Real-Life Applications of Matrix Systems in Grade 11

A farmer has two types of crops: corn and wheat. He sells corn for $3 per bushel and wheat for $4 per bushel. If he sells a total of 100 bushels for $360, how many bushels of each crop did he sell? Set up and solve the system using matrices.

• 50 bushels of corn and 50 bushels of wheat

• 20 bushels of corn and 80 bushels of wheat

• 40 bushels of corn and 60 bushels of wheat

• 30 bushels of corn and 70 bushels of wheat

A school is organizing a field trip and has two types of tickets: student tickets for $15 and adult tickets for $25. If they sold a total of 80 tickets for $1,500, how many student and adult tickets were sold? Use matrices to find the solution.

• 50 student tickets and 30 adult tickets

• 70 student tickets and 10 adult tickets

• 40 student tickets and 40 adult tickets

• 60 student tickets and 20 adult tickets

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, how many of each product can they produce? Solve using matrices.

• 20 units of product A and 10 units of product B

• 10 units of product A and 20 units of product B

• 15 units of product A and 5 units of product B

• 25 units of product A and 5 units of product B

A concert venue has two types of seating: regular seats and VIP seats. Regular seats are sold for $50 and VIP seats for $100. If the venue sold a total of 200 seats for $12,000, how many of each type of seat were sold? Set up the system and solve using matrices.

• 180 regular seats and 20 VIP seats

• 100 regular seats and 100 VIP seats

• 160 regular seats and 40 VIP seats

• 150 regular seats and 50 VIP seats

A bakery makes two types of cakes: chocolate and vanilla. Each chocolate cake requires 2 eggs and 1 cup of sugar, while each vanilla cake requires 1 egg and 2 cups of sugar. If the bakery has 100 eggs and 80 cups of sugar, how many of each type of cake can they make? Use matrices to find the solution.

• 50 chocolate cakes and 10 vanilla cakes

• 20 chocolate cakes and 40 vanilla cakes

• 30 chocolate cakes and 50 vanilla cakes

• 40 chocolate cakes and 20 vanilla cakes

A car rental company has two types of cars: sedans and SUVs. Sedans rent for $40 per day and SUVs for $60 per day. If the company rented a total of 50 cars for $2,800, how many of each type were rented? Solve the system using matrices.

• 10 sedans and 40 SUVs

• 5 sedans and 45 SUVs

• 15 sedans and 35 SUVs

• 20 sedans and 30 SUVs

A gym offers two types of memberships: basic and premium. A basic membership costs $30 per month and a premium membership costs $50 per month. If the gym has 200 members and collects $8,000 in membership fees, how many basic and premium memberships are there? Use matrices to solve the problem.

• 100 basic memberships and 100 premium memberships.

• 200 basic memberships and 0 premium memberships.

• 50 basic memberships and 150 premium memberships.

• 150 basic memberships and 50 premium memberships.

A bookstore sells two types of books: fiction and non-fiction. Fiction books are priced at $12 and non-fiction at $15. If the bookstore sold a total of 150 books for $1,800, how many of each type were sold? Set up and solve the system using matrices.

• Fiction: 90, Non-Fiction: 60

• Fiction: 80, Non-Fiction: 70

• Fiction: 100, Non-Fiction: 50

• Fiction: 60, Non-Fiction: 90

A factory produces two types of gadgets: Type X and Type Y. Type X requires 3 hours of machine time and Type Y requires 2 hours. If the factory has 120 hours of machine time available and produces a total of 40 gadgets, how many of each type can be produced? Use matrices to find the solution.

• 10 Type X gadgets and 30 Type Y gadgets

• 25 Type X gadgets and 15 Type Y gadgets

• 30 Type X gadgets and 10 Type Y gadgets

• 20 Type X gadgets and 20 Type Y gadgets

A clothing store sells two types of shirts: t-shirts and dress shirts. T-shirts are sold for $20 and dress shirts for $35. If the store sold a total of 100 shirts for $2,500, how many of each type were sold? Set up the system and solve using matrices.

• 80 t-shirts and 20 dress shirts

• 70 t-shirts and 30 dress shirts

• 60 t-shirts and 40 dress shirts

• 75 t-shirts and 25 dress shirts