Solving Linear Equations with Matrices: Real-World Challenges

A bakery produces two types of cakes: chocolate and vanilla. The cost to make one chocolate cake is $5 and one vanilla cake is $3. If the bakery spends $120 on ingredients, how many of each type of cake can they make? Set up a matrix equation to solve this problem.

• The bakery can make 15 chocolate cakes and 15 vanilla cakes.

• The bakery can make 30 chocolate cakes and 5 vanilla cakes.

• The bakery can make various combinations of chocolate and vanilla cakes, with maximums being 24 chocolate cakes and 0 vanilla cakes, or 0 chocolate cakes and 40 vanilla cakes.

• The bakery can make 20 chocolate cakes and 10 vanilla cakes.

A school is organizing a field trip and needs to transport students in buses. Each bus can hold 40 students. If there are 3 buses and 15 students are not going, how many students can go on the trip? Use a matrix to represent the situation and solve for the number of students attending.

• 80

• 105

• 90

• 100

A clothing store sells shirts and pants. The store sells shirts for $20 each and pants for $30 each. If the store made $600 in sales one day, how many shirts and pants did they sell? Create a matrix equation to find the solution.

• 10 shirts and 10 pants

• 0 shirts and 20 pants

• 20 shirts and 0 pants

• 5 shirts and 15 pants

A farmer has chickens and cows. Each chicken produces 2 eggs per week, and each cow produces 5 liters of milk per week. If the farmer has 10 chickens and 5 cows, how many eggs and liters of milk does he produce in a week? Use matrices to represent and solve the problem.

• 25 eggs and 20 liters of milk

• 10 eggs and 15 liters of milk

• 20 eggs and 25 liters of milk

• 15 eggs and 30 liters of milk

A car rental company has two types of cars: sedans and SUVs. The rental cost for a sedan is $50 per day and for an SUV is $80 per day. If a customer rents one of each type of car for 3 days, how much will the total cost be? Set up a matrix to solve this problem.

• $250

• $300

• 390

• $450

A concert hall has two types of seating: regular and VIP. Regular seats cost $30 each and VIP seats cost $50 each. If the hall sold 200 tickets and made $8000, how many of each type of ticket were sold? Use a matrix equation to find the solution.

• 100 regular tickets and 100 VIP tickets

• 50 regular tickets and 150 VIP tickets

• 200 regular tickets and 0 VIP tickets

• 150 regular tickets and 50 VIP tickets

A gym offers two types of memberships: basic and premium. A basic membership costs $25 per month and a premium membership costs $40 per month. If the gym has 100 members and collects $3500 in membership fees, how many of each type of membership does it have? Set up a matrix to solve this problem.

• 30 basic memberships and 70 premium memberships.

• 50 basic memberships and 50 premium memberships.

• 100 basic memberships and 0 premium memberships.

• 60 basic memberships and 40 premium memberships.

A bookstore sells fiction and non-fiction books. Fiction books are priced at $15 and non-fiction at $25. If the store sold 100 books and made $2000, how many of each type of book were sold? Create a matrix equation to find the solution.

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

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

• 100 fiction books and 0 non-fiction books were sold.

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

A factory produces two products: A and B. Product A requires 2 hours of labor and product B requires 3 hours. If the factory has 60 hours of labor available, how many of each product can be produced? Use a matrix to represent and solve the problem.

• (5, 25)

• (10, 15)

• (20, 10)

• The factory can produce combinations of products A and B such as (30, 0), (15, 10), (0, 20), etc.

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 150 meals and made $1800, how many of each type of meal were sold? Set up a matrix equation to find the solution.

• 90 vegetarian meals and 60 non-vegetarian meals were sold.

• 60 vegetarian meals and 90 non-vegetarian meals were sold.

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

• 80 vegetarian meals and 70 non-vegetarian meals were sold.