum number of notebooks if 5 pens are bought)

Maria has $50 to spend on books and magazines. If books cost $8 each and magazines cost $3 each, write an inequality to represent how many books and magazines she can buy. What is the boundary point if she decides to buy 4 books?

• The boundary point is 5 books and 4 magazines.

• The boundary point is 6 books and 2 magazines.

• The boundary point is 3 books and 9 magazines.

• The boundary point is 4 books and 6 magazines.

A gym charges a $30 membership fee plus $5 per class. If you want to spend no more than $100 in a month, write an inequality to represent the number of classes you can attend. What is the boundary point for the number of classes if you attend 5 classes?

• You can attend a maximum of 20 classes.

• You can attend a maximum of 10 classes.

• You can attend a maximum of 12 classes.

• You can attend a maximum of 14 classes.

A farmer has a budget of $200 to buy seeds and fertilizer. If seeds cost $10 per bag and fertilizer costs $15 per bag, write an inequality to represent the total cost. What is the boundary point if the farmer buys 6 bags of seeds?

• y ≤ 10 when x = 6

• y ≤ 8 when x = 6

• y ≤ 7 when x = 6

• y ≤ 9 when x = 6

A concert hall has a seating capacity of 500. If each ticket costs $15 and the total revenue must be at least $6000, write an inequality to represent the number of tickets that must be sold. What is the boundary point for ticket sales?

• x <= 450

• x >= 400

• x > 400

• x >= 300

A school is planning a field trip and has a budget of $300. If each student pays $10 and the bus costs $150, write an inequality to represent how many students can attend. What is the boundary point if 10 students have already paid?

• 18

• 20

• 15

• 12

A baker makes cookies and cupcakes. If cookies cost $2 each and cupcakes cost $3 each, and the total sales must be at least $100, write an inequality to represent the sales. What is the boundary point if the baker sells 20 cookies?

• y ≥ 20 when x = 20

• y ≤ 20 when x = 20

• y = 20 when x = 20

• y ≥ 30 when x = 20

A charity event has a goal to raise at least $500. If each ticket costs $25 and they have already sold 10 tickets, write an inequality to represent the number of additional tickets they need to sell. What is the boundary point for additional ticket sales?

• x <= 10

• x > 10

• x >= 10

• x < 10

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 miles they can drive. What is the boundary point if they drive 100 miles?

• m ≤ 150, boundary point at 100 miles is $50.

• m ≤ 250, boundary point at 100 miles is $70.

• m ≤ 300, boundary point at 100 miles is $80.

• m ≤ 200, boundary point at 100 miles is $60.

A local restaurant offers a special deal where a meal costs $12 and a drink costs $3. If a family wants to spend no more than $60, write an inequality to represent how many meals and drinks they can order. What is the boundary point if they order 2 meals?

• y ≥ 12

• y ≤ 12

• y < 12

• y = 12