Inequalities in Real Life: Writing & Analyzing Scenarios

A farmer has 100 meters of fencing to create a rectangular pen for sheep. If the length of the pen is represented by x and the width by y, write the inequality that represents the maximum area of the pen. What are the possible values for x and y?

• x + y ≤ 50, 0 < x < 50, 0 < y < 50

• x + y = 100, 0 < x < 75, 0 < y < 75

• x + y ≥ 50, 0 < x < 25, 0 < y < 25

• x + y < 100, 0 < x < 100, 0 < y < 100

A school is planning a field trip and has a budget of $500. The cost per student is $20 for transportation and $15 for admission. Write the system of inequalities that represents the number of students that can attend the trip. What is the maximum number of students?

• 12

• 14

• 18

• 10

A company produces two types of gadgets, A and B. Each gadget A requires 2 hours of labor and each gadget B requires 3 hours. If the company has 30 hours of labor available, write the inequality for the labor constraint. How many gadgets can they produce if they want to maximize production?

• 5 gadgets A and 5 gadgets B

• 15 gadgets A and 0 gadgets B or 0 gadgets A and 10 gadgets B.

• 10 gadgets A and 5 gadgets B

• 20 gadgets A and 0 gadgets B

A local gym offers two types of memberships: basic and premium. The basic membership costs $25 per month, and the premium membership costs $40 per month. If the gym wants to earn at least $1,000 in a month, write the inequality representing the number of each type of membership sold. What are the possible combinations of memberships?

• The combinations of memberships (x, y) must satisfy 25x + 40y ≥ 1000.

• 30x + 35y ≥ 1000

• 25x + 40y ≤ 1000

• 20x + 50y ≥ 1000

A 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 30 eggs, write the inequality that represents the maximum number of cakes they can make. What combinations of cakes can they produce?

• 2x + 3y ≤ 30; combinations include (0, 10), (1, 8), (2, 6)

• 4x + y ≤ 30; combinations include (0, 30), (1, 26), (2, 22)

• 3x + 4y ≤ 30; combinations include (0, 7), (1, 5), (2, 2)

• 3x + 2y ≤ 30; combinations include (0, 15), (1, 12), (2, 9), (3, 6), (4, 3), (5, 0)

A charity event is selling tickets for $10 each and has a goal to raise at least $1,200. Write the inequality that represents the number of tickets they need to sell. How many tickets must they sell to meet their goal?

• 200

• 150

• 120

• 100

A clothing store has a sale on shirts and pants. Shirts are $15 each and pants are $25 each. If the store wants to make at least $600 in sales, write the system of inequalities for the number of shirts (x) and pants (y) sold. What are the possible combinations of shirts and pants?

• 10x + 20y >= 600, x >= 0, y >= 0

• 15x + 30y >= 600, x >= 0, y >= 0

• 15x + 25y >= 600, x >= 0, y >= 0

• 15x + 25y <= 600, x >= 0, y >= 0

A student is saving money for a new laptop that costs $800. If they save $50 a week from their allowance and $20 a week from chores, write the inequality that represents the number of weeks needed to save enough money. How many weeks will it take?

• 10 weeks

• 15 weeks

• 20 weeks

• 12 weeks

A restaurant has a special on burgers and fries. Each burger costs $5 and each order of fries costs $3. If the restaurant wants to make at least $200 in one day, write the inequality representing the number of burgers (x) and fries (y) sold. What are the possible combinations?

• 5x + 3y ≤ 200

• 2x + 4y ≥ 200

• 5x + 3y ≥ 200

• 10x + y ≥ 200

A concert venue has a seating capacity of 500. If tickets are sold for $30 each and VIP tickets for $50 each, write the system of inequalities that represents the maximum revenue the venue can earn. What are the possible combinations of regular and VIP tickets sold?

• x + y ≥ 500, 30x + 50y ≤ R, where x ≥ 0, y ≥ 0.

• x + y ≤ 500, 30x + 50y ≤ R, where x ≥ 0, y ≥ 0.

• x + y ≤ 300, 30x + 50y ≤ R, where x ≥ 0, y ≥ 0.

• x + y ≤ 500, 30x + 50y ≥ R, where x ≥ 0, y ≥ 0.