Solving Real-World Problems with Systems of Equations

A farmer has 100 meters of fencing to enclose a rectangular garden. If the length of the garden is represented by x and the width by y, write the system of equations that represents the perimeter of the garden. What are the feasible dimensions of the garden?

• x + y = 50; x > 0, y > 0; feasible dimensions: any positive (x, y) such that x + y = 50.

• x + y = 100; x > 0, y > 0; feasible dimensions: any positive (x, y) such that x + y = 100.

• x + 2y = 100; x > 0, y > 0; feasible dimensions: any positive (x, y) such that x + 2y = 100.

• 2x + y = 100; x > 0, y > 0; feasible dimensions: any positive (x, y) such that 2x + 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 a system of inequalities to represent the number of students that can attend. How many students can they afford to take?

• 10

• 20

• 25

• 14

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 60 hours of labor available, write a system of inequalities to represent the production limits. What is the feasible region for the number of gadgets produced?

• 2x + 3y ≤ 70, x ≥ 0, y ≥ 0

• The system of inequalities is: 2x + 3y ≤ 60, x ≥ 0, y ≥ 0.

• 2x + 3y ≤ 50, x ≥ 0, y ≥ 0

• x + y ≤ 60, x ≥ 0, y ≥ 0

A concert hall has 300 seats. Tickets for adults are $15 and for children are $10. If the total revenue from ticket sales is $4000, write a system of equations to represent the number of adult and child tickets sold. How many of each type of ticket were sold?

• 100 adult tickets and 200 child tickets

• 250 adult tickets and 50 child tickets

• 200 adult tickets and 100 child tickets

• 150 adult tickets and 150 child tickets

Tags

CCSS.8.EE.C.8C

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 a system of inequalities to represent the maximum number of cakes that can be made. What is the feasible region for cake production?

• 3x + 2y ≤ 30, x ≥ 0, y ≥ 0

• 3x + 3y ≤ 30, x ≥ 0, y ≥ 0

• 4x + y ≤ 30, x ≥ 0, y ≥ 0

• 2x + 3y ≤ 30, x ≥ 0, y ≥ 0

A local gym offers two types of memberships: basic and premium. The basic membership costs $25 per month and the premium costs $40. If the gym wants to make at least $2000 in a month, write a system of inequalities to represent the number of each type of membership sold. What combinations of memberships meet this goal?

• 25x + 40y <= 2000, x >= 0, y >= 0

• 25x + 40y >= 2500, x >= 0, y >= 0

• 25x + 40y = 2000, x >= 0, y >= 0

• The system of inequalities is: 25x + 40y >= 2000, x >= 0, y >= 0.

A charity event is selling tickets for a dinner. Adult tickets are $50 and child tickets are $30. If they want to raise at least $3000, write a system of inequalities to represent the number of adult and child tickets that need to be sold. What are the possible combinations of tickets sold?

• 50x + 30y >= 3000, x >= 0, y >= 0

• 50x + 30y <= 3000, x >= 0, y >= 0

• 60x + 25y >= 3000, x >= 0, y >= 0

• 40x + 20y >= 3000, x >= 0, y >= 0

A factory produces two products, X and Y. Each product X requires 4 hours of machine time and each product Y requires 2 hours. If the factory has 40 hours of machine time available, write a system of inequalities to represent the production limits. What is the feasible region for the production of products?

• 4x + 3y ≤ 40, x ≥ 0, y ≥ 0

• 4x + 2y ≤ 30, x ≥ 0, y ≥ 0

• 3x + 2y ≤ 40, x ≥ 0, y ≥ 0

• The system of inequalities is: 4x + 2y ≤ 40, x ≥ 0, y ≥ 0.

A bookstore sells novels and textbooks. Each novel costs $12 and each textbook costs $20. If the bookstore wants to make at least $1000 in sales, write a system of inequalities to represent the number of novels and textbooks that can be sold. What combinations of books meet this sales goal?

• The combinations of novels (x) and textbooks (y) that meet the sales goal can be represented as pairs (x, y) where y >= (1000 - 12x) / 20, with x >= 0 and y >= 0.

• x >= 1000 / 12

• x + y <= 1000

• y <= (1000 - 20x) / 12

A sports team has a budget of $1500 for new uniforms. Each uniform costs $75 for players and $50 for coaches. Write a system of inequalities to represent how many uniforms can be purchased. What is the feasible region for the number of uniforms?

• 70x + 60y ≤ 1500, x ≥ 0, y ≥ 0

• 75x + 50y ≤ 1500, x ≥ 0, y ≥ 0

• 80x + 40y ≤ 1500, x ≥ 0, y ≥ 0

• 75x + 50y ≤ 1600, x ≥ 0, y ≥ 0