Solving Real-World Systems Inequalities: Grade 9 Challenge

A farmer has 100 acres of land to plant corn and wheat. Each acre of corn requires 2 hours of labor, and each acre of wheat requires 3 hours. If the farmer has a total of 240 hours of labor available, how many acres of each crop can he plant?

• 80 acres of corn and 20 acres of wheat

• 60 acres of corn and 40 acres of wheat

• 70 acres of corn and 30 acres of wheat

• 50 acres of corn and 50 acres of wheat

A school is organizing a field trip and has a budget of $500. The cost per student is $20 for transportation and $15 for admission. If the number of students is represented by x, write the system of inequalities that represents the budget constraints and find the maximum number of students that can attend.

• 10

• 14

• 12

• 18

A factory produces two types of toys: dolls and cars. Each doll requires 4 hours of labor and each car requires 3 hours. The factory has a maximum of 120 hours of labor available. Additionally, the factory can produce no more than 30 toys in total. Write the system of inequalities and determine the possible combinations of dolls and cars that can be produced.

• The possible combinations of dolls (x) and cars (y) must satisfy the inequalities: 4x + 3y <= 120 and x + y <= 30, with x, y >= 0.

• 2x + 5y <= 120 and x + y <= 20

• 3x + 4y <= 120 and x + y <= 35

• 4x + 2y <= 120 and x + y <= 25

A gym offers two types of memberships: basic and premium. A basic membership costs $30 per month, while a premium membership costs $50 per month. The gym wants to earn at least $1,200 in membership fees each month. Write the system of inequalities to represent this situation and find the minimum number of each type of membership needed to meet the goal.

• 0 basic and 24 premium memberships

• 10 basic and 10 premium memberships

• 5 basic and 20 premium memberships

• 15 basic and 5 premium memberships

A bakery sells two types of cakes: chocolate and vanilla. Each chocolate cake requires 2 pounds of flour and each vanilla cake requires 3 pounds. The bakery has 30 pounds of flour available. If the bakery wants to make at least 10 cakes in total, write the system of inequalities and find the possible combinations of cakes that can be made.

• (10, 1)

• Possible combinations of cakes: (0, 10), (1, 9), (2, 8), (3, 7), (4, 6), (5, 5), (6, 4), (7, 3), (8, 2), (9, 1), (10, 0)

• (5, 4)

• (0, 15)

A concert hall has a seating capacity of 500. Tickets for the front row cost $50, and tickets for the back row cost $30. The concert hall wants to earn at least $15,000 from ticket sales. Write the system of inequalities that represents this situation and determine the maximum number of tickets that can be sold for each row while meeting the revenue goal.

• Front row: 300, Back row: 200

• Front row: 500, Back row: 0

• Front row: 400, Back row: 100

• Front row: 250, Back row: 250

A company produces two products: A and B. Each product A requires 3 hours of labor and each product B requires 2 hours. The company has a total of 60 hours of labor available. Additionally, the company wants to produce at least 10 products in total. Write the system of inequalities and determine the possible combinations of products A and B that can be produced.

• 3x + 2y ≥ 60 and x + y ≤ 10

• x + y ≤ 10 and x, y ≥ 0

• 3x + 2y = 60 and x + y = 10

• The possible combinations of products A and B that can be produced are given by the inequalities: 3x + 2y ≤ 60 and x + y ≥ 10, with x, y ≥ 0.

A charity event is selling tickets for a concert. Each ticket costs $25, and the charity wants to raise at least $2,500. If they also have a goal of selling at least 100 tickets, write the system of inequalities that represents this situation and find the minimum number of tickets that need to be sold to meet the fundraising goal.

• 200

• 150

• 75

• 100

A restaurant offers two types of meals: vegetarian and non-vegetarian. Each vegetarian meal costs $10 and each non-vegetarian meal costs $15. The restaurant wants to earn at least $1,000 in a week. If they can serve a maximum of 100 meals in total, write the system of inequalities and determine the possible combinations of meals that can be served to meet the revenue goal.

• The system of inequalities is: 10x + 15y >= 1000, x + y <= 100, x >= 0, y >= 0.

• x <= 0, y <= 0

• x + y >= 100

• 10x + 15y <= 1000