Graphing and Analyzing Linear Inequalities Challenge

A farmer has a rectangular field with a length of 10 meters and a width of 6 meters. He wants to plant crops in a section of the field that is at least 2 meters away from the edges. Write and graph the inequalities that represent the area where he can plant his crops.

• 1 < x < 9 and 1 < y < 5

• The inequalities are: 2 < x < 8 and 2 < y < 4.

• 2 < x < 6 and 2 < y < 8

• 0 < x < 10 and 0 < y < 6

A school is organizing a fundraiser and needs to sell at least 200 tickets. Each adult ticket costs $10 and each student ticket costs $5. Write a system of inequalities to represent the number of adult and student tickets they need to sell, and graph the solution.

• x + y >= 150, x >= 0, y >= 0

• x + y <= 200, x >= 0, y >= 0

• The system of inequalities is: x + y >= 200, x >= 0, y >= 0.

• x + y >= 200, x < 0, y >= 0

A gym offers two types of memberships: a basic membership for $30 per month and a premium membership for $50 per month. If a customer wants to spend no more than $120 per month, write and graph the inequality that represents the number of each type of membership they can purchase.

• 30x + 50y = 120

• 30x + 50y ≤ 120

• 30x + 50y ≥ 120

• 30x + 50y < 120

A company produces two types of gadgets: Type A and Type B. Each Type A gadget requires 2 hours of labor and each Type B gadget requires 3 hours. If the company has a maximum of 12 hours of labor available, write and graph the inequalities that represent the production limits for each type of gadget.

• 2x + 3y ≤ 10, x ≥ 0, y ≥ 0

• 2x + 3y ≤ 12, x ≥ 0, y ≥ 0

• 2x + 3y ≤ 15, x ≥ 0, y ≥ 0

• x + y ≤ 12, x ≥ 0, y ≥ 0

A local bakery sells two types of cakes: chocolate and vanilla. Each chocolate cake requires 3 eggs and each vanilla cake requires 2 eggs. If the bakery has 18 eggs available, write and graph the inequalities that represent the maximum number of each type of cake that can be made.

• 3x + 2y ≤ 18, x ≥ 0, y ≥ 0

• 4x + y ≤ 18, x ≥ 0, y ≥ 0

• 3x + 3y ≤ 18, x ≥ 0, y ≥ 0

• 2x + 3y ≤ 18, x ≥ 0, y ≥ 0

A concert venue has a seating capacity of 500. If tickets for the front row cost $50 and tickets for the back row cost $30, and the venue wants to make at least $15,000 from ticket sales, write and graph the system of inequalities that represents the ticket sales.

• x + y = 500, 50x + 30y = 15000

• x + y ≥ 500, 50x + 30y ≤ 15000

• x + y ≤ 500, 50x + 30y ≥ 15000

• x + y ≤ 400, 50x + 30y ≥ 20000

A clothing store has a sale on jeans and shirts. Each pair of jeans costs $40 and each shirt costs $20. If a customer wants to spend no more than $200, write and graph the inequality that represents the maximum number of jeans and shirts they can buy.

• 2x + y ≤ 10

• 4x + y ≤ 5

• x + 2y ≤ 12

• 3x + y ≤ 8

A charity organization is collecting donations. They want to collect at least $1,000. If each individual donation is at least $25, write and graph the inequality that represents the number of donations needed to reach their goal.

• d >= 40

• d < 40

• d <= 50

• d >= 20

A delivery service charges $5 for each package delivered and an additional $2 for every mile traveled. If a customer wants to spend no more than $50, write and graph the inequality that represents the maximum number of miles they can have their packages delivered.

• 22

• 15

• 30

• 10

A restaurant offers two types of meal deals: a vegetarian meal for $12 and a non-vegetarian meal for $15. If a family wants to spend no more than $60 on meals, write and graph the system of inequalities that represents the number of each type of meal they can order.

• 12x + 15y = 60, x ≥ 0, y ≥ 0.

• 12x + 15y ≤ 50, x ≥ 0, y ≥ 0.

• The system of inequalities is: 12x + 15y ≤ 60, x ≥ 0, y ≥ 0.

• 12x + 15y < 60, x > 0, y > 0.