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.

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.

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.

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.

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.

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.

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.

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.

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.

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.