Solving Real-Life Problems with Matrix Equations

A farmer has two types of crops: corn and wheat. He sells corn for $3 per bushel and wheat for $4 per bushel. Last month, he sold a total of 200 bushels and earned $720. Formulate a system of equations and use matrices to find out how many bushels of each crop he sold.

• Corn: 80 bushels, Wheat: 120 bushels

• Corn: 100 bushels, Wheat: 100 bushels

• Corn: 50 bushels, Wheat: 150 bushels

• Corn: 90 bushels, Wheat: 110 bushels

A school is planning a field trip and has two types of tickets: adult tickets for $15 and student tickets for $10. They sold a total of 150 tickets and collected $1,800. Create a system of equations and solve it using matrix operations to determine how many adult and student tickets were sold.

• 60 adult tickets and 90 student tickets were sold.

• 70 adult tickets and 80 student tickets were sold.

• 50 adult tickets and 100 student tickets were sold.

• 40 adult tickets and 110 student tickets were sold.

A company produces two products, A and B. Product A requires 2 hours of labor and $5 in materials, while product B requires 3 hours of labor and $8 in materials. If the company has 100 hours of labor and $200 for materials, set up a system of equations and solve it using matrices to find the maximum number of each product they can produce.

• Product A: 10, Product B: 15

• Product A: 15, Product B: 5

• Product A: 20, Product B: 10

• Product A: 25, Product B: 8

In a concert, there are two types of tickets: VIP tickets for $100 and regular tickets for $50. If 300 tickets were sold for a total of $15,000, formulate the system of equations and use matrix operations to determine how many VIP and regular tickets were sold.

• 100 VIP tickets and 200 regular tickets

• 150 VIP tickets and 150 regular tickets

• 0 VIP tickets and 300 regular tickets

• 50 VIP tickets and 250 regular tickets

A bookstore sells two types of books: fiction and non-fiction. Fiction books cost $12 each, and non-fiction books cost $15 each. If the store sold a total of 100 books for $1,200, create a system of equations and solve it using matrices to find out how many of each type of book was sold.

• 20 fiction books and 80 non-fiction books were sold.

• 40 fiction books and 60 non-fiction books were sold.

• 30 fiction books and 70 non-fiction books were sold.

• 50 fiction books and 50 non-fiction books were sold.

A factory produces two types of gadgets: Type X and Type Y. Type X requires 4 hours of machine time and Type Y requires 3 hours. If the factory has 60 hours of machine time available and produces a total of 15 gadgets, set up a system of equations and solve it using matrix operations to find out how many of each type of gadget was produced.

• 12 Type X gadgets and 3 Type Y gadgets

• 15 Type X gadgets and 0 Type Y gadgets

• 8 Type X gadgets and 7 Type Y gadgets

• 10 Type X gadgets and 5 Type Y gadgets

A restaurant offers two types of meals: vegetarian and non-vegetarian. The vegetarian meal costs $10 and the non-vegetarian meal costs $15. If the restaurant sold a total of 200 meals for $2,500, formulate a system of equations and use matrices to determine how many vegetarian and non-vegetarian meals were sold.

• 80 vegetarian meals and 120 non-vegetarian meals were sold.

• 150 vegetarian meals and 50 non-vegetarian meals were sold.

• 100 vegetarian meals and 100 non-vegetarian meals were sold.

• 200 vegetarian meals and 0 non-vegetarian meals were sold.

A gym has two types of memberships: basic and premium. The basic membership costs $30 per month, and the premium membership costs $50 per month. If the gym has 200 members and collects $8,000 in membership fees, create a system of equations and solve it using matrix operations to find out how many basic and premium members there are.

• 200 basic members and 0 premium members

• 80 basic members and 120 premium members

• 100 basic members and 100 premium members

• 150 basic members and 50 premium members

A clothing store sells two types of shirts: casual and formal. Casual shirts are priced at $20 each, while formal shirts are priced at $30 each. If the store sold a total of 150 shirts for $3,600, set up a system of equations and solve it using matrices to find out how many casual and formal shirts were sold.

• 100 casual shirts and 50 formal shirts were sold.

• 60 casual shirts and 90 formal shirts were sold.

• 90 casual shirts and 60 formal shirts were sold.

• 80 casual shirts and 70 formal shirts were sold.

A car rental company has two types of cars: economy and luxury. The economy car rents for $40 per day, and the luxury car rents for $80 per day. If the company rented out a total of 50 cars and made $2,800 in revenue, formulate a system of equations and use matrix operations to determine how many economy and luxury cars were rented.

• 40 economy cars and 10 luxury cars were rented.

• 25 economy cars and 25 luxury cars were rented.

• 35 economy cars and 15 luxury cars were rented.

• 30 economy cars and 20 luxury cars were rented.