Matrix Systems: Solving Real-Life Linear Equations

A farmer has two types of crops: corn and wheat. The total area of the farm is 100 acres. If the area planted with corn is twice that of wheat, how many acres are planted with each crop? Use matrices to solve the system of equations.

• Wheat: 50 acres, Corn: 50 acres

• Wheat: 33.33 acres, Corn: 66.67 acres

• Wheat: 25 acres, Corn: 75 acres

• Wheat: 40 acres, Corn: 60 acres

A school is organizing a field trip and has two types of tickets: student tickets at $10 each and adult tickets at $15 each. If they sold a total of 200 tickets for $2,500, how many student and adult tickets were sold? Set up the system of equations and solve using matrices.

• 150 student tickets and 50 adult tickets were sold.

• 100 student tickets and 100 adult tickets were sold.

• 200 student tickets and 0 adult tickets were sold.

• 80 student tickets and 120 adult tickets were sold.

A company produces two products, A and B. The profit from product A is $5 per unit, and from product B is $8 per unit. If the company wants to make a total profit of $1,000 by selling 150 units of both products, how many units of each product should they produce? Use matrices to find the solution.

• 80 units of product A and 70 units of product B

• 100 units of product A and 50 units of product B

• 50 units of product A and 100 units of product B

• 120 units of product A and 30 units of product B

Two friends, Alex and Jamie, are saving money for a concert. Alex saves $20 a week, while Jamie saves $30 a week. If they want to save a total of $600 together, how many weeks will it take for them to reach their goal? Formulate the problem using a system of equations and solve with matrices.

• 10 weeks

• 12 weeks

• 8 weeks

• 15 weeks

A restaurant offers two types of meals: vegetarian and non-vegetarian. The vegetarian meal costs $12 and the non-vegetarian meal costs $15. If the restaurant sold a total of 150 meals for $1,800, how many of each type of meal were sold? Set up the equations and solve using matrices.

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

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

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

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

A bookstore sells two types of books: fiction and non-fiction. The fiction books cost $12 each, and the non-fiction books cost $15 each. If the bookstore sold a total of 200 books for $2,400, how many fiction and non-fiction books were sold? Use matrices to solve the system of equations.

• 100 fiction books and 100 non-fiction books

• 80 fiction books and 120 non-fiction books

• 150 fiction books and 50 non-fiction books

• 200 fiction books and 0 non-fiction books

In a class, there are two types of students: those who take math and those who take science. If the total number of students is 50 and the number of math students is 10 more than the number of science students, how many students are in each subject? Set up the system of equations and solve using matrices.

• 15 science students and 35 math students

• 20 science students and 30 math students

• 10 science students and 40 math students

• 25 science students and 25 math students

A car rental company has two types of cars: economy and luxury. The economy car rents for $30 per day, and the luxury car rents for $50 per day. If the company made $1,200 from renting 30 cars in one day, how many of each type of car were rented? Use matrices to find the solution.

• 15 economy cars and 15 luxury cars were rented.

• 20 economy cars and 10 luxury cars were rented.

• 25 economy cars and 5 luxury cars were rented.

• 10 economy cars and 20 luxury cars were rented.

A gym has two types of memberships: basic and premium. The basic membership costs $25 per month, and the premium membership costs $40 per month. If the gym has a total of 200 members and collects $6,000 in membership fees, how many basic and premium members are there? Solve the system using matrices.

• 200 basic members and 0 premium members

• 150 basic members and 50 premium members

• 80 basic members and 120 premium members

• 100 basic members and 100 premium members

A factory produces two types of gadgets: Type X and Type Y. Type X requires 2 hours of labor and Type Y requires 3 hours. If the factory has 120 hours of labor available and wants to produce a total of 40 gadgets, how many of each type should they produce? Set up the equations and solve using matrices.

• 10 Type X gadgets and 30 Type Y gadgets

• 40 Type X gadgets and 0 Type Y gadgets

• 30 Type X gadgets and 10 Type Y gadgets

• 20 Type X gadgets and 20 Type Y gadgets